Automatic Active Compensation Method of CrossCoupling in Multiple-receiver Resonant Inductive
Coupling Wireless Power Transfer Systems
Masataka Ishihara, Kazuhiro Umetani, Eiji Hiraki
Graduate School of Natural Science and Technology
Okayama University
Okayama, Japan

Published in: 2019 IEEE Energy Conversion Congress and Exposition (ECCE)© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be
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DOI: 10.1109/ECCE.2019.8913279

Automatic Active Compensation Method of CrossCoupling in Multiple-receiver Resonant Inductive
Coupling Wireless Power Transfer Systems
Masataka Ishihara
Graduate School of Natural
Science and Technology
Okayama University
Okayama, Japan
p4wv0vf6@s.okayama-u.ac.jp

Keita Fujiki
Graduate School of Natural
Science and Technology
Okayama University
Okayama, Japan
pu861z88@s.okayama-u.ac.jp

Abstract—The ability to charge to multiple receivers
simultaneously with a single transmitter is one of the advantagesof resonant inductive coupling wireless power transfer (RICWPT) technologies. However, in multiple-receiver RIC-WPT
systems, each receiver often suffers from the magnetic coupling
among receivers, i.e., cross-coupling. The cross-coupling not
only complicates the control of the receivers but alsosignificantly decreases the output power of each receiver. Hence,the purpose of this paper is to propose a compensation methodof the influence due to the cross-coupling. To achieve thispurpose, we first analyze the requirement to compensate for the
influence of the cross-coupling. As a result, we reveal that it isnecessary to control the phase of the current in all the receiver
to be orthogonal to the phase of the transmitter current. Then,
we propose the method to adjust the current phase of each
receiver automatically to the desired phase by using only thephase information of the transmitter current, which results inthe full compensation of the influence due to the cross-coupling.
Furthermore, the proposed method also compensates for the
influence of a detuning of the resonant frequency of each
receiver due to the natural tolerance. Experiments of a tworeceiver RIC-WPT system successfully verify the effectivenessof the proposed method.
Keywords—wireless power transfer, resonant inductive
coupling, multiple-receiver, cross-coupling, automatic active
compensation

I. INTRODUCTION
Recently, wireless power transfer (WPT) technologies
have been attracting significant public attention because the
WPT technologies remove physical cable connections, which
results in convenient, reliable, and safe power supplies.
Among the WPT technologies, resonant inductive coupling
WPT (RIC-WPT) technologies, which transfer the power via
the magnetic coupling between coils, are widely studied
owing to their comparatively high efficiency and high output
power. Because of the advantage, the RIC-WPT technologies
are expected to be applied to various application fields ranging
from a few milliwatts up to several kilowatts of output power.
One of the attractive advantages of the RIC-WPT is that asingle transmitter can transfer the power to multiple receivers
simultaneously. Recently, owing to this attractive advantage,
multiple-receiver RIC-WPT systems have been widely
studied for low power applications such as mobile devices,
wearable devices, and biomedical devices [1–7]. Usually, themultiple-receiver RIC-WPT system requires that the output
power of each receiver does not depend on the position andoutput power of other receivers [1, 4]. In this study, we refer

Kazuhiro Umetani
Graduate School of Natural
Science and Technology
Okayama University
Okayama, Japanumetani@okayama-u.ac.jp

Eiji Hiraki
Graduate School of Natural
Science and Technology
Okayama University
Okayama, Japan
hiraki@okayama-u.ac.jp

Multiple-receiver
WRX1

Capacitor

WRXn Capacitor…
Capacitor

Power load

AC current-source

Power load

WTX

Transmitter
Fig. 1.

Multiple-receiver resonant inductive coupling wireless powertransfer (RIC-WPT) system.

