298IEICE TRANS. FUNDAMENTALS, VOL.E96–A, NO.1 JANUARY 2013

PAPER

Reliable Data Transmission for Resonant-Type Wireless PowerTransfer

Shinpei NOGUCHI†a), Student Member, Mamiko INAMORI†b), and Yukitoshi SANADA†c), Members

SUMMARY Wireless power transfer research has been receiving agreat deal of attention in recent years. In resonant-type wireless powertransfer, energy is transferred via LC resonant circuits. However, systemperformance is dependent on the circuit components. To transfer powerefficiently and safely, information, such as frequency, required power andelement values, need to be transmitted reliably in the system. This pa-per investigates data communication using orthogonal frequency divisionmultiplexing (OFDM) modulation in resonant-type wireless power transfersystems. The equivalent circuit used in the transmitting and receiving an-tennas is a band pass filter (BPF) and its bandwidth is evaluated throughcircuit simulations and experimental measurements. Numerical results ob-tained through computer simulation show that the bit error rate (BER) per-formance is affected by the splitting resonant frequency.key words: OFDM, Wireless power transfer, BPF, communication, control

1. Introduction

Recent interest in wireless power transfer has been attract-ing a great deal of attention. Wireless power transfer will en-able advances in the use of electronic devices such as mobilephones, portable computers, etc.. Wireless power transfer iscurrently achieved via three techniques, with each systempossessing different characteristics in terms of distance andpower transfer efficiency.

The three techniques are electromagnetic induction,coupled radio frequency power transmission, and resonantcoupling. In electromagnetic induction, the magnetic fluxinduces the electric current, thus power is transferred wire-lessly to the received coil [1]. The efficiency of power trans-fer varies between 60–98% over a distance of several mil-limeters. To achieve coupled radio frequency power trans-mission, electromagnetic waves are converted to direct cur-rents, which provides power [2]. The efficiency of powertransfer is less than 50% over a distance of several meters.In the resonant coupling technique, two coils are tuned at thesame resonant frequency. Power transfer efficiency is ap-proximately 50% over a distance of several tens of centime-ters [3]. In 2006, MIT released “WiTricity”, which appliesthis resonant induction [4]. In this paper, the magnetic reso-nant coupling system is modeled for wireless power transfer.

Transmitting and receiving antennas in the resonantcoupling system need to induce a non-radiative magnetic

Manuscript received June 29, 2012.†The authors are with the Dept. of Electronics and Electrical

Engineering, Keio University, Yokohama-shi, 223-8522 Japan.a) E-mail: anoguchi@snd.elec.keio.ac.jpb) E-mail: inamori@elec.keio.ac.jpc) E-mail: sanada@elec.keio.ac.jp

DOI: 10.1587/transfun.E96.A.298

field. A practical implementation can be applied by us-ing loop antennas, in which changes to induced magneticfield are affected by the number of turns [5]. However, theself-resonant coils rely on the interplay between distributedconductance and distributed capacitance, which effects thepower transfer efficiency. The power transfer efficiency isaffected by the change of load at the receiver [6]. To en-able fast reaction, it is desirable to have the ability to changethe power signal according to the request of the receiverwhen providing power at the transmitter. When change isdetected at a transmitter, information such as frequency,required power and element values should be transmittedshortly and adapt to the desired power signal accordingly[6], [7]. Therefore, it is very important for wireless powertransfer systems to transmit these data fast and reliably.

This paper investigates the data transmission process.The equivalent circuit used in the transmitting and receiv-ing antennas is a band pass filter (BPF) and its bandwidthis evaluated through circuit simulations and experiments. Inthis paper, the transfer function |S 21| as measured experi-mentally and calculated from the circuit model are evalu-ated. The bandwidth to transmit the data information is thendecided. To satisfy the conditions for the high speed com-munication and reliability, orthogonal frequency divisionmultiplexing (OFDM) is applied as a modulation scheme.Bit error rate (BER) is calculated through MATLAB simu-lations. The required BER is set to 10−4, which is reliablefor data communication [8].

This paper is organized as follows. Section 2 intro-duces the system model and Sect. 3 outlines the experimen-tal setup. In Sect. 4, numerical results obtained throughcomputer simulations are presented. Section 5 gives ourconclusions and directions for future work.

2. System Model

2.1 Single Antenna

In this paper, a 3-turn coil as shown in Fig. 1 is used as atransmitting and receiving antenna. The equivalent circuit is

Fig. 1 Single antenna.

