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3200 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Quantitative Analysis of a Wireless Power Transfer Cell

With Planar Spiral Structures

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

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

An emerging technology of wireless power transfer technique based on electromagnetic resonant coupling, also known as witricity,has been drawing a lot of attention from academia as well as from practitioners since it was reported in 2007 by a group of researchers

from the Massachusetts Institute of Technology (MIT). In this paper, a prototype with square planar spiral structure based on witricityis proposed. To compute the resonant frequency, an equivalent circuit model is presented and simulated. The impedance matrix is com-puted by using a formula method and a 3-D finite-element method (FEM) of eddy-current magnetic field. The results indicate that thenumerical method has a better accuracy. In order to reduce the resonant frequency, different conditions are analyzed quantitatively tostudy the relationship between the parameters and the relation of the prototypes with their resonant frequencies. The findings are foundto offer a solid foundation for the optimization of witricity prototypes.

 Index Terms— Eddy-current magnetic field, equivalent circuit, impedance matrix, planar spiral inductor, resonant frequency, wirelesspower transfer.

I. I NTRODUCTION

A DVANCES in power electronics and magnetic materials

have made it possible to replace conventional energy

transmission using wires by contactless couplings in many

applications. Since the invention of the Tesla coil [1], re-

searchers from all over the world have made many attempts,

including near-field transmission based on magnetic coupling

and far-field transmission using microwaves and lasers, to

improve the technology of wireless power transfer [2]. In

essence, the success of wireless power transfer is dependent

on whether high power can be transmitted through a relatively

long distance in an ef ficient manner [3]. The Massachusetts

Institute of Technology (MIT) research team has presented a power transfer mechanism and they have successfully trans-

ferred 60 W of power over a distance in excess of 2 m with

ef ficiencies up to 40% [4]. It has been named “witricity” as in

wireless electricity. Witricity is a new technology of electro-

magnetic resonant coupling which satisfies the aforementioned

requirements for transmitting power over midrange distances

 based on strongly coupled magnetic resonance.

As an ef  ficient wireless nonradiative midrange energy

transfer method, witricity has triggered a lot of interests for 

charging popular electronic devices such as laptops, cell

 phones, robots, and PDAs, which all require frequent charging.

Witricity technique also has many medical applications.

Today, many microelectronic devices are implanted withinhuman body. Hitherto, replacement of implanted batteries

 poses a major health risk. To address such shortcoming and

use a technique along the direction of witricity, a research

team at the University of Pittsburgh has proposed a wireless

 power transfer (WPT) system to demonstrate the feasibility of 

transmitting power to implantable devices and sensors [2].

Manuscript received February 19, 2011; accepted April 20, 2011. Date of current version September 23, 2011. Corresponding author: X. Zhang (e-mail:[email protected]).

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.2011.2147768

The basic witricity system consists of two resonators which

operate with the same resonance frequency; one as the source

loop and the other as the device loop. The source loop is con-

nected to an alternating current (ac) power source. It generates

an oscillating magnetic field over the surroundings of the device

loop which is brought to the vicinity of the source loop. When

the device loop captures the oscillating magnetic field, it picks

up electromotive force to circulate a current in the connected

load.

In this paper, an equivalent circuit of a wireless power transfer 

system with planar spiral structures is presented. The parame-

ters of the circuit are computed using both analytical method

and a finite-element method (FEM). Their accuracies are com-

 pared with experimental results. The resonance frequency of 

the system is computed according to the circuit. The developedmodel is used to study the effects of changes in the design pa-

rameters and the physical connections quantitatively. It has been

used to design the WPT system operating at the optimal reso-

nance frequency which is dependent on the shapes and sizes of 

the prototypes.

II. COMPUTATION OF IMPEDANCE MATRIX

Based on the WPT system, a planar spiral inductor is chosen

to form the basic structure of the prototype [5]. In termsof layout

simplicity, the square spiral inductor becomes the first choice

among the various kinds of layouts including square, hexagonal,

octagonal, and circular.In order to describe the characteristics of the inductor, a math-

ematical model is required. Thekey factor to establish the model

is to include the effects of eddy current and relevant parasitic ca-

 pacitances. In the simulation, the two methods are used to com-

 pute the inductances and resistances.

