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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 62, NO. 4, APRIL 2015

Wireless Power Transfer With Zero-Phase-Difference
Capacitance Control
Shunta Iguchi, Student Member, IEEE, Pyungwoo Yeon, Student Member, IEEE, Hiroshi Fuketa, Member, IEEE,
Koichi Ishida, Member, IEEE, Takayasu Sakurai, Fellow, IEEE, and Makoto Takamiya, Senior Member, IEEE

Abstract—Wireless power transfer enables the frequent andubiquitous charging of electronic devices. However, the variationof the efﬁciency and the received power with the transmission
distance is an outstanding issue. To solve the problem of efﬁciency degradation of the magnetic resonance at short distances,zero-phase-difference capacitance control (ZPDCC), which issuitable for integration in large scale integrations (LSIs) is proposed in this paper. The proposed ZPDCC achieves adaptive
capacitance control by a newly proposed control algorithm witha current-sensing circuit to control variable capacitors at a ﬁxed
frequency. Additionally, a theoretical analysis of the total DC-DC
including a power ampower transmission efﬁciency
pliﬁer, coupled resonators, and a rectiﬁer is demonstrated in thispaper. The analysis indicates that the frequency (and capacitance)
is mainly due to the power ampliﬁer; addisplitting oftionally, the efﬁciency of the power ampliﬁer is maximized at theis short. A wirelesssplit peaks when the transmission distancepower transfer system in magnetic resonance with ZPDCC isfabricated in a 3.3 V, 180 nm CMOS. By introducing ZPDCC, theat 13.56 MHz increases 1.7 times from 16% tomeasured
27% at.
Index Terms—Magnetic resonance, power ampliﬁer, wirelesspower transmission, zero-phase-difference capacitance control.

I. INTRODUCTIONW

IRELESS power transfer has opened a new era of power
distribution without messy wire connections and the inconvenience of charging batteries. Wireless power transfer enables the frequent and ubiquitous charging of electronic devices(e.g., cell phones). However, the transmission efﬁciency is degraded by radiation loss and the resistive loss of antennas; additionally, the variation of the efﬁciency and the received powerwith the transmission distance is also an outstanding issue.
As ﬁrst proposed in 2007 [1], magnetic resonance has thepotential to realize more efﬁcient and stable wireless charging
at intermediate distances (1 cm–10 m) than a conventional
microwave beam [2] and magnetic induction [3]. Wirelesspower transmission systems with magnetic resonance consistof a power ampliﬁer, coupled resonators, and a rectiﬁer. The
total DC-DC power transmission efﬁciency
at theof the resonators is maxiinherent resonant frequency
mized at a certain distance, while
is reduced at short
Manuscript received August 31, 2014; revised December 11, 2014; accepted
December 23, 2014. Date of current version March 27, 2015. This work was
supported in part by Renesas Electronics Corporation. This paper was recommended by Associate Editor R. Gomez-Garcia.
S. Iguchi, H. Fuketa, T. Sakurai, and M. Takamiya are with the University ofTokyo, Tokyo 153-8505, Japan (e-mail: shiguchi@iis.u-tokyo.ac.jp).
P. Yeon was with the University of Tokyo, Tokyo 153-8505, Japan. He is now
with Georgia Institute of Technology, Atlanta, GA 30308 USA.
K. Ishida was with the University of Tokyo, Tokyo 153-8505, Japan. He is
now with Technische Universität Dresden, Dresden 01069, Germany.
Color versions of one or more of the ﬁgures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identiﬁer 10.1109/TCSI.2015.2388832

