8/12/2019 Analysis and Optimization of Magnetically Coupled

http://slidepdf.com/reader/full/analysis-and-optimization-of-magnetically-coupled 1/4

IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 11, NOVEMBER 2012 4511

Analysis and Optimization of Magnetically Coupled

Resonators for Wireless Power Transfer

Xiu Zhang, S. L. Ho, and W. N. Fu

Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

The technology of wireless power transfer has made a great contribution to the quality of life of many people, especially to those relyingon implantable devices in the past decades. In order to improve the performance of wireless power transfer systems, a dual-layer nestedoptimization method using differential evolution (DE) algorithm is proposed in this paper. In contrast to previous methods to derive thecompensated capacitance, this proposed method determines the capacitance values using optimization method. By testing a prototype,it is found that the proposed design can have much higher power transfer ef ficiency when compared to that of traditional method. The

dual-layer nested optimization method, based on the design constrains, is also used to determine the parameters of the coils to obtainthe maximum power transfer ef ficiency of the whole system. The result is validated using  finite element method (FEM).

 Index Terms— Capacitance, equivalent circuit, nested optimization method, power transfer ef ficiency, resonant frequency, wirelesspower transfer.

I. I NTRODUCTION

A CCORDING to a news report [1], the yearly revenues

of global medical device companies are in excess of 

200 billion US dollars. Among these, implanted devices play

a large part because it can help to extend and improve the

 patients’ quality of life. However, their applications are limited

 by the batteries’ size, their longevity, and the frequency of re-

 placements required. To address these issues, the technique of 

wireless power transfer has been receiving increasing attention

worldwide.

Depending on the applications, the power requirement of 

medical implanted devices can vary from a few microwatts to

tens of milliwatts [2], [3]. With non-transcutaneous wiring and

convenient charging features, wireless power transfer is oftenused in biomedical implanted devices to alleviate the trauma of 

 patients.

Hitherto, the most popular wireless power transfer technique

used in biomedical implanted devices is near-field inductive

coupling. Researches have indicated that if near-field techniques

are used and if the range of energy transfer distance is of the

order of tens of centimeters, the overall ef ficiency of the power 

 being transferred is only about 1%–2% [4].

In 2006, the magnetically coupled resonators were presented

for wireless power transfer. It now becomes possible to transmit

 power ef ficiently at ranges longer than that realized using induc-

tive coupling schemes [5]. The wireless power transfer system

 based on magnetic coupling resonators typically uses four coils,

two for input and two for output. The transmitter includes a

driver loop and a primary coil, the receiver includes a secondary

coil and a load loop as shown in Fig. 1(a). In this system, the

compensation capacitors are the key elements in addition to the

inductor coils to form the resonant system. Previous method to

determine the capacitance is based on the relationship of the

Manuscript received March 02, 2012; accepted April 05, 2012. Date of current version October 19, 2012. Corresponding author: X. Zhang (e-mail:09901605R@polyu.edu.hk).

Color versions of one or more of the  figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2012.2194731

Fig. 1. (a) Simplified schematic of the wireless power transfer system based onmagneticallycoupling resonator. and arethecouplingcoef ficients between each coil, respectively. (b) Equivalent circuit of this system.

inductance, the reflected mutual inductance and the resonance

frequency [6].

In this paper, a dual-layer nested optimization method using

differential evolution (DE) algorithm is applied to optimize the

wireless power system and finite element method (FEM) is used

to analyze the electromagnetic characteristics of the system to

evaluate its feasibility. The  first layer (outer layer) to optimize

the parameters of the coils based on its simulation models, andthe second layer (internal layer) is to optimize the compensation

capacitances to evaluate the performance of the whole system.

It means that once the parameters of the inductor change, the

compensation capacitances should be optimized.

It can be seen in Fig. 3 that the optimal results reported by

fellow co-researchers are inferior to the results derived using

the proposed optimization method.

II. SYSTEM OVERVIEW AND CIRCUIT MODEL

In this paper, the equivalent circuit method is applied to ana-

lyze the wireless power transfer system. Fig. 1 shows the spec-

ified   schematic and equivalent circuit of the wireless power 

transfer system based on magnetically coupling resonator.

0018-9464/$31.00 © 2012 IEEE

8/12/2019 Analysis and Optimization of Magnetically Coupled

http://slidepdf.com/reader/full/analysis-and-optimization-of-magnetically-coupled 2/4

4512 IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 11, NOVEMBER 2012

Fig. 2. Flowchart of the proposed optimization procedure.

Fig. 3. Power transfer ef ficiency versus different operating frequencies whenusing different capacitances.