to a receiver whose output power is not affected by the stateof other receivers as a decoupled receiver.
The influence which a certain receiver receives from otherreceivers is divided into the following two types by its
mechanism, and we must deal with two influences
simultaneously to realize the decoupled receiver.
1) The first is the influence caused by the change in theamplitude of the transmitter current according to the output
power of the receivers. The output power changes if theamplitude of the transmitter current changes because theinduced voltage on the receiver from the transmitter is
proportional to the amplitude of the transmitter current.
Usually, in a common transmitter composed of a series LC
resonant circuit, the resonance in the transmitter is excited by
the AC voltage source consisting of a DC voltage source anda voltage-fed inverter [8, 9]. Hence, the amplitude of thetransmitter current depends on the input impedance of thetransmitter. The input impedance of the transmitter depends
on not only parasitic resistance of the transmitter but also the
output power of each receiver. Therefore, the amplitude of
the transmitter current depends on the output power of each
receiver.
2) The second is the influence caused by the induced voltage
due to the magnetic coupling among receivers (i.e., crosscoupling). In this paper, we mainly focus on this influence.
The influence of the cross-coupling occurs remarkably when
the receivers are disposed of close to each other. Certainly,
we can avoid the influence of the cross-coupling when theseparation among the receivers is sufficiently larger than thesize of receiver coils [6]. However, as pointed in [7], when
there is the multiple-receiver in a limited space, we cannot
probably avoid the influence of the cross-coupling. In themultiple-receiver RIC-WPT systems, the output power of
each receiver may be significantly reduced when the crosscoupling occurs [1–3]. Furthermore, the control of thereceiver may become quite complicated because the output
power depends on the output power of the other receivers andthe relative positions of receiver coils [4].

rt

Between two influences, it is known that the first influencecan be solved relatively easily [1, 4]. To solve this problem,
we have only to use the AC current source to excite thetransmitter as shown in Fig. 1, where WTX is the transmittercoil and WRXi (i=1, …, n) are the receiver coils. As a result,
we can obtain the transmitter current with the constant
amplitude independent of the output power of each receiver,which eliminates the first influence. The AC current source
can be implemented by feedback control of the voltage-fed
inverter [10]. Alternatively, we may adopt an LCC topology[11] or a K-inverter [1] to the transmitter to obtain the loadindependent transmitter current.
Then, the second influence due to the cross-coupling canbe also solved theoretically by inserting an appropriate
reactance to each receiver. Based on the previous studies [3,4], the essence of the influence due to the cross-coupling is a
detuning of the resonant frequency of each receiver. Therefore,
the influence of the cross-coupling can be fully compensatedby inserting an appropriate reactance to each receiver to retune
the resonant frequencies [3, 4].
However, inserting the appropriate reactance to each
receiver according to various situations is practically difficult.
The appropriate reactance depends on the relative positions ofcoils and the output power of other receivers [3, 4]. Hence, wemust accurately dynamically adjust the resonant frequency ofeach receiver by using a variable reactance element such as avariable capacitor and a variable inductor after estimation of
the relative positions of coils and the output power of otherreceivers. Usually, this procedure is quite complicated.
Therefore, the purpose of this paper is to propose acompensation method of cross-coupling, which does not need
the estimation of the relative positions of coils and the output
power of other receivers. To achieve this purpose, we firstinvestigate the phase of the transmitter current and receivercurrents when the appropriate reactance is inserted into each
receiver. The result shows that it is necessary to control thephase of the current in all the receiver to be orthogonal to thephase of the transmitter current. This insight is promising tocompensate for the influence of the cross-coupling because
adjusting the phase of each receiver current may be easier thaninserting the appropriate reactance to each receiver. Then, we
propose the receiver with a simple switching circuit, which
adjusts the phase of the receiver current to the desired phase.
The proposed method can adjust the phase of each receivercurrent automatically dynamically to the desired phase byusing only the phase information of the transmitter current. As
a result, we can fully compensate for the influence due to thecross-coupling without the estimation of the relative positionsof coils and the output power of other receivers.
The remainder of this paper is structured into four sections.
Section II shows the requirement of the phase of each receivercurrent to compensate for the influence of the cross-coupling.
Section III shows the multiple-receiver RIC-WPT system withthe proposed compensation method. Section IV carries out
experiments to verify the effectiveness of the proposedcompensation method. Finally, section V describes theconclusions.

I1

Mt1

Ct

C1
L1

r1

C2

r2

R1

Lt

It

I2
Mt2

R2

L2

(a)

rt

Ct

Lt

L1

C1
jωMt1It

r1

L2

r2

I1
R1

−jωMt1I1
It−jωMt2I2

C2
jωMt2It

I2
R2(b)Fig. 2.

