Study of Applying Contactless Power Transmission System to

6
Study of Applying Contactless Power Transmission System to Battery Charge Kuen-Cheng Wang Che-Wei Hsu Tung- Jung Chan Tsung-Shih Chien Tsair-Rong Chen kuenbao @ms76.hinet.net sqall @abc.ncue.edu.tw jung @dragon.ccut.edu.tw rock @abc.ncue.edu.tw abc @abc.ncue.edu.tw Department of Electrical Engineering National Chang-hua University of Education Taiwan, ROC Abstract -- Contactless power transmission system with the advantages of safety and convenience has been applied to daily supplies. However, general contactless power transmission charger cannot control the current cause there is no charge controller in secondary side and the severe limitation between primary and secondary sides of the battery charger cause difficulty to design. This study provides the charge controller with half-bridge inverter and E-Type core as coupling converter in primary side; A Zeta DC converter is utilized to achieve the outcome of charge with constant voltage and to increase the charging distance between primary and secondary sides. To verify the feasibility of contactless power transmission system, the study completes the contactless charger with the output power of 30W. The result shows that the overall system efficiency is 57.8 % with 150 V/ 0.35A input and 15.2 V/2 A output. Keywords -- Contactless Power Transmission System, Zeta converter, charge controller I. INTRODUCTION The technology advances significantly. In recent years, the research has been concentrating on the applications in relation to our daily life. The demand of many portable electronic products such as notebook, PDA, cell phone, digital camera, MP3, etc. is getting more and more. The power for portable electronic products is supplied by the secondary battery which is rechargeable. The charge method is classified into metal contact and non-metal contact depending on the ways of power transmission. The charge system of most household appliances mainly applies traditional contact chargers. However, each type of portable electronic products needs to use their specific charger to charge the built-in batteries. Each charger requires a power converter to transform power into DC suitable for charging. Different types of chargers are not compatible with each other, which directly causes a waste of chargers and environmental pollution. In addition, too many chargers cause the inconvenience in identifying them and portability to users. Contactless power transmission system adopts induction to transmitting power. Electromagnetic induction generates inducted power. Such method doesn’t have contacts between conductors. By considering the safety upon operations, contactless power transmission technology is more advanced than contact power transmission system. Currently, among the chargers applied to contactless power transmission system, there is no charge controller with DC converter in the secondary sides. In addition, there is stricter limit in the distance between a charger and the primary sides. Based on the above reason, this paper will discuss the application of contactless power transmission to charge controllers. A contactless charger compatible with other chargers is designed so as to achieve charging at constant voltage. Furthermore, the charge distance between a charger and the primary side can be increased. With such design, the electronic products with contactless power transmission will become advantageous in the market. II. LITERATURE REVIEW Among the literature proposed so far, the structure consisting of converter, compensated circuit in the primary and secondary sides, inductive transformer and DC converter is most commonly seen. The structure of contactless power transmission system is shown in Fig. 1. Fig. 1. Structure of Contactless Power Transmission System The basic principle of contactless power transmission system is to use electromagnetic induction to implement transformation of electric energy and magnetic energy between two coils. First, alternating current is input at the primary-side coil to generate alternating magnetic field. Then, the secondary-side coil receives the magnetic field to transform it into utilized power and complete the transmission of contactless power. Currently, overseas studies focused on the technologies and theories relating charge with contactless power transmission have reached a certain level. The topics discussed cover electric energy converter, improvement on converting efficiency, coupling transformer’s relationships with different winding positions, clearances, deviations and coupling inductivity. For example, Choi et al. produced a charger applied to a cell phone by using PCB winding design in 2004. [1] Liu proposed the structure of multiple- layer array to a multi-purpose charging platform. [2] In 2005, Hui used a multi-purpose contactless battery charging PEDS2009 257

Transcript of Study of Applying Contactless Power Transmission System to

Page 1: Study of Applying Contactless Power Transmission System to

Study of Applying Contactless Power Transmission System to Battery Charge

Kuen-Cheng Wang Che-Wei Hsu Tung- Jung Chan Tsung-Shih Chien Tsair-Rong Chenkuenbao