 A. Formula Method 

The mathematical model should consist of 1) series re-

sistances and inductances of the spiral conductor,

2) crossover capacitance between the spiral and the

center-tap, 3) capacitance between the spiral and the substrate

, 4) substrate ohmic loss, and 5) substrate resistance

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Fig. 1. (a) The circuit model of a spiral inductor. (b) The sketch map of theinductor.

and capacitance [6]. The circuit model of a spiral inductor 

is shown in Fig. 1.

The inductance of the square spiral is computed using the

Wheeler formula [5]

(1)

where is the number of turns; is the permeability of free

space; and are coef  ficients depending on the shapes of 

the coils; they are equal to 2.34 and 2.75, respectively, for coils

having a square shape; is the fill ratio defined as

, where and represent the inner and

outer diameters of the inductor, respectively.

Under direct current (dc) excitation, the current density in a

wire is uniform, and could be obtained by the product of re-

sistance per unit length and wire length. However, as frequency

increases, the current tends to flow on the surface of the wire

 because of skin effect and proximity effect and thus the effec-

tive resistance is increased. To address eddy-current effect, the

most crucial parameter is the skin depth which is defined as

(2)

where , and represent the resistivity in , permeability

in H/m, and frequency in Hz, respectively. The series resistance

can be expressed as [6]

(3)

where and represent the thickness and length of the wire,

respectively.

In view of the parasitic capacitive coupling between input andoutput ports of the inductor, the capacitance is the sum of all

overlap capacitances, which is equal to

(4)

where is the oxide thickness between the spiral and under-

 pass; is the permittivity of the oxide which is equal to 3.45

10 F/cm; and is the number of overlap.

The oxide capacitance , and substrate capacitance and re-

sistance and can be, respectively, expressed as [6]

(5)

(6)

(7)

Fig. 2. (a) The basic structure of the prototype. (b) One loop of the prototypeshowing the segment of the conductor.

where and are the conductance and capacitance per unit

area for the substrate.

 B. Computation of the Inductance Matrix Using FEM 

Since the planar spiral inductor has a multiconductor struc-

ture, the eddy currents are also induced by currents in other 

segments due to proximity and skin effects. To study the ef-fect of magnetic mutual coupling, an eddy-current magnetic

field solver based on 3-D FEM is employed [6]. By using the

 parameter extraction method presented by Fu and Ho [7], an

impedance matrix including self inductance of each segment

conductors, mutual inductance among segments of conductors,

and the other mutual inductance between the two loops of the

system can be computed precisely.

After the impedance matrix is obtained with the aforemen-

tioned two methods, the Simulink of Matlab are used to plot the

graphs to describe the trends of impedances in the equivalent

circuit that vary with frequency in order to help finding the res-

onance frequency of the circuit.

III. EQUIVALENT CIRCUIT OF THE PROTOTYPE

The prototype is constructed on the basis of a thin plastic

lamella with a permittivity which serves as the insulator as

shown in Fig. 2(a). On the one side of the plastic lamella, a

copper tape is applied to form a square planar spiral inductor.

On the other side, four strips of the same size are af fixed along

the axis of the four borders of the inductor. These copper 

strips cover all the turns of the opposite copper tapes to form

capacitors.

In order to apply the witricity system to different situations,

the size of the source loop and the device loop should be dif-ferent but their resonance frequencies are the same. To ensure

the resonance frequencies of the two loops are identical, special

efforts are needed before the model can be made in laboratory.

The use of an equivalent circuit of the prototype is an effective

method to dealing with this problem.

Observing from Fig. 2(b), the whole inductor is segmented

into several sections by the copper strips making up the capac-

itors. The numbers of resistors, inductors, and capacitors are

4 , and respectively, where represents the

number of turns in the inductor. The capacitors along the same

 border are connected together.

The basic equivalent circuit of one loop is shown in Fig. 3.

In the simulation, the inductance of each segment includes the

self-inductance and two kinds of mutual inductance which are

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3202 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Fig. 3. The equivalent circuit of the basic prototype.