As illustrated in Fig. 1(b), each coil is modeled as a distribu-

tive RLC network. Because the power transferred is a func-

tion of frequency, the operating frequency should be several

megahertz in order to obtain maximum power transferred ef-

ficiency [5]. In addition, it is essential to reduce the copper loss

in the coils in order to decrease the power dissipation and to

increase the power transferred ef ficiency. At high frequencies,

the resistances of the coils are greatly increased because of skin

effect and proximity effect. To mitigate against these effects,

multi-strand Litz wires are used [6].The self-inductance of one circular turn is calculated as [8]

(1)

where is the space permeability, and is the diameter of the

conductor wire , and is the diameter of one

turn.

The mutual inductance of two parallel single turns can be

approximated as [9]

(2)

where and are the wireradius ofthetwocoils; and arethe

respective relative distance and lateral misalignment between

the two coils, respectively; and are the zero- and   first-

order Bessel functions, respectively. For perfectly aligned coils

, the above function can be simplified by

(3)

where , and and are

the complete elliptic integrals of the  first and second kind, re-

spectively.

The stray capacitance of the coil is [6]

(4)

where and are the layer number, the turn number per 

layer and the total number of the coil, respectively; is the par-asitic capacitance between two nearby turns in the same layer,

and is the parasitic capacitance between different layers as

expressed

(5)

(6)

where and are the average diameter of each

coil, wire radius, thickness, and relative permittivity of strand

insulation and separation between two layers, respectively.Considering the skin and proximity effect, the ac resistance

of coils can be expressed by

(7)

where is the frequency at which power dissipation is twice

the dc power dissipation and is given by

(8)

where and are the dc resistance of the coil, radius

of each single strand, number of strands per branch, and the area

ef ficiency of the branch, respectively.

The following matrix is derived by applying the circuit theory

to the system:

(9)

where for ; else

.

In order to obtain power transfer ef ficiency, the above matrix

equation is solved in the frequency domain and the ef ficiency is

taken as the objective function for optimization.

8/12/2019 Analysis and Optimization of Magnetically Coupled

http://slidepdf.com/reader/full/analysis-and-optimization-of-magnetically-coupled 3/4

ZHANG et al.: ANALYSIS AND OPTIMIZATION OF MAGNETICALLY COUPLED RESONATORS FOR WIRELESS POWER TRAN SFER 4513

TABLE IDESIGN CONSTRAINTS

TABLE IIPARAMETERS OF COILS FOR  TEST

III. OPTIMIZING DESIGN AND A NALYSIS

In this paper, the differential evolution method is used to op-

timize the system. The procedure of the optimization process

includes two layers as shown in Fig. 2.

 A. Design Constraints and Initial Values of Parameters

Considering the receiver is to be implanted in patients’ heads,

the size of the implantable receiver part should be as small as

 possible. In this paper, the outer diameter of the receiver part

is chosen as 20 mm, while its height is 5 mm; the

transferred distance is 40 mm.

According to electromagnetic theory, to a circular coil, the

relationship of the magnetic-field strength and the distance

along the axis of the coil can be described as

(10)

where is the radius of the circular coil. From the above equa-

tion, it can be seen that can be maximized when ;

therefore, the outer diameter of the secondary coil can be chosen

from . The design constraints and initial valuesof the parameters are listed in Table I.

In this paper, a 22-strand Litz wire is used to construct the

four coils. The diameter of the wire is 1 mm, while the strand

radius is 0.04 mm.

 B. Optimization for Compensated Capacitance

In order to validate the feasibility of the optimization method

to determine the compensated capacitance, the initial wireless

 power transfer system before the inductor is optimized is used

as a reference for comparison.

In the test, the single copper wire is used to construct four 

coils, and the parameters are listed in Table II.

The compensated capacitances obtained from the two dif-

ferent methods at 0.65 MHz are given in Table III.

TABLE IIICOMPENSATED CAPACITANCE  VALUES FROM  TWO METHODS

Fig.4. Effectof the numberof layers(primarycoilanddrive loop) tothe power 

transfer ef ficiency.

Fig. 3 shows the power transfer ef ficiency as a function of 

the operating frequencies based on the proposed optimization

method and the traditional compensated capacitance method.

From the results, it can be seen that the maximum power trans-

ferred ef ficiency from the optimization method is almost twice

of that obtained using traditional method.

From the curve of the result based on traditional method, it

can be seen that the power transferred ef ficiency reaches its

maximum value at about 0.8 MHz which is shifted from the

resonant frequency 0.65 MHz. On the contrary, the power trans-

ferred ef ficiency reaches its maximum value at the operating fre-

quency if optimal capacitance is used. This is another advantage

of using the optimization method rather than using the tradi-

tional method.