Equivalent circuit of two-receiver RIC-WPT system withoutcross coupling. (a) Model based on coupling circuit. (b) Model
based on induced voltage

II. REQUIREMENT FOR COMPENSATION OF CROSS-COUPLING
In this section, we first derive the output power of thedecoupled receiver by analyzing the equivalent circuit
ignoring the cross-coupling. The derived output power is used
as a criterion to determine whether the decoupled receiver has
been achieved. Then, we review the appropriate reactance forcompensation of the influence due to the cross-coupling. In
this paper, we specifically focus on the phase of the current in
the transmitter and receivers when the appropriate reactanceis inserted into each receiver. As a result, we show that thephase of the current in all the receiver must be orthogonal tothe phase of the transmitter current to compensate for the
influence of the cross-coupling.
In this study, a two-receiver RIC-WPT system is discussed
as a representative example for simplicity. Furthermore, we
assume that the quality factors of the resonators are highenough to adopt the first harmonic approximation analysis.
A. Output Power of Decoupled ReceiverFig. 2 shows the equivalent circuit of Fig. 1 ignoring thecross-coupling. In Fig. 2, It, I1, and I2 are the transmittercurrent and the receiver currents, respectively; Lt, L1, and L2
are the self-inductances of WTX, WRX1, and WRX2,
respectively; rt, r1, and r2 are the parasitic resistances of WTX,
WRX1, and WRX2, respectively; R1 and R2 are the equivalentvalues of load resistances; Ct, C1, and C2 are the capacitancesof the resonant capacitors; Mt1 is the mutual inductance
between WTX and WRX1; Mt2 is the mutual inductance between
WTX and WRX2. The magnetic couplings of Fig. 2 (a) can be
replaced with the induced voltage as shown in Fig. 2 (b).
Usually, in the RIC-WPT systems, the receiver is required
to obtain the output power as high as possible from a given
induced voltage generated by the transmitter. Therefore, thetotal reactance of the self-inductance of the coil and thecapacitance of the resonant capacitor is designed to be zero atthe operating frequency, i.e., ωL1−1/ωC1=0 andωL2−1/ωC2=0. In this case, because the receivers are resistive
circuits, the induced voltages from the transmitter, i.e., jωMt1It
and jωMt2It, achieve a unity power factor. The output powerof each receiver, i.e. P1 and P2, can be expressed as2

P1  R1

2

j M t1I tj M t 2 I t, P2  R2.
r1  R1
r2  R2

Receiver 1


rt





Equation (2) is identical to optimal load reactances tocompensate for the influence of the cross-coupling revealed in[4] (See (22) of [4]). The appropriate reactances depend on theload resistances (i.e., the output powers), the parasitic
resistances, and the mutual inductances (i.e., the relative
positions of coils). Therefore, as pointed in [4], inserting theappropriate reactance may require the estimation of the load
resistances, the parasitic resistances, and the mutual
inductances. However, as shown in this paper, we cancompensate for the influence of the cross-coupling bydetecting the phases of the transmitter current and receivercurrents and adjusting the phase of each receiver current
instead of inserting the appropriate reactances after estimating
the output powers, the parasitic resistances, and the mutual
inductances.
III. PROPOSED METHOD
In this section, we propose the method to adjust the phaseof each receiver current and compensate for the influence ofthe cross-coupling. First, we show the circuit configuration of
the multi-receiver RIC-WPT system with the proposed

M12

Lt

It

B. Phase Condition of Resonator Currents forCompensation of Cross-Coupling
Then, we discuss the appropriate reactance forcompensation of the influence due to the cross-coupling. Fig.
3 shows the equivalent circuit of Fig. 1 considering the crosscoupling, where M12 is the mutual inductance due to the crosscoupling, Xopt1 and Xopt2 are the reactances to compensate forthe influence of the cross-coupling. As in Fig. 2, the magnetic
coupling of Fig. 3 (a) can be replaced with the induced voltage
as shown in Fig. 3 (b). Note that jωM12I2 and jωM12I1 are theinduced voltages due to the cross coupling.

 X opt1    M 12 M t 2  r1  R1  M t1  r2  R2  , X opt 2    M 12 M t1  r2  R2  M t 2  r1  R1  .

I1
r1
L1 C1

R1

Xopt1

The equations of (1) show the output powers of the decoupled
receiver because Fig. 2 does not consider the cross-coupling.