Fig. 4. (a) Graph of impedance versus frequency simulated using the formulamethod. (b) Graph of impedance versus frequency simulated with FEM.

the mutual inductance among each segment and the mutual in-

ductance between the two loops of the system. Between port 1

and port 2, the parameters of , and are all

included as shown in Fig. 1(a).

All the simulations are based on the structure of the prototype

as shown in Fig. 2(a). The width and thickness of the copper tape

are6.35 mm and 0.04 mm, respectively. The model is composedof six turns with an inner diameter of 114 mm and an outer 

diameter of 208 mm. The thickness of the middle plastic lamella

is 0.1 mm, and the width of the copper stripes making up the

capacitors is 25.5 mm.

IV. A NALYSIS AND R ESULT

With the first approach, the inductances are calculated using

a formula, and it is divided into several parts according to the

length of each segment. The equivalent circuit is simulated

using Simulink. The graph of the impedance which is observed

from the terminals of the equivalent circuit versus frequency is

shown in Fig. 4(a). Reducing the resonance frequency to makeit as low as possible is the primary consideration in this research

study. Along this direction, the first resonance frequency thus

found is as shown in Fig. 4(a).

Alternatively, the 3-D model of eddy-current magneticfield is

solved using FEM. The conductors of the wire are split into sev-

eral parts and the impedance matrix is extracted and the values

of each element are put into the equivalent circuit. Then the res-

onant frequency is computed as shown in Fig. 4(b). The value

of this prototype is 65.6.

Observing from Fig. 4(b), the impedance of the equivalent

circuit reaches its maximum value at 4.63 MHz and this is the

first resonant frequency.

With the prototype depicted in Fig. 2(a), it is found experi-

mentally that the resonating wireless power transfer occurs at

TABLE IR ESONANT FREQUENCY OF THE PROTOTYPE

Fig. 5. Influence of different parameters to resonance frequency.

about 5.01 MHz. The input effective voltage is 5 V and the ef-

fective current is about 0.15–0.2 A. As the transmitted power is

suf ficient to light up an LED (0.2 W–0.8 W), the ef ficiency is

estimated to be at least 20%. Table I compares the resonant fre-

quencies from two simulation methods and actual measurement.

It can be observed that the difference between the magnetic

field simulation and measurement result is below 8%, which in-

dicates that the method of field simulation has a higher accuracy

than the formula method. Therefore, the following analysis will

use the field simulation only.

For witricity to be used successfully in different applications,

it is important to ensure the prototypes are designed with ap- propriate sizes to cater for the needs of different applications. In

addition, the resonant frequency of the source and device loops

should be the same in order to facilitate ef ficient transfer of en-

ergy from the source loop to the device loop. Moreover, it is

worthnoting that there are many factorsinfluencing the resonant

frequency which are dependent on the parameters of the proto-

types, the different connection ways and so on. In this paper, the

relationship between each factor and the resonant frequency are

studied in details and several aspects will be analyzed.

 A. Parameters of Prototype Versus Resonant Frequency

In order to investigate the relationship between resonance fre-quency and the parameters of the prototype, two important pa-

rameters includingthe widthof the capacitor and the inner diam-

eter of the inductor are analyzed using the developed equivalent

circuit.

Obviously, the resonance frequency varies with capacitance.

Fig. 5 indicates qualitatively the trend between the width of 

the capacitors and resonant frequency. It can be seen that the

resonant frequency is reduced as the width of the capacitors

increases.

The inner diameter is the key parameter which affects the

size of the prototype. In the simulation, the inner diameter of 

the prototype with six turns is varied from 60 to 200 mm in

steps of 10 mm. Fig. 5 shows the resonant frequency obtained

 by simulation with different inner diameters.

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ZHANG et al.: QUANTITATIVE ANALYSIS OF A WIRELESS POWER TRANSFER CELL WITH PLANAR SPIRAL STRUCTURES 3203

Fig. 6. (a) All the capacitors connected together. (b) The impedance versusfrequency.

Fig. 7. (a) All the capacitors are connected together and then connected to theoutermost turn of the inductor. (b) The impedance versus frequency.

Fig. 8. (a) With a single-turn copper coil in the vicinity of the basic prototype.(b) The impedance versus frequency.