distances (e.g., 1 cm). This efﬁciency degradation at shortdistances is a unique phenomenon of magnetic resonance andis not observed in conventional magnetic induction.
To address this issue, several techniques [4]–[20] andtheoretical studies [21]–[23] have been reported. Frequency
tracking [4]–[9] controls the transmission frequency corresponding to the transmission distance, although frequency
deviation is not allowed in many radio bands (e.g., the ISM
band [24]). A repeater coil array [10], [11] has a misalignment-tolerant design without frequency deviation; however,the number of transmission coils has to be increased to covera large misalignment. This increases the size and cost of thetransmitter. Supply voltage
control [12], [13] controls
the output power of a power ampliﬁer to regulate the received
power, althoughis greatly reduced by the loss of the
DC-DC converter. To address this degradation of efﬁciency,
adaptive impedance matching [14]–[18] has been introduced.
The optimum load impedance of a power ampliﬁer has beenrealized using variable capacitors [15]–[18], while in several
studies, a bulky and expensive directional coupler [14], [15]and impedance analyzer [16], [17] were required as detectors.
A theoretical analysis ofincluding a power ampliﬁer, coupled resonators, and a rectiﬁer is newly demonstrated inthis paper. The results indicate that the frequency (and capacitance) splitting ofis mainly due to the power ampliﬁer
and that the efﬁciency at short distances is maximized at the split
peaks. This veriﬁes the effect of zero-phase-difference capacitance control (ZPDCC) [19]. The proposed ZPDCC is suitablefor integration in large scale integrations (LSIs) to reduce efﬁciency degradation of the magnetic resonance at short distances.
The proposed ZPDCC achieves adaptive capacitance control bya newly proposed control algorithm with a current-sensing circuit to control variable capacitors at a ﬁxed frequency.
An outline of this paper is given as follows. In Section II, atheoretical analysis of the efﬁciency degradation of the magnetic
resonance at short distances is given. In Section III, a methodthat increases
at short distances without frequency deviation and the need for a bulky detector circuit is proposed. In
Section IV, the measured results for a wireless power transfer
circuit with ZPDCC are reported. In Section V, conclusions are
given.
II. ANALYSIS OF EFFICIENCY OF MAGNETIC RESONANCE
In this section, a theoretical analysis of the efﬁciency degradation of the magnetic resonance at short distances is given, inparticular, the frequency dependence of the efﬁciency of couand a power ampliﬁer
is clariﬁed
pled resonators
by theoretical calculations and simulations. These calculations
and simulations indicate that frequency splitting is not observed

1549-8328 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

IGUCHI et al.: WIRELESS POWER TRANSFER WITH ZERO-PHASE-DIFFERENCE CAPACITANCE CONTROL

939

inwith asymmetric port impedances, while it is observedin. Several studies [4], [7], [15], [16] have investigated theincrease in the efﬁciency between coupled resonators with port
impedances of 50 . The efﬁciency is calculated frommeasured by a vector network analyzer. However, these studies
gave limited conclusions because not only coupled resonators
but also a power ampliﬁer made a large contribution to.
This study includes a new theoretical analysis ofand.
frequency splitting while taking into account the effect ofIn this section, the frequency dependence ofwith apower ampliﬁer, coupled resonators, and a rectiﬁer is theoretically analyzed to clarify the effect of a power ampliﬁer.
A. Transmission Efficiency Between Coupled Resonators
To analyze the efﬁciency degradation at short distances anddiscuss the frequency splitting in the case of asymmetric port
impedances, the frequency dependence ofis ﬁrst analyzed. Figs. 1(a) and (b) show a schematic of a wireless powertransfer system and the equivalent circuit in magnetic resonancewith a power ampliﬁer, coupled resonators, and a rectiﬁer, respectively.
is the supply voltage of the power ampliﬁer,
is the inductor in each resonator,
is the capacitor
in each resonator,
is the load capacitor at the output of therectiﬁer,
is a load resistor at the output of the rectiﬁer,
is the coupling coefﬁcient of the coupled resonators,isthe equivalent series resistor of theis the mutual inductor corresponding tois the output voltage of theis the output current of the power amplipower ampliﬁer,
ﬁer,
is the input resistor of the rectiﬁer, andis the input impedance of the coupled resonators. Additionally,
the input power to the power ampliﬁer, the output power of thepower ampliﬁer, the input power to the rectiﬁer, and the load
power are denoted as , , , and , respectively. Then,the efﬁciency of the power ampliﬁer, coupled resonators, andrectiﬁer, and the total DC-DC power transmission are respectively deﬁned as
(1)
(2)
(3)
(4)

Fig. 1. Schematic of a wireless power transfer system. (a) Block diagram ofsystem with a power ampliﬁer, coupled resonators, and a rectiﬁer. (b) Equivalentcircuit.