Even if the cross-coupling occurs, we can compensate forthe influence of the cross-coupling by adjusting the reactancesof Xopt1 and Xopt2 so that the phase of each receiver current isorthogonal to the phase of the transmitter current. Fig. 3 (c)shows the phasor diagrams at the adjustment, where, the phaseangle of It is defined as −π/2. Furthermore, in Fig. 3 (c), It, I1,
and I2 denote the effective values of It, I1, and I2, respectively.
As shown in Fig. 3 (c), in each receiver, the phase of theinduced voltage due to the cross-coupling is orthogonal to thephase of the receiver current, which means that the induced
voltage of the cross-coupling behaves as the reactance of thereceiver. The voltages of Xopt1 and Xopt2 operate to cancel the
induced voltages of the cross-coupling. At this condition, each
receiver receives only the effective power from the transmitterand does not receive the effective power from another receiver.
Therefore, the receivers only exchange reactive power. As aresult, the output power of each receiver is identical to (1).
Furthermore, from Fig. 3 (c), the appropriate reactances tocompensate for the influence of the cross-coupling can bederived as

Mt1

Ct

−jXopt1I1
I2

Cross-coupling

Mt2

r2
L2 C2

R2

Xopt2
Receiver 2−jXopt2I2(a)Receiver 1
rt

Ct

Lt

L1
I1

C1

r1

R1

Xopt1
ωMt1It −jωM12I2−jωMt1I1
It

L2−jωMt2I2
I2

C2−jXopt1I1
r2

R2

Xopt2

Receiver 2
ωMt2It −jωM12I1−jXopt2I2(b)

Receiver 1

Receiver 2ImIm
I1 ωMt1It

0

It
Xopt1I1I2 ωMt2It
0Re

ωM12I2It
Xopt2I2

ReωM12I1(Xopt1I1=ωM12I2 and X1= 0)(Xopt2I2=ωM12I1 and X2= 0)(c)Fig. 3.

Equivalent circuit with appropriate reactance for compensating
cross coupling. (a) Model based on coupling circuit. (b) Model
based on induced voltage. (c) Phasor diagram of two receivers.

compensation method. Then, we describe its operating
principle.
A. Circuit Configuration
As a method to adjust the phase of the receiver currents,
we apply the variable reactance element to each receiver.
Recently several techniques have been proposed to configure
the variable reactance element, such as a capacitor matrix [12–14], DC-voltage-controlled variable capacitor [15], gatecontrolled series capacitor [16], mechanical variable capacitor
controlled by the stepping motor [17], variable inductor [18,19], and simple switching circuit named automatic tuning
assist circuit (ATAC) [20–22]. Among these techniques, theATAC is more attractive than other variable reactanceelements for the compensation of the influence due to thecross-coupling. The ATAC can automatically adjust the phaseof the receiver current to the desired phase without detecting
the receiver current. Hence, in this paper, we propose anapplication of the ATAC to each receiver to compensates forthe influence of the cross-coupling.
The ATAC is originally proposed by [20] for a single
receiver SS topology of the RIC-WPT. The previous study[20] approached a problem where the resonant frequency of
the transmitter has the natural tolerance due to the
manufacturing tolerance by proposing the ATAC. Usually, thevariation in the resonant frequency of the transmitter is a
critical issue for the RIC-WPT system because it decreases thepower factor of the power source, which results in lowering
the output power and efficiency. The previous study [20]revealed that the transmitter with ATAC automaticallyachieves a unity power factor of the power source without
detecting the transmitter current even if there is the variationin the resonant frequency of the transmitter. On the other hand,in this paper, we reveal that the receiver with the ATAC can
automatically compensate for the influence of the crosscoupling.
Fig. 4 shows the multiple-receiver RIC-WPT system with
the ATACs. As shown in Fig. 4, the ATAC comprises the halfbridge circuit. The DC bus of the half-bridge circuit has only
the smoothing capacitor. Note that the DC bus of the halfbridge circuit does not have any additional voltage supply.
The smoothing capacitor does not contribute to the resonant
frequency of the receiver because the smoothing capacitor hasa sufficiently large capacitance than the resonant capacitor.
The half-bridge circuit of the ATAC operates at the same
operating frequency as the transmitter current. Therefore, inthe equivalent circuit, the ATAC can be described as the ACvoltage source, where VA1_dc and VA2_dc are the DC voltages ofthe smoothing capacitors, VA1 and VA2 are the output voltagesof the ATACs.
B. Operating Principle
To compensate for the influence of the cross-coupling, thehalf-bridge circuit of each ATAC has only to operate with thefixed phase difference shifted by π against the transmittercurrent. Hence, the ATAC does not require to detect the phaseof the receiver currents to adjust the phase of the receivercurrent to the desired phase. Fig. 5 shows the phasor diagrams
at this operation, where, the phase angle of It is defined as −π/2
as a reference. Furthermore, in Fig. 5, VA1 and VA2 denote theeffective values of VA1 and VA2, respectively. Fig. 6 shows the
key waveforms of Fig. 4 in the steady state. Ideally, the ATAC
does not have any resistive components because the ATAC
consists of only the half-bridge circuit and the smoothing
capacitor, which means that the ATAC does not receive theeffective power in the steady state. Therefore, in the steadystate, the phase of the receiver current must be orthogonal tothe phase of the output voltage of the ATAC. Hence, if we set
the phase of the output voltage of the ATAC in advance, thephase of the receiver current is automatically determined sothat the phase of the receiver current is orthogonal to the phaseof the output voltage of the ATAC. This means that the ATAC
inserts the reactance to the receiver and adjust the phase of thereceiver current to the target phase. Therefore, the amplitudeof the output voltage of the ATAC is automaticallydetermined according to the value of the reactance required
for the phase of the receiver current to adjust to the target
phase.
Then, based on the operating principle of the ATAC, we
derive the output powers and the output voltages of the
ATACs. According to Kirchhoff’s voltage law, based on Fig.
5, the operation of the receivers can be described as jVA1   M t1 It  j M12 I 2   r1  R1   jX 1  I1 , 
 jVA2   M t 2 It  j M12 I1   r2  R2   jX 2  I 2 .