@ms76.hinet.net sqall

@abc.ncue.edu.tw jung

@dragon.ccut.edu.tw rock

@abc.ncue.edu.tw abc

@abc.ncue.edu.tw

Department of Electrical Engineering National Chang-hua University of Education

Taiwan, ROC

Abstract -- Contactless power transmission system with the

advantages of safety and convenience has been applied to daily supplies. However, general contactless power transmission charger cannot control the current cause there is no charge controller in secondary side and the severe limitation between primary and secondary sides of the battery charger cause difficulty to design. This study provides the charge controller with half-bridge inverter and E-Type core as coupling converter in primary side; A Zeta DC converter is utilized to achieve the outcome of charge with constant voltage and to increase the charging distance between primary and secondary sides. To verify the feasibility of contactless power transmission system, the study completes the contactless charger with the output power of 30W. The result shows that the overall system efficiency is 57.8 % with 150 V/ 0.35A input and 15.2 V/2 A output.

Keywords -- Contactless Power Transmission System, Zeta

converter, charge controller

I. INTRODUCTION The technology advances significantly. In recent years,

the research has been concentrating on the applications in relation to our daily life. The demand of many portable electronic products such as notebook, PDA, cell phone, digital camera, MP3, etc. is getting more and more.

The power for portable electronic products is supplied by the secondary battery which is rechargeable. The charge method is classified into metal contact and non-metal contact depending on the ways of power transmission. The charge system of most household appliances mainly applies traditional contact chargers. However, each type of portable electronic products needs to use their specific charger to charge the built-in batteries. Each charger requires a power converter to transform power into DC suitable for charging. Different types of chargers are not compatible with each other, which directly causes a waste of chargers and environmental pollution. In addition, too many chargers cause the inconvenience in identifying them and portability to users.

Contactless power transmission system adopts induction to transmitting power. Electromagnetic induction generates inducted power. Such method doesn’t have contacts between conductors. By considering the safety upon operations, contactless power transmission technology is more advanced than contact power transmission system.

Currently, among the chargers applied to contactless power transmission system, there is no charge controller with DC converter in the secondary sides. In addition, there is stricter limit in the distance between a charger and the primary sides. Based on the above reason, this paper will discuss the application of contactless power transmission to charge controllers. A contactless charger compatible with other chargers is designed so as to achieve charging at constant voltage. Furthermore, the charge distance between a charger and the primary side can be increased. With such design, the electronic products with contactless power transmission will become advantageous in the market.

II. LITERATURE REVIEW Among the literature proposed so far, the structure

consisting of converter, compensated circuit in the primary and secondary sides, inductive transformer and DC converter is most commonly seen. The structure of contactless power transmission system is shown in Fig. 1.

Fig. 1. Structure of Contactless Power Transmission System

The basic principle of contactless power transmission system is to use electromagnetic induction to implement transformation of electric energy and magnetic energy between two coils. First, alternating current is input at the primary-side coil to generate alternating magnetic field. Then, the secondary-side coil receives the magnetic field to transform it into utilized power and complete the transmission of contactless power.

Currently, overseas studies focused on the technologies and theories relating charge with contactless power transmission have reached a certain level. The topics discussed cover electric energy converter, improvement on converting efficiency, coupling transformer’s relationships with different winding positions, clearances, deviations and coupling inductivity. For example, Choi et al. produced a charger applied to a cell phone by using PCB winding design in 2004. [1] Liu proposed the structure of multiple-layer array to a multi-purpose charging platform. [2] In 2005, Hui used a multi-purpose contactless battery charging

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platform designed with multiple-layer hexagonal spiral PCB coil. [3] In 2007, Kuo et al. suggested to use contactless charging equipment with full-duplex. [4] The above mentioned studies focused on the primary-side control for contactless chargers. Less studies and production have been made on the secondary-side charging control for contactless chargers.

Therefore, the research and production of the charger for this paper are mainly focused on charge control circuit at contactless secondary side.

The efficiency of contactless power transmission system is lowered when the air gap for the primary side and secondary side increases. Consequently, the distance of power transmission is limited. There are two ways to increase the power transmission distance. One is to increase the output at the primary side. However, current efficiency for contactless power transmission system is not high. Therefore, the increase of output at the primary side is just a waste of power. The other way is to adopt the structure proposed by this paper. That is to use boost/buck converter at the secondary side. When the input voltage is higher than that required by a charger under operation, the converter can help to control the output current at a constant current. Contrarily, when the converter voltage is lower than the battery voltage, the boost converter can be used to increase the output voltage to that required by the working battery. However, such way only focuses on increasing power transmission distance. When the charger at the secondary side is far away from the primary side at a certain distance, it cannot induct voltage and no charge can be done accordingly. [5]

The primary side for contactless power transmission system applies a converter to achieve alternating current for output. The use of half-bridge converter is the commonest which is not only two power switches less than a full-bridge converter but also suitable for the application in lower power supply. As a result, this paper chooses half-bridge converters.