The result shows that the capacitance optimization method

is much better than the traditional capacitance method. It also

strongly proves the feasibility of this proposed method.

C. Optimization for Inductors

In order to get high coupling coef ficient, the drive loop is

wrapped over the primary coil, while the load loop is also

wrapped over the secondary coil. According to the design

constrains listed in Table I, the size of the receiver part is deter-mined  first. The number of layers of the load loop is 1, while

the number of layers of the secondary coil is 6. The number of 

turns of the load loop and secondary coil are both 5.

As shown in Table I, the numbers of turns of the transmitter 

 part (drive loop and primary coil) are both 10. The number of 

layers of the drive loop and primary coil are parameters to be

optimized for maximum power transfer ef ficiency. From the re-

sults given in Fig. 4, it can be seen that power transfer ef ficiency

reaches its maximum value when the number of layers of the

drive loop and primary coil are both 3.

Secondly, Fig. 5 shows the effect of the number of turns of 

the drive loop and primary coil for optimal power transfer ef fi-

ciency. When the turn numbers are both 10, the power transfer 

ef ficiency reaches its maximum value (88.1%).

8/12/2019 Analysis and Optimization of Magnetically Coupled

http://slidepdf.com/reader/full/analysis-and-optimization-of-magnetically-coupled 4/4

4514 IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 11, NOVEMBER 2012

Fig. 5. Effect of the number of turns (primary coil and drive loop) to the power transfer ef ficiency.

Fig. 6. Model of the wireless power transfer system.

Fig. 7. Distribution of magnetic flux linkage without optimization.

Then Fig. 6 is the model of wireless power transfer system

with the optimal parameters.

IV. VALIDATION  USING FEM

All the parameters of the wireless power transfer are deter-

mined using optimization algorithm described. In order to vali-

date this system, the  finite element method is applied to analyze

the system.

The distributions of magnetic flux linkage in the receiver part

are shown in Figs. 7 and 8, respectively. It is obvious that the

magnetic  flux linkage in the receiver part is higher after opti-

mization.

Fig. 8. Distribution of magnetic flux linkage after optimization.

V. CONCLUSION

In this paper, a novel dual-layer nested optimization method

is proposed to optimize the wireless power transfer system. The

internal layer can determine the optimal values of capacitances.The outer layer optimizes the design parameters of the coils. A

higher power transfer ef ficiency is obtained using the proposed

optimization method when compared to the traditional method.

The maximum power transfer ef ficiency of 88.1% based on the

optimal parameters is nearly twice as high as that realized using

traditional methods.

ACKNOWLEDGMENT

This work was supported by the Research Grant Council of 

the Hong Kong SAR Government under project PolyU 5184/

09E.

R EFERENCES

[1] [Online]. Available: http://247wallst.com/2011/07/18/the-eleven-most-implanted-medical-devices-in-america/.

[2] G. Wang, W. Liu, M. Sivaprakasam, M. Zhou, J. D. Weiland, and M. S.Humayun, “A dual band wireless power and data telemetry for retinal prosthesis,” in   Proc. IEEE EMBS Conf., Aug. 30–Sep. 3, 2006, pp.28–38.

[3] A. K. RamRakhyani, S. Mirabbasi, and M. Chiao, “Design and opti-mization of resonance-based ef ficient wireless power delivery systemsfor biomedical implants,”  IEEE Trans. Biomed. Circuits Syst., vol. 5,no. 1, pp. 48–63, 2011.

[4] S. Ahson and M. Ilyas , RFID Handbook: Applications, Technology,

Security, and Privacy. Boca Raton, FL: CRC, 2008.[5] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and

M. Soljacic, “Wireless power transfer via strongly coupled magneticresonances,” Science, vol. 317, no. 5834, pp. 83–86, 2007.

[6] Z. Yang, W. Liu, and E. Basham, “Inductor modeling in wireless linksfor implantable electronics,”  IEEE Trans. Magn., vol. 43, no. 10, pp.3851–3860, Oct. 2007.

[7] C.-S. Wang, G. A. Covic, and O. H. Stielau, “Power transfer capabilityand bifurcationphenomena of loosely coupled inductive power transfer systems,” IEEE Trans. Ind. Electron., vol. 51, no. 1, pp. 148–157, Feb.2004.

[8] N. Sadiku , Elements of Electromagnetics. Orlando, FL: SoundersCollege Press, 1994.

[9] C. Zierhofer and E. Hochmair, “Geometric approach for coupling en-hancement of magnetically coupled coils,” IEEE Trans. Biomed. Eng.,vol. 43, no. 7, pp. 708–714, Jul. 1996.