In previous studies [4], [7], [10], [14]–[17], [23] with a port
impedance of 50 ,was deﬁned by. Integrated
wireless power transfer systems are implemented using a
digital power ampliﬁer (e.g., class-D [8], [9], [19] or class-E. The[12], [13], [18], [20]) to maximize
andoutput impedance corresponding to the on-resistance of apower transistor is lower than 50 ; additionally, the input.
impedance of a rectiﬁer varies with the load resistance
Therefore, the port impedances of the coupled resonators are
not symmetric. A previous theoretical study [21] showed thatthe frequency splitting ofis not observed in the case ofasymmetric port impedances, while it is observed in the caseof symmetric port impedances. This conclusion was obtained
as shown in [21]. To
by differential calculations ofsupport the discussions ofin the next section, a discussion
and ﬁndings regarding
in the case of asymmetric port
impedances are given in this section.
It is ﬁrst assumed that the coupled resonators of the transmitter and receiver are conﬁgured by the same components andthat the output impedance of the power ampliﬁer is negligible,
compared with the input impedance of the rectiﬁer. Then,in Fig. 1(b) is given by (5), where the is the Q factor of theis the reso, is the angular carrier frequency, andnant angular frequency of theand. By differentiating (5) with respect to , the angular frequency
athas a maximum value
the maximum
is given by (6).
at, and which means thatin the case of asymmetricport impedances does not show frequency splitting. Under the, the maximum
is given
condition

(5)
(6)
(7)

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 62, NO. 4, APRIL 2015

Fig. 3.
dependences of (a)and (b)for a power ampliﬁer obtainedby load pull simulation at 13.56 MHz. Blue dots show the impedances offor, 0.2, and 0.5 with coupled resonators and a rectiﬁer.

Fig. 2. Simulated frequency dependences offor, 0.2, and 0.5
with the parameters in Table I. The simulations include a power ampliﬁer, coupled resonators, and a rectiﬁer as shown in Fig. 1(a). The simulated frequency
do not show frequency splitting even with the nonlindependences of
earity induced by the power ampliﬁer and rectiﬁer.

increase whenis decreased and. However,increases proportionally to ; therefore,
anddecrease with increasing .
To clarify the frequency dependence of the, the frequency dependence ofis theoretically analyzed from theequivalent circuit in Fig. 1(b).
First,
is given by

TABLE IPARAMETERS IN SIMULATIONS

by (7) (see equations at bottom of next page).
is amonotonically increasing function of because the derivative of(7) with respect to is positive for all excluding. Theseresults indicate that
increases inversely proportionally tothe transmission distance without frequency splitting when theport impedances are asymmetric.
Fig. 2 and Table I show the simulated frequency dependencesofand the parameters used in the simulations, respectively. The parameters in Table I are determined to achieve
at a transmission distance and carrier frequencyof 30 mm and 13.56 MHz, respectively. The frequency dependences ofin Fig. 2 were simulated by SPICE simulation [25] including a power ampliﬁer, coupled resonators, anda rectiﬁer as shown in Fig. 1(a). The simulated result for
demonstrates thatis maximized atand increases
with . This result is consistent with the conclusion that
increases inversely proportionally to the transmission distancewithout frequency splitting. It should be noted thatisapproximately equal towhen
is small (e.g., lessinthan 100 under the conditions in Table I), whilecreases whenis large. In this study, the deviation ofis negligible because
is small.

assuming thatfor conciseness. Then,are respectively given by

(8)
and
(9)

(10)
is maximized at
Equation (9) shows that
increases proportionally to . This dependence ofalso veriﬁed in Fig. 3.
To increase
and, the condition
be satisﬁed. When
, is given by

andisshould

(11)
(12)

(13)
B. Frequency Dependence ofThe efﬁciency of the power ampliﬁer is of fundamental importance in a wireless power transfer system because the frequency splitting ofis attributed to. Figs. 3(a) and(b) show thedependences of the output powerandof a power ampliﬁer obtained by a load
drain efﬁciency
pull simulation, respectively.
andare fundamentally determined by. The simulated results show that
and

where
,
, and
are a low value of , anintermediate value of corresponding to , and a high value, respectively. Equations (11) and (13)of withare only valid when satisﬁes(14)