As to the selection of an induction transformer, it is considered to use E-type iron easy to obtain so as to design and implement the coupling transformer required by this paper.

Finally, the secondary-side converter in the contactless power transmission system applies Zeta DC converter as the charging circuit. A micro-computer is used to control the current and voltage to a constant level for charging.

III. PREPARE YOUR PAPER BEFORE STYLING The system design of this paper includes three parts:

half-bridge resonant converter with contactless power transmission, Zeta DC charging circuit and a micro-computer charge controller.

A. Circuit design with half-bridge resonant converter in series connection The circuit structure of half-bridge resonant converter in

series connection is shown in Fig. 2. This structure includes two capacitors and two switches. In addition, a capacitor Cr is in series connection before the primary side of the induction transformer. Such connection aims at generating resonance so as to create the resonant frequency similar to the operating frequency of the switches. It further generates induction, voltage of a capacitor and current wave form close to sinusoidal wave and makes the output become voltage source [6].

Fig. 2. Half-bridge Resonant Converter in Series Connection

TL494 is a control IC designed with voltage PWM. Its

circuit diagram is shown in Fig. 3. Inside it, there is a sawtooth wave with adjustable frequency. The control elements cover RT and CT, the vibration frequency can be obtained by formula (1):

1.1

sT T

fR C

≈⋅ . (1)

The comparisons are made after external return signals and reference voltage are input to an error amplifier. Error control signals are created after being linearly amplified. Then the error control signals are compared with the forward sawtooth waves generated through CT. When the sawtooth wave is bigger than the error control signal, PWM signals will be output. Otherwise, PWM signals will not be output. Consequently, we can increase or decrease error control signals to adjust the PWM duty cycles. Meanwhile, TL494 can output two sets of PWM signals of the same duty, which can work as the driving signals for a symmetrical half-bridge converter. The operating frequency of the power switches of a converter is determined by RT and CT. The switch frequency is designed at 100 kHz.

VCC 12

C1 8

C2 11

E1 9

E2 10

OC 13

REF 14

DT 4

GND 7

RT6

CT5

IN1+1

IN-2

FB3

IN2-15

IN2+16

U1

TL494

+17C6

4.7nF

R12 DT_500k

R14FB_500k

R9

10R10

RT_500k

FB

FB

HoutLout

R112k(7.5m

A).11W

D2

LED+17

+17

hole

1

F2HOLE

hole

1

F1HOLE

C7 100u/35V

C10CAP

Fig. 3. PWM Control Circuit Diagram

PWM control signals generated by TL494 are not sufficient to push the power switch. Meanwhile, it requires separating upper and lower energy levels while the control signals are pushing the power switches at upper and lower

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bridges. Therefore, the design applying IR2110 as gate circuit separating driving circuit can help input the two sets of PWM control signals generated by TL494 to IR2110 and then to generate the driving signals at upper and lower bridge.

VDD9

HIN10

SD11

LIN12

VSS13 HO 7

VB 6

VS 5

VCC 3

COM 2

LO 1

U2 IR2110

C1.1u/50V

+17

C2

.1u/50V

C4.1u/50V

D1500V

+17

+17

HoutLout R_S

R_hi

R_lo

C51u/50V

C31u/50V

Q5MOS

Q6MOS

R13

10

R16

10

POWER

12 J2

IT_out

R_lo

R_hi

R_S

R15250

R17250

100pF

C9Cap2

100pF

C12Cap2

100pF

C8Cap

100pF

C11Cap

Fig. 4. Half-bridge Converter Circuit

Fig. 5 shows the resonant compensated circuit diagram for half-bridge converter. The primary and secondary resonant compensated circuits adopt the structure of the primary-side compensation in series connection and the secondary-side compensation in parallel connection [7].

Fig. 5. SP Resonant Compensated Circuit Diagram.