Copyright c© 2013 The Institute of Electronics, Information and Communication Engineers

NOGUCHI et al.: RELIABLE DATA TRANSMISSION FOR RESONANT-TYPE WIRELESS POWER TRANSFER299

Fig. 2 Equivalent circuit of antenna.

Fig. 3 Resonant coupling system with two coils.

Table 1 Parameters in single antenna.

Rr L C0 C1

36 mΩ 50 μH 5.7 pF 47 pF

shown in Fig. 2 [5]. In Fig. 2, L represents self-inductance,Rr represents the radiation resistance of the coil, C0 repre-sents the stray capacitance, and C1 represents the load ca-pacitance. The conductor losses are ignored in the circuitmodel. From Neumann’s formula, the self inductance, L, isgiven by

L =μ0

4π

∮1

∮2

d�1 · d�2r12

, (1)

where d�1 and d�2 are small line elements on a coil, and r12

is the thickness of the coil [9]. The radiation resistance of acoil Rr is given by

Rr = 20

(2πλ

)4 (πp2G

)2(2)

where G is the number of turns, p is the radius of a coil.The corresponding free space wavelength λ = c/ f wherec = 3.00 × 108 m/s and f represents the source frequency[10]. Figure 3 shows the antenna model. The diameter ofthe coil, D, is 30 cm and the thickness is 5 cm in the experi-mental model. In this paper, the parameter values, L, C0 andRL measured in the experimental model are applied. Fol-lowing which, the load capacitance, C1, is determined forthe resonant frequency of 10 MHz [11]. The values of eachparameter in this model are shown in Table 1.

Fig. 4 Equivalent circuit of the power transfer system.

Fig. 5 Coupling coefficient k vs. distance between two antennas dz.

2.2 Resonant Coupling System

The equivalent circuit of this system is shown in Fig. 4 [5].The load impedance, Z0, is set to 100Ω. From Neumann’sformula, the mutual inductance between the antennas isgiven by

M =μ0

4π

∮1

∮2

dL1 · dL2

dz, (3)

and

M = k√

L1L2, (4)

where dz is the distance between antennas, k is the couplingcoefficient, and L1, L2 are the self inductance of the receiv-ing antenna as given in Eq. (1) [9]. From Eqs. (3) and (4)with assuming L = L1 = L2, the coupling coefficient, k, iscalculated as shown in Fig. 5. With the value for the cou-pling coefficient, k, and Eq. (4), the transfer function, |S 21|,which represents the power transfer efficiency, is calculatedfor the circuit model.

2.3 Communication Model

In the communication model for data transmission, theequivalent circuit used in the transmitting and receiving an-tennas is regarded as a BPF, which has to be custom de-signed in order not to cause interference. To satisfy theseconstraints, OFDM is applied for data transmission in thepower transfer system. Suppose the information symbol on

300IEICE TRANS. FUNDAMENTALS, VOL.E96–A, NO.1 JANUARY 2013

the kth subcarrier is s[k] (k = 0, ...,N − 1), the OFDM sym-bol is given by

u[n] =1√N

N−1∑k=0

s[k]e j 2πnkN , (5)

where n (n = 0, ...,N − 1) is the time index and N is thenumber of subcarriers. The guard interval is added beforethe data transmission. The baseband signal at the output ofthe filter is given by x(t) =

∑P−1n=0 u[n]Ct(t−nTs), where Ct(t)

is the impulse response of the transmitting filter, P is thelength of the impulse response, and Ts is the OFDM symbolduration.

In this system, the antennas are fixed and multipath fad-ing is not assumed. The received signal is given by

y(t) =P−1∑n=0

u[n]h(t − nTs) + v(t), (6)

where v(t) is the additive white Gaussian noise (AWGN),h(t) is the impulse response of the composite channel and isgiven by

h(t) = Ct(t) ⊗Cr(t), (7)

where ⊗ denotes convolution and Cr(t) is the impulse re-sponse of the receiving filter. The frequency response ofchannel in the communication model, H, is equivalent to|S 21| in the power transfer system.

3. Experimental Measurement

The experimental single antenna with 3-turn coil is shownin Fig. 6. The measurement equipment is shown in Table 2.

Fig. 6 Experimental antennas.

Table 2 Measurement equipment.