IGUCHI et al.: WIRELESS POWER TRANSFER WITH ZERO-PHASE-DIFFERENCE CAPACITANCE CONTROL

Fig. 4. Simulated frequency dependences of phase between
andfor, 0.2, and 0.5 with the parameters in Table I. The simulation includes,
a power ampliﬁer, coupled resonators, and a rectiﬁer. Black dots show
, andgiven by (11)–(13) for.
andare deﬁned
as shown in Fig. 1(b) and are equivalent to the output voltage and output currentof the power ampliﬁer, respectively. The phase is deﬁned as the delay ofrelative toat ; atandare equivalent because thecorresponds approximately to that of .
frequency dependence ofThis means that there are three solutions (,, and) satisfying
when thetransmission distance is short, while there is only one solution
when the transmission distance is long.
Fig. 4 shows the simulated frequency dependences of thephasebetween the input voltage
and input current
to the coupled resonators in Fig. 1(b). The simulated freonly atquency dependences of demonstrate thatwhenand 0.2, while
at
,
, and
when
. This veriﬁes theresults of analysis using (11)–(14).
To increaseand, a smallerwithshouldbe used when the transmission distance is short. The expressions
for
at
,
, and
are given by
(15)
(16)
Then, the relationships among, andare given by

at

,

(17)
Equation (17) indicates that
and
at
and
are larger than those atbecauseatandis smaller than that at
when the transmission distance is short. It should be noted that
andatare higher than those atbecause the power dissipation induced by switching loss anddue to the skin effect increase in proportion to the frequency.
Fig. 5 shows the simulated frequency dependences of.
When
and 0.2,
is maximized at,
is maximized at
and
when
while

941

Fig. 5. Simulated frequency dependences offor, 0.2, and 0.5
with the parameters in Table I. The simulation includes a power ampliﬁer, cou,
, andpled resonators, and a rectiﬁer. Black dots show
given by eqs. (11)–(13) for.

Fig. 6. Simulated frequency dependences offor, 0.2, and 0.5
with the parameters in Table I. The simulation includes a power ampliﬁer, coupled resonators, and a rectiﬁer. Black dots show for the maximum
at each .

. with the maximum
at each distance in Fig. 5
corresponds to the points satisfying
atinFig. 4. This means that should be controlled under the conat
depending on the transmission
ditiondistance in order to maximize. Using this modiﬁed ,is maximized even with the frequency splitting ofwhen thetransmission distance is short.
C. Frequency Dependences ofandincreases proportionally towhich corresponds
to the output power of the power ampliﬁer; therefore, thefrequency dependences ofcorrespond approximately to.
that ofFig. 6 shows the simulated frequency dependences of. Sinceis the product of
,
, and
,
also exhibits frequency splitting when thetransmission distance is short. The maximum efﬁciency isachieved atwhen
and 0.2, while
is maximized at
when
.

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 62, NO. 4, APRIL 2015

III. ZERO-PHASE-DIFFERENCE CAPACITANCE CONTROLThe origin of the frequency splitting ofin a wireless power transfer system was explained in the previous section. However, adaptive frequency control (at) is not permitted in many radio bands. In this study,
is moved fromto a ﬁxed
the lower peak oftarget frequency
by changing
in order to increaseat short distances for the ﬁxed
frequency of 13.56 MHz. Conventional studies [15]–[18] on
capacitance control require bulky and expensive detectors because these algorithms for capacitance control must detect[15] or[16], [17]. On the other hand, the proposed algorithm of zero-phase-difference capacitance control (ZPDCC)
only requires the phasebetweenandfor the coupledresonators in Fig. 1(b). This means that the proposed ZPDCC
achieves efﬁcient implementation in a small space using a current monitor, which is easily implemented into integrated circuits.
The duality between the capacitance dependence and the frequency dependence is given by substituting(18)
in (8)–(17). In particular, capacitance splitting correspondingtoat a ﬁxed frequency
isobserved at

(19)
(20)