B. Design of Zeta DC Charge Controller Zeta converter is a buck/boost converter. It consists of

Buck-Boost-Buck pattern. The circuit structure of a Zeta converter is shown in Fig. 6. When the power switch M1 is in conduction, Vi will charge L1 and iL1 will gradually increase until VL1 voltage equals to Vi. At the same time, C1 is charging L2 and iL2 will gradually increase until VL2 voltage equals to Vi. When the power switch M1 is off, the inducted L1 will change the direction of magnetic field based on Faraday Principle. Therefore, the voltage pole reverses. Then L1 will discharge the capacitor C1. With the same principle, the inducted L2 discharges its load. At the same time, iL1 and iL2 display the decreasing trend until the power switch is conductive again. If the power switch cannot be conductive in time, then iL1 and iL2 will drop to zero and go into the consecutive conduction mode. Based on the principle of circuit operation, all power transmission has to pass through C1 which will bear great charging/discharging current. Therefore, attention should be paid to the selection of a capacitor. [8], [9]

Fig. 6. Circuit Diagram of a Zeta Converter

The charge controller described in this paper works under a continuous mode. Under a stable and continuous conduction mode, we can obtain the input/output voltage conversion rate of a Zeta converter from the following formula:

D

DViVo

−=

1. (2)

D stands for Duty cycle. When the duty cycle is smaller than 0.5, the converter acts as a buck type. Contrarily, the converter acts as a boost type when the duty cycle is bigger than 0.5. First, let’s define ripple current rate of an inductor:

AVGLIIr

,

Δ= . (3)

IΔ : stands for the peak-to-peak value of inductor current

AVGLI , : stands for the average value of inductor current

For achieving r=0.4 under the conditions that Zeta converter operates in continuous mode and under maximum load, the following design is based on the condition of r=0.4 as reference:

1) Selection of L1 and L2 Inductors:

frIDV

LLo

i

⋅⋅−⋅

==)1( minmax,

21 . (4)

max,iV : maximum input voltage

minD : minimum working cycle

oI : nominal output current f : switching frequency

2) Selection of C1 Capacitor:

fV

DIC

r

o

⋅⋅

= max1 . (5)

rV : continuous waves of output voltage

maxD : maximum working cycle 3) Selection of power switch M1 and diode D1:

oiM VVV +=1 (6)

oiD VVV +=1 (7)

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4) Effective value of current input to capacitor Ci:

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−= DrDI

DDI ormsCi 12

11

2

, . (8)

5) Effective value of current output to capacitor Co:

12

2

,rII ormsCo = . (9)

Based on system requirements, select suitable element values obtained from formula (2) ~ (9) in order to prepare the charger [8-10].

The charge controller mentioned in this paper consists of 4 parts: Zeta DC charge circuit, single chip PWM control circuit, optical coupling separation circuit and gate driving circuit. The main circuit of the charger supplies power energy after secondary-side rectification and filtering of the contactless transformer. The power passes through Zeta converter to boost/buck voltage for the use of battery charge.

The driving circuit for the upper-arm power switch of the Zeta DC converter has a different ground level from that of Zeta converter. For ensuring that the power switch can operate normally, it is necessary to use optical coupling isolation circuit to isolate the system ground. Though the power activated for turning the power switch is little, the influence of the capacitor at the gate source end on the power switch will be greater peak current upon on and off of the power switch. The optical coupling isolating circuit and gate driving circuit diagram is shown in Fig. 7.

Q6NPN

Q5NPN

Q7PNP

VSS

R10

1K

R81K

15V

R9

100DRIVE_SIGNAL

PWM

GNDVSS

15V

11

22

33

44 5 56 67 78 8IC2

TLP250

Fig. 7. Optical Coupling Isolating Circuit and Gate Driving Circuit

Diagram

Zeta charge controller circuit diagram is shown in Fig. 8. The Zeta charger circuit prepared by this paper reaches a constant current and constant voltage through micro-computer controller so as to make charge control and boost/buck voltage control. When the charge controller approaches to the primary-side charge base, the micro-computer picks up Zeta input voltage to determine if it will start charging. Upon starting charging, the micro-computer determines the constant charge current by referring to the charge current. In the meantime, the micro-computer also picks up the battery voltage to determine if it is overcharging. If it reaches the critical charge voltage, it will become the mode of charge at a constant voltage. Finally, the battery is fully charged under the constant voltage if the charge current is detected below 0.01C. The indicator lights

up to inform a user that the battery is fully charged. The micro-computer charge controller is shown in Fig. 9. The flow chart of micro-computer charge control design is shown in Fig. 10. [11]