Approximation
C1

L1

VA1

r1

VA1_dc
I1

VA1
rt

R1

Lt

Ct

ATAC 1
ωMt1It−jωMt1I1
It−jωM12I2−jωMt2I2
C2

L2

r2

VA2_dcApproximation

I2

VA2

R2

VA2
ATAC 2
ωMt2ItFig. 4.

Two-receiver RIC-WPT system with proposed compensation
method of cross coupling.

Receiver 1
Im

Receiver 2
Im

VA1

VA2

I1 ωMt1It
0It

I2 ωMt2It
0Re

ωM12I2
Fig. 5.

−jωM12I1

Re

It
ωM12I1

Phasor diagram of receivers in Fig. 4.

Voltage [V] or Current [A]It
tTransmitter

Orthogonal phase

I1 VA1t

Receiver 1I2 VA2Same phaset

Receiver 2

Fig. 6.

Key waveforms of Fig. 4 in zero-voltage-switching (ZVS)
operation.

From (3), the output power of each receiver can be obtained
respectively as2

2

  M t1 I t   M t 2 It 
P1  R1 
 , P2  R2 
 .
r

R
 1
1 
 r2  R2 The results of (4) and (1) are identical, which indicates that the
proposed compensation method achieves the decoupled
receiver. Then, the output voltages of the ATACs can beobtained respectively as

2
VA1   M t 2 M 12 I t  r2  R2    M t1 X 1 I t  r1  R1  , 

2
VA2   M t1 M 12 I t  r1  R1    M t 2 X 2 I t  r2  R2  .

The first terms on the right-hand side of (5) are the voltages tocompensate for the influence of the cross-coupling. On theWRX2 of receiver 2 (moved) R2

Voltage [V] or Current [A]It
tTransmitter

Position 8
I1t

Receiver 1
VA2
Receiver 2

Fig. 7.

Capacitive
operation

WRX1 of receiver 1 (fixed)

Capacitive
operation

WTX of transmitter (fixed)
Fig. 8.

IV. EXPERIMENTIn this section, we experiment to verify that the proposed
method is effective to compensate for the following two
influences:
1) Influence of the cross-coupling2) Influence of the variation in the resonant frequency of thereceiver

Variable DC
voltage source

InverterWaveforms of Fig. 4 in hard switching operation.

The loss of the ATACs should be suppressed as much as
possible for the high efficiency. Therefore, the half-bridge
circuit of the ATAC must avoid the hard-switching operation.
In other words, the half-bridge circuit of the ATAC must
maintain the zero-voltage-switching (ZVS) operation. To
achieve the ZVS operation, VA1 and VA2 must be positive when
the phase angle of It is defined as −π/2. In this case, the ZVS
operation is achieved because the relations between VA1 andI1 as well as VA2 and I2 are inductive, respectively. However,based on (5), VA1 and VA2 may be negative depending on thepolarities of Mt1, Mt2, and M12. The smoothing capacitor of the
ATAC cannot charge negative voltage owing to the body
diodes of the half-bridge circuit. Therefore, when VA1 and VA2of (5) fall below the zero, the ATAC operate as the shorted
circuit because the output power of the ATAC is zero. Even if
VA1 and VA2 of (5) fall below the zero, to obtain the positive
voltage in the smoothing capacitor of the ATAC, the ATAC
must operate so that the phase of the output voltage of the
ATAC is identical to the phase of the transmitter current asshown in Fig. 7. However, in this case, the relations between
VA1 and I1 as well as VA2 and I2 are capacitive. In the operationof Fig. 7, although the influence of the cross-coupling can becompensated, the half-bridge circuit of the ATAC cannot
avoid the hard-switching operation. Therefore, in some cases,
we must design X1 and X2 in advance so that VA1 and VA2 of (5)are positive under all values of the supposed mutual
inductances.