(21)
Fig. 7 shows simulated capacitance dependences of the phasebetweenandfor the coupled resonators in Fig.
is maximized at1(b). Similarly to the previous section,andwith capacitance splitting when thetransmission distance is short, while it is maximized at
at longer distances. In ZPDCC, the appropriate
is searched for under the conditionat. Thiscondition determines whether the transmission distance is shortor long.
Fig. 8 shows a ﬂow chart of the proposed algorithm for
ZPDCC. To compensate for the offset of caused by parasitic
capacitances and the delay of the current monitor, this algorithm requires calibrations of the capacitance before and after
shipment. Details of the proposed algorithm are given below.
A) Calibrations before shipment
1) To compensate for parasitic capacitance and inductance on the PCB and mismatches in fabrication, thecorresponding to the maximum
issearched for by the hill climbing method when thetransmission distance is sufﬁciently long.
2) The obtainedis assigned as the initial valueof.
results in the maximum
atwhen the capacitance splitting
is not observed.
ofFig. 7. Simulated capacitance dependences of phase between
and
at
for
, 0.2, and 0.5 with the parameters in. The simulation includes a power ampliﬁer, coupled
Table I excluding,, andresonators, and a rectiﬁer. Black dots show
given by (19)–(21) for.

B) Calibrations after shipment
3) is measured at the calibrated
and the mea. In
sured is assigned as the initial value ofthe proposed ZPDCC, the difference between andis used to discriminate whether the transmission
distance is short or large. In ZPDCC, the lower peakis searched for because fewer capacitor banks are required than for a search for the higher peak. Therefore, the capacitance is ﬁnally reduced from i to i-1.
4) is measured at the reduced
corresponding to
i-1 and the measured is compared with.
, the con5) When the measured is smaller thanditionat
is satisﬁed in ZPDCC
without capacitance splitting. This means that thetransmission distance is large and thatshould be used as the modiﬁed.
6) When the measured is larger than
, the transmission distance is short and capacitance splitting isobserved. Therefore,should be searched
for and set to. In this process, is repeatedly
untilmeasured and compared while reducing
the conditionis satisﬁed.
7) When the measured is equal to,cor; therefore,
is assigned toresponds to.
8) When the measured is less than
, the resolutionof the capacitor bank is larger than the resolution of
the phase detector. To prevent the over tune of,is assigned to.
Fig. 9 shows simulated capacitance dependences offor, 0.2, and 0.5. Capacitance splitting is only observed. Using the proposed ZPDCC,
is determinedforso that the maximum
is achieved, which depends on
the transmission distance. When
and
,
only
, then, using the proposed ZPDCC, it is found thatatas shown in Fig. 8 (case5). On the other hand,
at
,
, and
when
, then, using the proposed ZPDCC, it is foundIGUCHI et al.: WIRELESS POWER TRANSFER WITH ZERO-PHASE-DIFFERENCE CAPACITANCE CONTROL

Fig. 8. Flow chart of algorithm of ZPDCC.
denotesmodiﬁedis digitally controlled.
by ZPDCC. In this algorithm, it is assumed thatis given by the integer value i.
The digital code ofFig. 9. Simulated capacitance dependences offor, 0.2, and. The simulation includes a
0.5 with the parameters in Table I excluding
power ampliﬁer, coupled resonators, and a rectiﬁer. Black dots showcorresponding to the maximum
for each , which is determined by
ZPDCC.

that
modiﬁedshown in Fig. 9.

as shown in Fig. 8 (case 7 or 8). The
gives the maximum
for each as

IV. MEASUREMENT RESULTS AND DISCUSSION
To demonstrate the improvement of
upon using the
proposed ZPDCC, a wireless power transfer system in magnetic
resonance with the ZPDCC is implemented. Fig. 10 shows a circuit schematic of the wireless power transfer system in magnetic
resonance with the ZPDCC. The class-D PA in the transmitterand the rectiﬁer in the receiver are designed and fabricated in a
3.3 V, 180 nm CMOS process. The
are fabricated on anis the same as that in [10].
FR4 PCB and the layout of the
The capacitors on the PCB are implemented by ceramic capacitors.
In the circuit implementation of ZPDCC, is measured as
the phase difference between the voltage
and current
in the transmitter. is converted to a voltage by a non-inverting
ampliﬁer, which is implemented using an operational ampliﬁer

943

Fig. 10. Circuit schematic of wireless power transfer system in magnetic resonance with ZPDCC. All the simulation results in this paper are shown on thisschematic.

