Coupling-Dependent Data Flipping in Wireless Powerand Data Transfer System
Hao Qiu, Takayasu Sakurai, and Makoto Takamiya
Institute of Industrial ScienceThe University of Tokyo, Tokyo, Japan
Email: hqiu@iis.u-tokyo.ac.jp
Abstract—Load modulation is a common method to transfer
data from the receiver (RX) side to the transmitter (TX) side in amagnetic resonance coupling wireless power transfer system.
However, coupling-dependent data flipping (CDDF), that thedata can be flipped depending on the coupling between TX andRX coils, is found for the first time using the conventional voltage
monitoring across the TX coil. An analytic formula of the critical
coupling coefficient (kC) of the coils that determines CDDF isderived. To avoid CDDF, a TX input voltage monitoring method
is proposed. Both the CDDF in the conventional method and thecorrect data transfer without CDDF in the proposed method aredemonstrated in the measurement.
Keywords—Coupling-dependent data flipping, critical coupling
coefficient, load modulation, magnetic resonance coupling,transmitter input voltage monitoring, wireless power transfer,wireless data transfer

Transmitter (TX)ITXCTXRSVSVLCkIRXCRXVL LTX

LRXrTX

rRX

SW

RL

Power

Proposed TX
input voltage
monitoring

Load modulation
Data (backscatter)

Fig. 1. Equivalent circuit model of a wireless power and data transfer system.
The impedance matching networks (IMNs) in both TX and RX sides are notdrawn for simplicity.
SWOn

I. INTRODUCTION
Wireless power transfer using magnetic resonance couplinghas been applied in a wide range of subjects such as electricvehicles, mobile devices, and biomedical implants [1]. In awireless power transfer system, when the coupling coefficient(k) between the TX and RX coils changes, both the coil-to-coilefficiency [2] and power losses in circuit components [3-4] areaffected. In order to control and regulate the power in the RXcoil, the establishment of a RX-to-TX communication (uplink)
which is irrespective of k is required. As is shown in Fig. 1, ina wireless power and data transfer system, load modulation [5]has been widely used due to its simple architecture in which
the change of the RX coil’s loading condition is reflected in theTX coil and the voltage across the TX coil (VL) is monitored.
However, most of the previous research [6-8] has focused onthe case where k is a constant and few has discussed its
possible effects.

Receiver (RX)OffData 0

Data 0

Data 1

Data 1

11

Data 1TimeVL00

if 0 < k < kC(a) Conv.
VL monitoring

VL
if kC < k < 1(b) Proposed TX
input voltage (VLC)
monitoring

VLC01

Normalmode

Time
Coupling-dependent data flipping (CDDF)
10Abnormal
mode

Time
Data shown in blue are incorrect.
00 Correct communication
irrespective of k11TimekC: Critical kFig. 2. Data backscatter based on (a) conventional VL monitoring and (b)proposed VLC monitoring.

II. CDDF AND THE SOLUTION
In this work, the effects of k on data transfer in a wirelesspower and data transfer system are discussed. As shown in Fig.
2(a), when k is smaller than a critical k (kC), the data aredemodulated depending on the amplitude of VL. Here, data ‘1’is defined as large VL and data ‘0’ is defined as small VL. Whenk > kC, on the other hand, the relation between the data and theamplitude of VL is flipped and incorrect data are demodulated,which we call coupling-dependent data flipping (CDDF). kC is
the critical point, at which VL does not change its value duringload modulation and thus data cannot be transferred from the

978-1-7281-0397-6/19/$31.00 ©2019 IEEERX side to the TX side. Thus, we propose to monitor the TX
input voltage (VLC) rather than VL in Fig. 1. As shown in Fig.
2(b), where data ‘1’ is defined as small VLC and data ‘0’ isdefined as large VLC, an uplink with a correct data transferrobust against CDDF is established.
III. CIRCUIT ANALYSIS OF CDDF
In this chapter, the origin of CDDF is analyzed. Fig. 1
shows the equivalent circuit model of a series-series topology,

TABLE I.