Load

ATAC

I2

Schematic of experimental setup.

0.3
Coupling coefficient

other hand, the second terms on the right-hand side of (5) are
the voltages to compensate for the influence due to the natural
tolerance of the resonant frequency in the receiver. Usually,
the self-inductance and the capacitance of the receiver havethe natural tolerance due to the manufacturing tolerance, thetemperature characteristic, and the aging deterioration (i.e.,
X1≠0, X2≠0). Therefore, to make consistent the resonant
frequency of each receiver with the operating frequency ispractically difficult. The natural tolerance of the resonant
frequency in the receiver decreases the output power as wellas the efficiency. The proposed compensation method can
automatically compensate not only the influence of the crosscoupling but also the influence of the natural tolerance in thereceivers.

Load

R1
RectifierPosition 1t

Rectifier

ATAC

……

VA1

k12 (Coupling coefficient
between WRX1 and WRX2)

0.25

kt2 (Coupling coefficient
between WTX and WRX2)

0.2
0.15
0.1
0.05
0
1

Fig. 9.

2

3

4
5
6
Position of WRX2

7

8

Coupling coefficient.

TABLE I.
CIRCUIT PARAMETERS FOR VERIFICATION OF
EFFECTIVENESS AGAINST CROSS-COUPLING
Symbols / Parameters

ValuesLt

Self-inductance of WTX

140.95 μH

L1

Self-inductance of WRX1

55.15 μH

L2

Self-inductance of WRX2

55.24 μHrt

Parasitic resistance of transmitter

0.24 Ω

r1

Parasitic resistance of receiver 1

0.13 Ω

r2

Parasitic resistance of receiver 2

0.13 Ω

Ct

Capacitance of transmitter

7.12 nF

C1

Capacitance of receiver 1

17.92 nF

C2

Capacitance of receiver 2

17.97 nF

kt1

Coupling coefficient between WTX and WRX2

0.11

It

Transmitter current

1.0 A
160.10 kHz

fs

Operating frequency

R1

Equivalent load resistance of receiver 1

4.56 Ω

R2

Equivalent load resistance of receiver 2

2.02 Ω

A. Verification of Effectiveness Against Cross-Coupling
Fig. 8 shows the schematic of the experimental setup of
the proposed system. In this paper, we refer to the system withthe proposed method as the proposed system. The AC currentsource of the transmitter is implemented by the voltage-fed
inverter and the variable DC voltage source. The positions of
WTX and WRX1 of the receiver 1 are fixed. Hence, Mt1 is aconstant value. On the other hand, to evaluate characteristics
dependence on the cross-coupling, WRX2 of the receiver 2 is
moved through eight different vertical positions. Hence, Mt2
and M12 are different depending on the position of WRX2,
respectively. In this subsection, we evaluate the output power,
the efficiency, and the voltages of the ATACs on the receivers
at each position of WRX2. Fig. 9 shows the coupling
coefficients according to the position of WRX2, where,
kt2=Mt2/(LtL2)1/2 and k12=M12/(L1L2)1/2. Other circuitOutput power P1 [W]25
20
Exp.: w/ cross-coupling (proposed)
Exp.: w/ cross-coupling (uncompensated)
Exp.: decoupled receiver (w/o proposed method)Cal.: decoupled receiver