1000uF

C8Cap Pol1

100mH

L4Inductor Iron

100mH

L3

Inductor Iron100uF

C7

Cap Pol1

D540EPF06 1000uF

C9Cap Pol1

D2

G1

S 3Q8

IRF64012

P6

Header 2H

GND

DRIVE_SIGNAL

100K

R12Res1

VCC

10K

R13Res1

BT_V

10K

R14Res Adj1

VSS

D4

Diode

BT1Battery

D65V

11 22 33 4 4

5 5

6 6

5V7

GN

D8

Vou

t9

U1LTS-25NP

5V

BT_I

10K

R11Res1

10K

R15Res Adj1D7

5V

ZETA_VI

Fig. 8. Zeta DC Charge Circuit

GND

BT_V

PWM

BT_I

5V

PB51

PB42

PA33

PA24

PA15

PA06

PB37

PB28

PB19

PB010

VSS11

PC012

PC113

PC214 PC3 15PC4 16PD0 17PD1 18RES 19VDD 20OSC 21OSC 22PA7 23PA6 24PA5 25PA4 26PB7 27PB6 28IC1

HT46R23

D3 Photo SenVCC

R6

1KY1

4.000MHZ

R710K

S1SW-PBC6

10uF

ZETA_VI

Fig. 9. Micro-computer Charge Controller

Fig. 10. Flow Chart of Micro-computer Charge Control Design.

IV. SYSTEM TEST AND RESULT There are two parts in the test of contactless charge

controller. One is half-bridge resonant converter, and the

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other is Zeta DC converter. The design specifications are listed in TABLE I.

TABLE I DESIGN SPECIFICATIONS OF CONTACTLESS CHARGE CONTROLLER

Loosely Coupling Transformer coupling coefficient k= 0.68 Operation frequency 100 kHz Primary side self-inductance Lp=1 mH Secondary side self-inductance Ls=13 uH Prinary side leakage inductance Llk=575 uH Resonant frequency fo=100 kHz Primary side compensated capacity Cs=47 nF Secondary side compensated capacity Cp=0.3 uF

Zeta Converter Switching frequency f =31.25 kHz Inductance L1 300 uH Inductance L2 300 uH Capacitor C1 10 uF Input capacitor Ci 220 uF Output capacitor Co 330 uF Output current 2 A Output voltage 15 V Duty cycle 13 %

The input voltage of the half-bridge resonant converter of this system is DC 150 V and its current is 0.35 A. Fig. 11. shows the input voltage and current waveforms of half-bridge resonant current converter with the voltage at 75.3 V and the electric current at 1.243 A. The Fig. 12 . demonstrates the voltage and current waveforms of the secondary-side resonant tank in parallel connection of the induction transformer. The measured voltage is 69.62 V, and the electric current is 13.54 A; therefore the efficiency of half-bridge resonant converter is 75 %. The input voltage and waveforms of Zeta charge controller is shown in Fig. 13. The input voltage is 63.47 V and the input electric current is 627 mA. The voltage and current waveforms of Zeta charge controller is shown in Fig. 14. Its output voltage is 15.19 V and the output electric current is 2.13 A. Therefore, the efficiency of Zeta charge controller is 81.23 % and the whole efficiency of contactless charge controller is 61.57 %. The efficiency of the contactless charge controller at each level is shown in TABLE II.

Fig. 11. Output Voltage (CH1) and current (CH2) waves of Half-bridge resonant converter

Fig. 12. Voltage (CH1) and current (CH2) wave forms of the secondary-

side resonant tank in parallel connection of an induction transformer

Fig. 13. Input voltage (CH1) and current (CH2) waveforms of Zeta

charge controller after bridge rectifier

Fig. 14. Charge voltage and current waveforms of Zeta charge controller

TABLE II

Efficiency of charge controller with contactless power transmission system at different levels

Efficiency of Half-Bridge Converter

Efficiency of Zeta Converter

Overall Efficiency of Contactless Charger

75 % 81.23 % 61.57 %

Fig. 15. and Fig. 16. show the voltage and current waveforms upon induction and power switch when Zeta converter is charging. The comparisons of various conditions of contactless charge controller by air gap are shown in Table III. The system input voltage is controlled at DC150V. The comparisons of the test of the charge gap show that even though the air gap is bigger this system can still reach a charging condition at constant voltage. The picture of a contactless charge controller prepared by this paper is shown in Fig. 17.