Equipment SpecificationVector network analyser Agilent 8753ETVNA control software Agilent technology

Intuilink (Version 1.3)Circuit simulator PSpice circuit simulatorTx antenna Loop antenna

(D = 30 cm)Rx antenna Loop antenna

(D = 30 cm)

In this experimental system, |S 21| was measured with thevector network analyzer (VNA). It is assumed that the an-tenna is only moved along the z-axis. The experimentallymeasured inductance of the coil at the transmitting and re-ceiving antenna, L̂1, is applied to the values in the circuitmodel, L1 and L2.

4. Simulation Results

4.1 |S 21| Characteristic

Figures 7 and 8 show |S 21| characteristic as measured exper-imentally and calculated from the equivalent circuit model.The distance between the transmitting and receiving antennaon the experimental measurements, dz, is set to 10 cm and40 cm, the coupling coefficient, k, on the circuit simulator isset to 0.16 and 0.07 from Fig. 5, respectively. In Fig. 7, whendz = 10 cm, both the theoretical curve based on the circuitmodel and the experimental measurement curve show thesplitting of resonant peak. As the coupling between the coils

Fig. 7 Transfer function |S 21 | (k = 0.16, dz = 10 cm).

Fig. 8 Transfer function |S 21 | (k = 0.07, dz = 40 cm).

NOGUCHI et al.: RELIABLE DATA TRANSMISSION FOR RESONANT-TYPE WIRELESS POWER TRANSFER301

at the transmitting and receiving antenna becomes stronger,the peak splits into two. Moreover, the theoretical curvebased on the circuit model does not fit the experimental mea-surement curve. It is due to the mismatch of derived valueson the experimental measurement model and equivalent cir-cuit model, which are chosen from parameters such as resis-tances, stray capacitances and self inductances. The param-eters used in the transmitter and the receiver are assumedto be the same in the circuit model as described in Sect. 3.Therefore, the mismatch comes from the difference of thecoupling coefficient, k, between the circuit model and theexperimental measurement. From Fig. 8, when dz = 40 cm,both the theoretical curve based on the circuit model and theexperimental measurement curve show that the peak doesnot split. In the experimental measurement, the asymme-try curve is observed. The reason is that the transmit andreceive antennas are not physically identical in this experi-mental model.

4.2 Impulse Response

To investigate the influence of the transmitting and receiving

Fig. 9 Impulse response of |S 21 | from the experimental measurement(k = 0.16, dz = 10 cm).

Fig. 10 Impulse response of |S 21 | from the experimental measurement(k = 0.07, dz = 40 cm).

antennas, the impulse responses of |S 21| is shown. Figures 9and 10 display the impulse response of the channel fromthe experimental measurement in the delay domain betweenthe antennas when dz = 10 cm. In the data transmissionsystem, OFDM is employed for the 2nd modulation, andthe bandwidth of OFDM is designed to fit the relatively largeimpulse response of the channel in the guard interval period.Thus, the number of the subcarriers is derived to satisfy thiscondition:

N/Ts ≤ �W. (8)

Here, �W is the bandwidth of the composite filters, whichis measured at half-power points (3 dB) from the peak.

4.3 BER Performance

4.3.1 Simulation Model

BER performance is evaluated through computer simula-tion. The simulation model is shown in Fig. 11 and the sim-ulation conditions are shown in Table 3. Information bits aremodulated with quadrature phase shift keying (QPSK) or 64quadrature amplitude modulation (QAM) on each subcar-rier. The number of discrete Fourier transform (DFT) pointsis set to 32 and 16, which are fit to �W given from exper-imentally measured |S 21| characteristic as shown in Figs. 7and 8, respectively. The guard interval is set to 8 and 4,which are 1/4 of the number of subcarrier N. The channelmodel used is a quasi-static multipath channel, which is thepath between the transmit antenna and the receive antenna.The phase compensation is assumed to be perfect.

4.3.2 Simulation Results

From Figs. 12 to 15, the BER performances on the AWGN

Fig. 11 Simulation model.

Table 3 Simulation conditions.

Modulation scheme 1st : QPSK/64QAM2nd : OFDM

Bandwidth 1.33 MHz 0.36 MHzFFT size 32 16

Number of data subcarriers 32 16Number of guard interval 8 4

Channel model quasi-static multipath channelNumber of OFDM symbols 10, 000, 000

dy 0 cmdz 10 cm 40 cm

302IEICE TRANS. FUNDAMENTALS, VOL.E96–A, NO.1 JANUARY 2013

Fig. 12 BER performance of QPSK (k = 0.16, dz = 10 cm).