where the inductors and compensation capacitors are connected
in series in both TX and RX sides. The TX side, consisting ofan inductor (LTX) with an equivalent series resistance (rTX) anda compensation capacitor (CTX), is driven by a voltage source(VS) with an internal resistance (RS). The RX side is composedof an inductor (LRX) with an equivalent series resistance (rRX)
and a compensation capacitor (CRX). RL is the load resistance.
The currents flowing in the TX and RX sides are ITX and IRX,
respectively.
Applying Kirchhoff’s voltage law to the circuit, we obtainthe following relations between the currents and voltages at theresonance frequency (f0):

TX coil
Coil diameterjω0 MI TX = I RX ( RL + rRX + jω0 LRX + 1 / ( jω0CTX ))RX coil
300 mmCoil thickness

19 mm

14 mm

Wire diameter

1 mm

Coil turns

10

Resonance frequency (f0)

153 kHzInductor

LTX=66.2 μHEquivalent series resistance (ESR)rTX=0.5 Ω

rRX=1.0 ΩCompensation capacitor

CTX=16.4 nF

CRX=14.7 nF

Quality factor

12771

ω0 = 2π f 0 = 1 / LTX CTX = 1 / LRXCRX
VS = I TX ( RS + rTX + jω0 LTX + 1 / ( jω0CTX )) − jω0 MI RX

PARAMETERS OF TX AND RX COILS

LRX=73.8 μH

1.6. (1)Conventional
VL monitoring

1.4

M = k LTX LRX

Data 0 (SW=On)
Data 1 (SW=Off)The ratio of VL to VS at f0 can be described as:

VL I TX ( jω0 LTX + rTX ) − I RX jω0 M=VSVSkC

1.00.80.6( R + r )( jω0 LTX + rTX ) + ω0 k LTX LRX= L RX.
( RS + rTX )( RL + rRX ) + ω0 2 k 2 LTX LRX
2|VL/VS|

1.2

Here, M is the mutual inductance between the TX and RX
coils. j is the imaginary unit.

2(2)Normalmode

0.4
0.0

Abnormalmode

0.2

0.4

Calculation
0.6

0.8

1.0

Coupling coefficient (k)Its amplitude is:

VL=VS( RL + rRX )2 ω0 2 LTX 2 +  ( RL + rRX )rTX + ω0 2 k 2 LTX LRX ( RS + rTX )( RL + rRX ) + ω0 2 k 2 LTX LRX

Fig. 3. k dependence of calculated |VL/VS|.

2.

(3)
Based on the design parameters listed in Table I, a
numerical calculation was performed. Fig. 3 shows kdependence of the calculated |VL/VS| in the conventional VL
monitoring. kC is defined when

VL / VS R = VL / VS R =0 Ω .
LL(4)

It can be clearly seen that the data flips in the abnormal
mode when k > kC (~0.26). To understand the key parameters
determining kC, we derived its analytic formula by assuming
rTX and rRX as zero. That is:

kC =RL (ω0 2 LTX 2 − RS 2 ).
2 RSω0 2 LTX LRX(5)Since ω0, LTX, LRX are determined by the coil design, wediscuss the dependence of kC on RL and RS. The RL dependenceof kC is shown in Fig. 4(a), where RS equals 50Ω. Equation (5)gives the same positive R L dependence as the numericalcalculation based on (4), though with a deviation which comesfrom neglecting rTX and rRX. This deviation becomes smallerwhen RL becomes larger. The RS dependence of kC is shown inFig. 4(b), where RL equals 10Ω. When RS becomes smaller
than 5Ω, kC will become larger than 1 and CDDF cannot occur.

However, the impedance matching networks (IMNs) areusually inserted in both TX and RX sides to optimize thepower transfer efficiency, and thus RS seen from the TX coil’s
point of view equals RL [9]. Thus, in the conventional VL
monitoring, CDDF cannot be avoided.
On the other hand, in the proposed VLC monitoring, theamplitude of the ratio of VLC to VS at f0 is described as:

VLCI r= 1 − TX TX
VSVS= 1−

( RL + rRX ) RS.
( RS + rTX )( RL + rRX ) + ω0 2 k 2 LTX LRX(6)Fig. 5 shows k dependence of the calculated |VLC/VS| in the
proposed VLC monitoring. It is seen that, irrespective of k,

VLC / VS R < VLC / VS R =0 Ω .
LL(7)That means CDDF never happens with VLC monitoring andan uplink with a correct data transfer can be established.
Before discussing the measurement results, we give more
explanations of why k C exists in the conventional V L
monitoring and why CDDF never happens in the proposed VLC
monitoring. Fig. 6 gives the simplified circuit model of Fig. 1,assuming rTX and rRX to be zero. The equivalent resistance (r)