In general, the resonant frequency is dependent directly on the

variation of the parameters. From the trend of the two curves,

the capacitor plays a more important role in this model. For fu-

ture research, those changes that combine two or three different

 parameters will be analyzed so as to find an ideal prototype with

suitable size and low resonant frequency.

 B. Different Connection Versus Resonant Frequency

To the prototype, there are a number of different connection

methods based on the square spiral structure. In order to facili-tate the display, only one loop is shown in the following. In fact,

the two loops have the same connection method.

Fig. 6 indicates one connection which connects all the ca-

 pacitors together. The resonant frequency is 4.01 MHz which is

smaller when compared with the first resonating frequency of 

the same basic structure. The -factor value is 148.8.

Another connection is to connect all capacitors together and

then connect the capacitor to the outermost turn of the inductor,

as shown in Fig. 7.

In this connection, the resonant frequency is about 2.03 MHz

which means the resonance frequency has been decreased by

more than 50% when compared to the resonating frequency of 

4.63 MHz. The corresponding -factor is 103.3.

C. Add a Single-Turn Coil Versus Resonant Frequency

The third method to alter the resonant frequency is to place

a single-turn copper coil in the vicinity of the basic prototype

with a 1-mm distance. The basic parameters of the coil includea 200-mm major diameter and a 10-mm minor diameter.

Due to the mutual inductance between the coil and the orig-

inal prototype, the resonant frequency of the new prototype is

expected to be lower. Indeed the simulation result is 4.25 MHz

which is 7% smaller when compared with that of the basic pro-

totype without a coil. The -factor value is 92.1. In this proto-

type, the single-turn coil serves as a transformer, and the output

voltage is increased by 20% as verified experimentally.

V. CONCLUSION

To compute the resonant frequency of the prototype, an

equivalent circuit is presented and evaluated by comparingthe computed findings with those obtained experimentally. It

is found that the impedance matrix computed using 3-D field

computation has higher precision than that of the formula

method. The equivalent circuit is also convenient and ef ficient

in obtaining the resonant frequency.

Several different situations have been simulated using the

equivalent circuit based on parameters which are extracted from

eddy-current magnetic field computation. It provides the foun-

dation for finding the optimal designs of the prototypes that op-

erate at a lower resonant frequency as far as possible so as to

reduce the electromagnetic pollutions to the environment.

ACKNOWLEDGMENT

This work was supported by the Research Grant Council of 

the Hong Kong SAR Government under Project PolyU 5184/

09E.

R EFERENCES

[1] N. Tesla, “Apparatus for transmitting electrical energy,” U.S. Patent 1119 732, 1902.

[2] X. Y. Liu, F. Zhang, S. A. Hackworth, R. J. Sclabassi, and M. G. Sun,“Modeling and simulation of a thin film power transfer cell for medicaldevices and implants,” in Proc. IEEE Int. Symp. Circuits Syst., Taipei,Taiwan, May 24–27, 2009, pp. 3086–3089.

[3] T. Imura, H. I. Okabe, and Y. Hori, “Basic experimental study on he-lical antennas of wireless power transfer for electric vehicles by usingmagnetic resonant couplings,” in Proc. IEEE Veh. Power Propulsion

Conf., 2009, pp. 936–940.[4] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and

M. Soljacic, “Wireless power transfer via strongly coupled magneticresonances,” Science, vol. 317, pp. 83–86, Jul. 2007.

[5] S. Sunderarajan, M. del M. H. Mohan, S. P. Boyd, and T. H. Lee,“Simple accurate expressions for planar spiral inductances,” IEEE J.Solid Solid-State Circuit , vol. 34, no. 10, pp. 1419–1424, Oct. 1999.

[6] C. P. Yue and S. S. Wong, “Physical modeling of spiral inductors onsilicon,” IEEE Trans. Electron Devices, vol. 47, no. 3, pp. 560–568,Mar. 2000.

[7] W.N. FuandS. L. Ho, “A direct circuit parameterextractionmethodof eddy-current magnetic field,” in Proc. CEFC , Chicago, IL, May 9–12,2010, p. 1.