Fig. 13 BER performance of 64QAM (k = 0.16, dz = 10 cm).

model with QPSK and 64QAM are shown, when dz is10 cm and 40 cm. In Figs. 12 and 13, BER performances ofdz = 10 cm appear degraded between 2–4 dB at 10−4 whencompared to the AWGN theoretical curve due to the fre-quency selective channel, which is caused by the unbalancedsplitting resonant frequency used. Moreover, the BER curvewith experimental frequency response is worse than that ofthe calculated frequency response from the circuit model.This is because the OFDM signal is affected by the splittingresonant frequency in the experimental measurement. Onthe other hand, in Figs. 14 and 15, when dz = 40 cm, bothBER curves with circuit simulation and experimental mea-surement are close to the AWGN theoretical curve. Thisis because the splitting resonant frequency is not observedand the bandwidth of OFDM is fit to �W in Fig. 8. Whendz = 10 cm, either one of the peak frequencies can be chosenas the passband for data communication. In such a case, theBER performance is similar to the results shown in Figs. 14

Fig. 14 BER performance of QPSK (k = 0.07, dz = 40 cm).

Fig. 15 BER performance of 64QAM (k = 0.07, dz = 40 cm).

and 15, because a narrow bandwidth is used at dz = 40 cmand it is not affected by the splitting resonant frequency.

5. Conclusions

In this paper, data transmission for power transfer systemshas been investigated. Resonant coupling is used to deliverpower from one coil to another coil wirelessly. In the wire-less power transfer system, information, such as frequency,required power and element values, need to be transmittedinitially to ensure safe power transfer. The equivalent cir-cuit of the antenna is BPF, and the transfer function |S 21|is regarded as the impulse response of the channel in thedata transmission. In this paper, the transfer function |S 21| isgiven from calculation on the circuit model and from exper-imental measurements.

In the data transmission model, OFDM is used as the2nd modulation and the impulse response of |S 21| in thetime domain is designed to fit within the guard interval pe-

NOGUCHI et al.: RELIABLE DATA TRANSMISSION FOR RESONANT-TYPE WIRELESS POWER TRANSFER303

riod. As the distance between antennas was fixed, the chan-nel is assumed to be AWGN. From simulation results, BERperformance of dz = 10 cm is degraded compared to theAWGN theoretical curve due to the splitting resonant fre-quency. This is because the shorter distance between an-tennas make mutual inductance strong. In this paper, it isassumed that the system parameters are transmitted as in-formation in the system. Therefore, this research is valid forlow data rate transmission with narrow bandwidth. Furtherwork will consider the data transmission with power trans-ferring for control system adjustments.

Acknowledgement

This work is supported in part by a Grant-in-Aid for YoungScientists (B) under Grant No.24760304 from the Ministryof Education, Culture, Sport, Science, and Technology andKeio Gijuku Academic Development Funds in Japan.

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Shinpei Noguchi was born in Tokyo, Japanin 1987. He received his B.E. degrees in elec-tronics engineering from Keio University, Japanin 2011. Since April 2011, he has been a gradu-ate student in School of Integrated Design Engi-neering, Graduate School of Science and Tech-nology, Keio University. His research interestsare mainly concentrated on control system forwireless power transfer.

Mamiko Inamori was born in Kagoshima,Japan in 1982. She received her B.E., M.E., andPh.D. degrees in electronics engineering fromKeio University, Japan in 2005, 2007, and 2009,respectively. Since October 2009, she has beenan assistant professor in Keio University. Shereceived the Young Scientist Award from Eric-sson Japan in 2010. Her research interests aremainly concentrated on software defined radio.

Yukitoshi Sanada was born in Tokyo in1969. He received his B.E. degree in electricalengineering from Keio University, YokohamaJapan, his M.A.Sc. degree in electrical engi-neering from the University of Victoria, B.C.,Canada, and his Ph.D. degree in electrical engi-neering from Keio University, Yokohama Japan,in 1992, 1995, and 1997, respectively. In 1997he joined the Faculty of Engineering, Tokyo In-stitute of Technology as a Research Associate.In 2000 he joined Advanced Telecommunica-

tion Laboratory, Sony Computer Science Laboratories, Inc, as an associateresearcher. In 2001 he joined Faculty of Science and Engineering, KeioUniversity, where he is now a professor. He received the Young EngineerAward from IEICE Japan in 1997. His current research interests are insoftware defined radio, cognitive radio, and ultra wideband systems.