CTX

1.0
Calculation(a)Critical k (kC)

0.8

RS

RL (ω0 LTX − RS )2RSω02 LTX LRX
2kC =22

VSVL

RS=50Ω

0.6LTX
r=ω02k2LTXLRX/RL

VLC
r=VSr + RS

2r + RS

Proposed TX
input voltage
monitoring

RL=10Ω in this work

0.4
0.20.0VLC

r 2 + ( ω0 LTX )VL=VSFig. 6. Simplified circuit model of Fig. 1, in which rTX and rRX are assumed
to be zero. r is the equivalent resistance of the RX side seen from the TX side.
110100RL (Ω)|VL/VS| at f0 is

1.0

r 2 + (ω0 LTX )VL.
=VSr + RS2(b)Critical k (kC)

0.80.6r 2 + ω0 2 LTX 2 = r + RS .

Calculation
kC =0.20.0|VL/VS| equals 1 when RL is shorted. When RL is loaded,since r depends on k, kC can exist to satisfy thatRS=50Ω
in this work

0.4(10)At that point, |VL/VS| also equals 1, which makes (4) hold.

RL (ω0 2LTX 2 − RS2 )2RSω02 LTX LRXOn the other hand, |VLC/VS| at f0 is

RL=10Ω

1(9)

10

VLC
r=.
VSr + RS

100RS (Ω)(11)

It can be easily seen that (7) holds based on (8) and (11).

Fig. 4. (a) RL and (b) RS dependence of calculated kC.

IV. EXPERIMENTAL RESULTS
1.2
1.0Fig. 7 shows the photo of the fabricated coils based on theparameters in Table I. A signal generator with RS=50Ω wasused to generate a sinusoidal wave signal at 153kHz. k wasmeasured according to the method described in [11] andefficiency (η) is defined as the ratio of the power directlytransferred to RL to the power extracted from the power source[10]. Fig. 8 gives the dependence of measured k and η on thedistance (d) between the TX and RX coils.

Calculation

Proposed
VLC monitoring|VLC/Vs|

0.8
0.6
0.4
0.2
0.0
0.0Fig. 9 shows k dependence of measured |VL/VS|. kC exists,
as predicted in Fig.3. Compared with the calculation results,
measured |VL/VS| matches well when SW is Off but shows adeviation when SW is On. It can be ascribed to the unavoidable
fact that the f0 of the TX and RX coils can mismatch and thereflected reactance from the RX side will then affect the TX
side. The effect is greater when SW is On. This is also thereason why the measured kC (~0.43) in Fig. 9 does not matchthe calculated kC (~0.26) in Fig. 3.

Data 0 (SW=On)
Data 1 (SW=Off)
0.20.4

0.6

0.8

1.0

Coupling coefficient (k)Fig. 5. k dependence of calculated |VLC/VS|.

of the RX side seen from the TX side at f0 can be described as[10]:r = ω0 2 k 2 LTX LRX / RL .

(8)

On the other hand, Fig. 10 shows the k dependence ofmeasured |VLC/VS| we proposed. As predicted in Fig. 5, (7)holds irrespective of k and CDDF never happens in theproposed VLC monitoring. In addition, measured |VLC/VS| in Fig.
10 matches calculation results in Fig. 5 well, which is different
from the results of |VL/VS| especially when SW is On. This isRX coil

1.6

TX coil

1.4

Conventional
VL monitoring

Data 0 (SW=On)
Data 1 (SW=Off)|VL/VS|

d300 mm1.2
kC

1.00.8
Normal
mode

0.6
0.4
0.0

0.2

0.4

Abnormalmode
Measurement
0.6

0.8

1.0

Coupling coefficient (k)Fig. 7.

Photo of TX and RX coils.

Fig. 9.