(OPA847ID [26]) and two resistors. The gain of the ampliﬁer is
set to. In the measurement, theand is measured by an oscilphase difference between
loscope, and the capacitance is changed by manually replacing
the ceramic capacitors with a minimum resolution of 0.5 pF.
The capacitance is tuned in accordance with the ﬂow chart in
Fig. 8.
To achieve automated control, the implementation of a phasedetector, capacitance controller, and communication link between the transmitter and receiver is required for the integration of LSIs. First, the phase detector could be implemented
in the LSIs using a time-to-digital converter (TDC) with a resolution of 20 ps (at 13.56 MHz) and 290 pJ/conversion-step [27]. The digitized phase data from the TDC is input
to the capacitance controller (= state machine corresponding to
the algorithm of ZPDCC), and the capacitance controller controls the 7-bit binary capacitor bank. The capacitor bank could
be tuned by relays [15], [28] in the range of 15–45 pF on thetransmitter and 30–90 pF on the receiver with a minimum resolution of 0.5 pF. In high-power applications, the on-resistanceof the switches reduces
if
is not scaled in accordance with the transmission power. The large current ﬂow in theswitches consumes a huge amount of power. On the other hand,the power consumption in the switches is not increased if
is increased using high-voltage technologies (e.g., LDMOS and
IGBT) depending on the transmission power. Such high-voltage
technologies would realize highly efﬁcient implementation withcapacitance control even in high-power applications. Additionally, the on-resistance of the switches ([28]) is smaller. This implies that the loss due to the on-rethansistance is not dominant in the whole system. Finally, the communication link between the transmitter and receiver could be
implemented by backscattering [29], [30]. Wireless communication at 6.78 Mbps [30] without any extra antennas has been reported. The capacitor bank on the receiver is controlled in accordance with the received data. This whole system, which includes
a current monitor, phase detector, capacitance controller, andcommunication link, is easily implemented into integrated circuits. Compared with conventional capacitance control methods

944IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 62, NO. 4, APRIL 2015

Fig. 11. Photographs of transmitter and receiver on PCB, LSIs of PA and rectiﬁer, and measurement equipment.
,

TABLE II
, AND Q FACTOR OF
OBTAINED BY EM SIMULATION AND
MEASUREMENT

using a directional coupler [15] and a vector network analyzer[16], [17], ZPDCC is more suitable for the integration in LSIs.
Fig. 11 shows photographs of the transmitter and receiver inthe wireless power transfer system in magnetic resonance. The
LSIs of the PA and rectiﬁer, and the measurement equipment
are also shown in Fig. 11. The size of thefabricated on
the PCB in the transmitter and receiver is 40 mm 40 mm. The
andcore sizes of the PA and rectiﬁer are, respectively.
Table II shows a comparison of,, and the Q factor
obtained by EM simulation and measurement atof the13.56 MHz. The measurement results are in good agreementwith the values in Table I. This means that the simulated results
in previous sections and the measurement results are consistent.
Fig. 12 shows a comparison offor coupled resonators
at transmission distancesof 5 mm, 15 mm, and 25 mm obtained by EM simulation and measurement. The measurement
results are consistent with the simulated results and frequency
splitting at
is observed.
Fig. 13 shows the simulated transmission distance dependence of the coupling coefﬁcientat 13.56 MHz. This resultshows that the parameters (and) used in pre, 15 mm,
vious sections approximately correspond toand 25 mm, respectively.
Fig. 14 shows the measured frequency dependences ofat, 15 mm, and 25 mm. Whenand 25 mm, the frequency dependences of
do notexhibit frequency splitting; therefore,
is maximized at
13.56 MHz. In contrast, the frequency dependence ofatexhibits frequency splitting.
at
is maximized at the lower peak corresponding to.
Fig. 15 shows the measured capacitance dependences ofat 13.56 MHz when
, 15 mm, and 25 mm. Whenand 25 mm,
once, which corresponds towith the maximum. In contrast,

Fig. 12. EM-simulated and measured frequency dependences ofin couof 5 mm, 15 mm, and 25 mm.
pled resonators at transmission distancesFig. 13. Simulated transmission distance dependence of coupling coefﬁcientat 13.56 MHz.