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Fig. 15. The voltage (CH1) and current (CH2) waveforms at L1 on a

charge controller and the voltage (CH3) and current (CH4) waveforms at L2

Fig. 16. The voltage waveforms at Vgs (CH1) and Vds (CH2) of Zeta

charge controller

half-bridge inverter and it’s driving circuit

contactless transformer and compensated circuit

rectifier andZeta converter

Fig. 17. Charge controller applying contactless power transmission

TABLE III

COMPARISONS OF VARIOUS CONDITIONS OF CONTACTLESS CHARGE CONTROLLER BY AIR GAP

Air gap 1.5 mm 3.0 mm 4.5 mm

System input voltage 150 V 150 V 150V

System input current 0.35 A 0.44 A 0.29 A

Charger input voltage 63.47 V 95.98 V 86.80 V

Charger input current 628 mA 490 mA 415 mA

Output voltage 15.19 V 15.30 V 15.10V

Output current 2.0 A 2.0 A 1.5 A

Overall efficiency 57.8 % 54 % 50 %

V. CONCLUSIONS The contactless charge controller in this paper is

prepared based on contactless power transmission and a Zeta DC converter with charge controller. The following conclusions have been obtained through theoretical analysis and test results: contactless charger adding a controller at secondary-side charger will reach a constant current and constant voltage for charging. Such structure prolongs the battery life. Finally, the charge controller with nominal output power at 30W is substantially completed so as to verify the feasibility of contactless charge controller proposed by this paper.

REFERENCES [1] B. Choi, J. Nho, H. Cha, T. Ahn, and S. Choi, "Design and

implementation of low-profile contactless battery charger using planar printed circuit board windings as energy transfer device," IEEE Trans. Industrial Electronics, vol. 51, pp. 140-147. Feb. 2004

[2] X. Liu, and Hui. S.Y., "Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery Charging Platform," industry Applications Conference, 41st IAS Annual Meeting., pp.2568-2575, Oct. 2006.

[3] Hui, S.Y.R., Ho, W.W.C., "A new generation of universal contactless Battery Charging platform for portable Consumer Electronic equipment," IEEE Trans. Power Electronics, vol. 20, pp. 620-627, May. 2005.

[4] K. K. Shyu, K. W. Jwo, Z. Y. Chen, and C. H. Lo, "Inductive Power Supply System with Fast Full-Duplex Information Rate Device," in Proc. 2007. Computer as a Tool Conf., pp. 1382-1386.

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[6] X. Liu and S. Y. R. Hui, "Equivalent circuit modeling of a multilayer planar winding array structure for use in a universal contactless battery charging platform," IEEE Trans. Power Electron., vol. 22, no. 1, pp. 21–29, Jan. 2007.

[7] P. Si, A. P. Hu, J. W. Hsu, M. Chiang, Y. Wang, S. Malpas and D. Budgett, "Wireless power supply for implantable biomedical device based on primary input voltage regulation," in Proc. 2nd IEEE Conf. Industrial Electron., pp. 235-239, May 2007.

[8] P. Si, A. P. Hu, D. Budgett, S. Malpas, J. Yang, and J. Gao, "Stabilizing the operating frequency of a resonant converter for wireless power transfer to implantable biomedical sensors," in Proc. 1st Int. Conf. Sensing Technology., New Zealand, Palmerston North, 2005, pp. 477-482.

[9] G. Wang, W. Liu, M. Sivaprakasam and G. A. Kendir, "Design and analysis of an adaptive transcutaneous power telemetry for biomedical implants," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, pp. 2109-2117, Oct. 2005.

[10] C. S. Wang, G. A. Covic, and O. H. Stielau, "Power transfer capability and bifurcation phenomena of loosely coupled inductive power transfer systems," IEEE Trans. Ind. Electron., vol. 51, pp. 148-157, Feb. 2004.

[11] X. Liu, P. W. Chan, and S. Y. R. Hui, "Finite element simulation of a universal contactless battery charging platform," in Proc. 20th Annu. Appl. Power Electron. Conf., pp. 1927-1932, Mar. 2005.

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