15
10
5
0
1

3

4
5
Position of WRX2

parameters are summarized in Table I, where kt1=Mt1/(LtL1)1/2.
In the experiments of this subsection, the inductance and thecapacitance of the receivers are well-tuned to satisfy X1≈0 and
X2≈0 at the operating frequency. Furthermore, the coils arearranged so that the polarities of all mutual inductances are
positive.
Fig. 10 shows the photograph of the experimental setup of
the proposed system. In this paper, we generate the gating
signals for the ATACs and the inverter of the transmitter byusing a synchronized function generator (FG). Furthermore,
we use a common external power source as a power source forthe gate drive circuits for the ATACs and the inverter of thetransmitter. Certainly, the proposed method requires anadditional synchronization technique to drive the ATACs withthe phase difference of π from the transmitter current if we
apply the proposed method to practical multi-receiver RICWPT systems. However, the purpose of this paper is to show
the feasibility of the proposed method to compensate for the
influence of the cross-coupling. Therefore, thesynchronization technique is out of the scope of this paper.
The synchronization technique may be studied in future
papers.
Fig. 11 shows the output power of each receiver according
to the position of WRX2. In this paper, we refer to the system
which does not compensate for the influence of the crosscoupling as an uncompensated system. Hence, theuncompensated system does not have the proposed method.
When we measure the output power of the decoupled receiver,
we measure the output powers separately for each receiver,and the unmeasured side of the receiver is opened. As shownin Fig. 11 (a), in the proposed system, the output power of thereceiver 1 is almost constant regardless of the position of WRX2.
This result well corresponds to the experimental result of thedecoupled receiver. Furthermore, in the proposed system, theoutput power of the receiver 2 can obtain almost the same
power of the decoupled receiver. Fig. 12 shows theexperimental waveforms of the proposed system at position 4.
As shown in Fig. 12, the phase of each receiver current isorthogonal to the phase of the transmitter current. Hence, we
can compensate for the influence of the cross-coupling.
Meanwhile, in the uncompensated system, the output powerof receiver 1 significantly decreases as WRX2 is close to WRX1.
Furthermore, in the uncompensated system, the transition of
the output power in receiver 2 largely deviates from thetransition of the output power in the decoupled receiver. Fig.
13 shows the experimental waveforms of the uncompensatedsystem at position 4. As shown in Fig. 13, the phase of each
receiver current is not orthogonal to the phase of thetransmitter current. Therefore, the output power of each

6

7

8

(a)

Photograph of experimental setup.

25
Output power P2 [W]Fig. 10.

2

Exp.: w/ cross-coupling (proposed)
Exp.: w/ cross-coupling (uncompensated)
Exp.: decoupled receiver (w/o proposed method)Cal.: decoupled receiver

20
15
10
5
0
1

2

3

4
5
Position of WRX2

6

7

8

(b)
Fig. 11.

Experimental results of output power at each position of WRX2.
(a) Receiver 1. (b) Receiver 2.

It (500mA/div)

I1 (1A/div)
VA1 (10V/div)

I2 (1A/div)
2µs/div

Fig. 12.

Experimental waveforms of proposed system at position 4.

It (500mA/div)
I1 (1A/div)

I2 (1A/div)
2µs/div

Fig. 13.

Experimental waveforms of uncompensated system at position
4.

receiver suffers from the influence of the cross-coupling.
Certainly, in positions 5–8, the output power of receivers 2 ofthe uncompensated system are more significant than the
output powers of the decoupled receiver because the receiver
1 operates as a repeater [21] to relay the magnetic field to
WRX2 from WTX [2]. However, this is not practical for theVA1 (cal.)
VA1 (exp.)
VA2 (cal.)
VA2 (exp.)

35
30
25

Output power P1 [W]

20
15
10
5
0
1

4
5
Position of WRX2

6

7

8

15
10
5
0

w/ cross-coupling (proposed)
decoupled receiver (w/o proposed method)w/ cross-coupling (proposed)
decoupled receiver (w/o proposed method)

25

0.96

8
6

0.88

4

0.84

2

0.8

0
1

2

3

4
5
Position of WRX2

6

7

-10

10

0.92

Fig. 15.

20

Experimental results of output voltages of ATACs at eachposition of WRX2.

1

Efficiency

3

Power loss [W]Fig. 14.

2

Cal.: w/ cross-coupling (proposed)
Exp.: w/ cross-coupling (proposed)
Cal.: decoupled receiver (w/o proposed method)Exp.: decoupled receiver (w/o proposed method)25

Output power P2 [W]Output Voltage of ATAC [V]

40

-5
0
5
Variation in C1 from initial designed value [%](a)10Cal.: w/ cross-coupling (proposed)
Exp.: w/ cross-coupling (proposed)
Cal.: decoupled receiver (w/o proposed method)Exp.: decoupled receiver (w/o proposed method)

20
15
10
5

8
0
-10

Experimental results of Efficiency and power loss at eachposition of WRX2.
Fig. 16.