Fig. 14. Measured frequency dependences ofwhen, 15 mm, and 25 mm.

when
,
at
and
modiﬁed fromtoproposed ZPDCC with the condition

at

.
at

is
by theIGUCHI et al.: WIRELESS POWER TRANSFER WITH ZERO-PHASE-DIFFERENCE CAPACITANCE CONTROL

Fig. 15. Measured capacitance dependences of at 13.56 MHz when
, 15 mm, and 25 mm. is measured by an oscilloscope.

when the transmission distance is short. The relay
switches should have an operation time of 1 ms [28] to 5 ms [15]and be the slowest block in the automated ZPDCC. The maximum iteration step is determined at the minimum transmission
distance. At the minimum distance of 2.5 mm, the capacitor is
tuned from 37 pF to 20 pF with a minimum step of 0.5 pF. This
corresponds to 35 steps and a settling time of less than 200 ms.
Fig. 16 shows the measured capacitance dependences ofat 13.56 MHz when
, 15 mm, and 25
mm. Whenand 25 mm,
is maximized atof 37 pF. In contrast,atis maxiof 25 pF. Using the proposed ZPDCC,
mized atis increased from 25% to 34% with the capacitance control of
from
to
. The
at
is also increased frommeasured load power
4.8 mW to 8.4 mW. The maximumof 56 mW is achievedat. On the other hand, the measured
atis lower than the simulated
owing tothe coarse minimum resolution ofand themismatches ofbetween the transmitter and receiver.
at short distances will be increased if the ﬁne minimum resolution ofand a calibration method between
the transmitter and receiver are realized.
Fig. 17 shows the measured transmission distancedependence ofat 13.56 MHz. The conventional constantcapacitance method and the proposed ZPDCC are compared.
When is longer than 10 mm, ZPDCC does not modify
from. Therefore,
for the proposed ZPDCC
and the conventional constant capacitance method would
be equivalent under ideal conditions. In the measurement,
however,for ZPDCC is 1–7% lower than that forthe conventional constant capacitance method because of theresistive loss of 0.1 for the current monitor shown in Fig. 10.
In contrast, when is less than 10 mm,
for ZPDCC
is higher than that for the conventional constant capacitancemethod, which indicates that the increase incaused by
ZPDCC exceeds the decrease incaused by the resistive
loss. For example,
increases 1.7-times from 16% toupon tuningfrom 37 pF to 20 pF. In
27% atZPDCC, the maximum
is 49% at.

945

Fig. 16. Measured capacitance dependences of, 15 mm, and 25 mm.

at 13.56 MHz when

Fig. 17. Measured distance dependences ofusing conventional constant capacitance method and proposed ZPDCC at 13.56 MHz.

Table III shows a comparison with the results for previously
reported wireless power transfer systems at a ﬁxed frequency.
At a ﬁxed frequency, only
control [13] and impedance
matching [15] target the efﬁciency degradation. This work is
the ﬁrst report of capacitance control including a power ampliﬁer and a rectiﬁer; additionally, the directional coupler used in
the previous impedance-matching method is not required. The
control method does not include the loss of the DC-DC
converter. The efﬁciency of the corresponding state-of-the-art
DC-DC converter is 60–85% in the voltage range 0.6–2.5 V[31]. This implies that the efﬁciency of the previous
controlmethod is greatly reduced by the low efﬁciency of the DC-DC
converter.
V. CONCLUSION
In this paper, zero-phase-difference capacitance control(ZPDCC), which is suitable for integration in LSIs was proposed to solve the problem of efﬁciency degradation of themagnetic resonance at short distances. The proposed ZPDCC
achieves adaptive capacitance control by a newly proposed
control algorithm in whichatwith acurrent-sensing circuit to control variable capacitors at a ﬁxed

946IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 62, NO. 4, APRIL 2015

TABLE IIICOMPARISON WITH RESULTS FOR PREVIOUSLY REPORTED WIRELESS POWER TRANSFER SYSTEMS AT FIXED FREQUENCY†DC-DC converter is not included. ‡PA and rectiﬁer are not included.