1.0

1.2
1.0

0.8

Efficiency (η)|VLC/VS|

0.4

0.6
0.4

Coupling coefficient (k)0.20.2050100150200250

0.00.0300

d dependence of measured k and η.

another advantage of the proposed VLC monitoring that itsupports an uplink robust against f0 variations compared withthe conventional VL monitoring.
Here, more discussions are given. Series-series topology
has been analyzed in this work, analyses in series-parallel,parallel-series, and parallel-parallel topologies will be included
in our future work. In addition, the coil parameters werechosen mainly for EV applications. The universality of thephenomenon of CDDF will be discussed in several otherapplication scenarios, such as mobile charging and biomedical
applications.
V. CONCLUSIONS
To the best of our knowledge, the issue of CDDF wasfound for the first time in a wireless power and data transfer
system. An analytic formula of kC which shows a CDDF
boundary was also derived. In order to solve CDDF, we
proposed to monitor the transmitter input voltage (VLC). Circuit
analysis and measurement were performed to demonstrate ourconclusions.

Data 0 (SW=On)
Data 1 (SW=Off)
0.2

0.4

0.6

0.8

1.0

Coupling coefficient (k)TX-RX distance (d) (mm)Fig. 8.

Measurement

Proposed
VLC monitoring

0.8

0.60.0

k dependence of measured |VL/VS|.

Fig. 10.

k dependence of measured |VLC/VS|.

ACKNOWLEDGMENT
This work was partially supported by JST ERATO Grant
Number JPMJER1501, Japan.
REFERENCES
[1]

[2]

[3]

[4]

M. Kiani and M. Ghovanloo, “The circuit theory behind coupled-mode
magnetic resonance-based wireless power transmission,” IEEE Trans.
Circuits Syst. I, Reg. Papers, vol. 59, no. 9, pp. 2065–2074, Sep. 2012.
H. Qiu, Y. Narusue, Y. Kawahara, T. Sakurai, and M. Takamiya,“Digital coil: transmitter coil with programmable radius for wirelesspowering against distance variation,” in IEEE Wireless Power Transfer
Conf., Jun. 2018, pp. 1–4.
A. Ayachit, F. Corti, A. Reatti, and M. Kazimierczuk, “Zero-voltage
switching operation of transformer class-E inverter at any coupling
coefficient,” IEEE Trans. Ind. Electron., vol. 66, no. 3, pp. 1809–1819,
Mar. 2019.
T. Nagashima, X. Wei, E. Bou, E. Alarcon, M. K. Kazimierczuk, and H.
Sekiya, “Analysis and design of loosely inductive coupled wirelesspower transfer system based on class-E2 DC-DC converter for
efficiency enhancement,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol.
62, no. 11, pp. 2781–2791, Nov. 2015.

[5]X. Shi, A. N. Parks, B. H. Waters, and J. R. Smith, “Co-optimization ofefficiency and load modulation data rate in a wireless power transfersystem,” in Proc. IEEE Int. Symp. Circuits Syst., May 2015, pp. 698–701.
[6] Y. Jang, J. Han, S. Cho, G. Moon, J. Kim, and H. Sohn, “Wirelesspower and data transfer system for smart bridge sensors,” in Proc. IEEEAppl. Power Electron. Conf. Expo., Mar. 2016, pp. 3690–3696.
[7] I. Nam, R. Dougal, and E. Santi, “Novel control approach to achieving
efficient wireless battery charging for portable electronic devices,” inProc. IEEE Energy Convers. Congr. Expo., Sept. 2012, pp. 2482–2491.
[8] H.-M. Lee, H. Park, and M. Ghovanloo, “A power-efficient wirelesssystem with adapative supply control for deep brain stimulation,” IEEE
J. Solid-State Circuits, vol. 48, no. 9, pp. 2203–2216, Sep. 2013.
[9] E. Bou, R. Sedwick, and E. Alarcon, “Maximizing efficiency throughimpedance matching from a circuit-centric model of non-radiative
resonant wireless power transfer,” in Proc. IEEE Int. Symp. Circuits
Syst., May 2013, pp. 29–32.
[10] M. Fu, H. Yin, X. Zhu, and C. Ma, “Analysis and tracking of optimalload in wireless power transfer systems,” IEEE Trans. Power Electron.,
vol. 30, no. 7, pp. 3952–3963, Jul. 2015.
[11] K. Hata, T. Imura, and Y. Hori, “Simplified measuring method of kQ
product for wireless power transfer via magnetic resonance couplingbased on input impedance measurement,” in Proc. IEEE IECON, Oct.
2017, pp. 6974–6979.