Then, Fig. 14 shows the output voltages of the ATACs
according to the position of WRX2. The ATACs automaticallyadjust the output voltage by itself so that the phase of each
receiver current is orthogonal to the phase of the transmittercurrent. The voltages of the ATACs increase as WRX2 is close
to WRX1 because the induced voltage due to the cross-coupling
to be compensated by the ATAC increases. The experimental
results are in relatively good agreement with the theoretical
calculation results.

30

Output Voltage of ATAC [V]10

Experimental results of output power against variation in C1 frominitial value of Table I. (a) Receiver 1. (b) Receiver 2.

multiple-receiver RIC-WPT system because the decoupled
receiver is not achieved.

Next, we evaluate the power loss from inserting the
ATACs. Fig. 15 shows the comparison results of theefficiency and power loss. The efficiency and the power loss
consider the power loss of the transmitter. In Fig. 15, we
define the input/output power of the decoupled receiversystem as the sum of the powers measured separately for each
receiver. From Fig. 15 and Fig. 14, the additional power loss
from inserting the ATACs tends to be large as the output
voltages of the ATACs increase. Hence, the additional power
loss from inserting the ATACs is assumed to be mainly causedby the switching loss of the ATACs. However, owing to the
ZVS operations of the ATACs, the additional power loss from
inserting the ATACs is at most a few watts. Therefore, theproposed system can compensate for the influence of thecross-coupling with only a slight loss. From the above results,
the effectiveness of the proposed method against the influenceof the cross-coupling can be verified.

-50
5Variation in C1 from initial designed value [%]
(b)

25
20
15
VA1 (cal.)
VA1 (exp.)
VA2 (cal.)
VA2 (exp.)

10
5
0
-10

Fig. 17.

-50
5Variation in C1 from initial designed value [%]10

Experimental results of output voltages of ATACs against
variation in C1 from initial value of Table I.

B. Verification of Effectiveness Against Variation in
Resonant Frequency of Receiver
Finally, we show that the proposed method can suppress
the lowering the output power due to the variation in theresonant frequency of the receiver. In the experiments for thissubsection, the receiver 2 is fixed to the position 3. The othercircuit parameters are the same as the values of Table I. In thissubsection, we evaluate the characteristics when the resonant
frequency of the receiver 1 changes. The variation in theresonant frequency of the receiver 1 is achieved by changing
C1 from the initial designed value of Table I by ±10%.
Fig. 16 and Fig. 17 show the results of the output power
and the output voltages of the ATACs against the variation inC1 from initial designed value, respectively. In the decoupled
receiver system, the output power of receiver 1 decreases as
C1 deviates from the initial designed value because residual
reactance of X1 restricts the current flow in the receiver 1. On
the other hand, in the proposed method, the output power ofthe receiver 1 is almost constant regardless of the variation in
C1. As shown in Fig. 17, the ATAC on the receiver 1
automatically adjust the output voltage to compensate for thevoltage of the residual reactance due to the variation in C1. The
output voltage of the ATAC on the receiver 2 does not dependon the variation in C1 because the current in the receiver 1 isconstant owing to the operation of the ATAC on the receiver
1. From the above results, it is verified that the proposed
method can also compensate for the influence of the variationin the resonant frequency of the receiver.
V. CONCLUSION
The decoupled receiver is usually required to realize thepractical multiple-receiver RIC-WPT systems. However, torealize the decoupled receiver is practically difficult due to thecross-coupling. Hence, in this paper, we first showed that the
influence of the cross-coupling can be compensated fully
when the phase of the current in each receiver is orthogonal tothe phase of the transmitter current. Then, we proposed thereceiver with the ATAC to adjust the phase of the current ineach receiver to the desired phase. The proposed method canfully compensate for the influence of the cross-coupling byonly driving the ATAC with the fixed phase difference of π tothe transmitter current. Furthermore, the proposed method
also can compensate for the influence of the detuning of theresonant frequency of the receiver due to the natural tolerance.
Certainly, when we apply the proposed method to the practicalmulti-receiver RIC-WPT systems, the ATACs require an
additional synchronization technique to synchronize the phaseof each receiver current to the transmitter current. However,the proposed method does not need the complicatedestimations of the disposition of the receivers and the output
power of other receivers. Furthermore, the proposed method
does not need to detect the phase of the receiver currents tocompensate for the influence of the cross-coupling. The
effectiveness of the proposed method is successfully verified
by the experiments of the two-receiver RIC-WPT system. The
experimental results suggest that the proposed method is
promising to realize the decoupled receiver for the practicalmulti-receiver RIC-WPT systems.
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