frequency. Additionally, a theoretical analysis ofincluding a power ampliﬁer, coupled resonators, and a rectiﬁer
was demonstrated in this paper. A wireless power transfer
system in magnetic resonance with ZPDCC is fabricated in a
3.3 V, 180 nm CMOS. By introducing ZPDCC, the measured
at anof 13.56 MHz increases 1.7-times from
16% to 27% at.
ACKNOWLEDGMENT
The authors thank Masayuki Mizuno, Koichi Yamaguchi,
Haruya Ishizaki, Hideki Sasaki, Tatsuaki Tsukuda, Hiroki
Sugimoto, Yuji Shinohara, and Tomotoshi Nureki of Renesas
Electronics Corporation for encouragement and discussions.
The VLSI chips in this study were fabricated as part of thechip fabrication program of VLSI Design and Education Center(VDEC), the University of Tokyo, in collaboration with Rohm
Corporation and Toppan Printing Corporation.
The author Shunta Iguchi is supported by Japan Society for
the Promotion of Science through the Program for Leading
Graduate Schools (MERIT).
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Shunta Iguchi (S'12) received the B.S. degree
in electronic engineering from the University ofElectro-Communications, Tokyo, Japan, in 2011
and the M.S. degree in electrical engineering andinformation systems, from the University of Tokyo,
Tokyo, in 2013, where he is currently pursuing a
Ph.D. degree. His research interests include thedesign of low-power RF transceiver circuits, crystal
oscillators, and wireless power transmission circuits.
From August 2011 to September 2011, he worked
at Analog Devices, Tokyo. From August 2013 to
September 2013, he worked at Toshiba, Kawasaki, Japan. From August 2014
to October 2014, he worked at TSMC, Hsinchu, Taiwan. All of his industrial
experience was as an intern. He is a recipient of the best paper award at the2013 IEEE Wireless Power Transfer Conference.

Pyungwoo Yeon (S'14) received the B.Sc. degree
in electrical and computer engineering from Seoul
National University, Seoul, Korea, in 2010, and the
M.S. degree in electrical engineering and information systems from the University of Tokyo, Tokyo,
Japan, in 2012. He is now pursuing his doctoral
degree in the electrical and computer engineering at
Georgia Institute of Technology, Atlanta, GA, USA,and working on developing wirelessly powered
implantable biomedical system at the GT-Bionics
Lab.
From February 2012 to May 2014, he worked as an analog IC designer at
Samsung Electronics, Yongin, Korea, designing wireless power receiver IC formobile devices. His research interests include analog/mixed-signal integrated
circuit design, wireless power/data transfer, energy harvesting, and biomedical/
implantable system design.

Hiroshi Fuketa (S'07–M'10) received the B.E. degree from Kyoto University, Kyoto, Japan, and the
M.E. and Ph.D. degrees in information systems engineering from Osaka University, Osaka, Japan, in
2002, 2008 and 2010, respectively.
Currently, he is a Research Associate with Institute of Industrial Science, the University of Tokyo,
Tokyo, Japan. His research interests include ultra-low
power circuit design and large area electronics withorganic transistors. Dr. Fuketa is a member of IEICE.

947

Koichi Ishida (S'00–M'06) received the B.S. degree
in electronics engineering from the University ofElectro-Communications, Tokyo, Japan, in 1998,
and received the M.S. and Ph.D. degrees in electronics engineering from the University of Tokyo,
Tokyo, in 2002 and 2005, respectively.
He joined Nippon Avionics Co., Ltd. Yokohama,Japan, in 1989, where he developed high-reliability
hybrid microcircuits for aerospace programs. From2005 to 2007, he worked for CMOS analog and RF
circuits at Tokyo Institute of Technology, Yokohama,Japan. From 2007 to 2012, he worked for on-chip power supply circuits and organic electronics circuits at the Institute of Industrial Science, the University ofTokyo, Tokyo. Since July 2012, he has been working at Chair for Circuit Design and Network Theory, Technische Universität Dresden, Dresden, Germany.
His research interests include low-voltage low-power CMOS analog circuits,
on-chip power supply circuits, and large-area ﬂexible electronics. Dr. Ishida isa member of IEICE.

Takayasu Sakurai (S'77–M'78–SM'01–F'03) received the Ph.D. degree in EE from the Universityof Tokyo, Tokyo, Japan, in 1981. In 1981 hejoined Toshiba Corporation, where he designed
CMOS DRAM, SRAM, RISC processors, DSPs,
and SoC Solutions. He has worked extensively
on interconnect delay and capacitance modelingknown as Sakurai model and alpha power-law MOS
model. From 1988 through 1990, he was a visiting
researcher at the University of California Berkeley,
where he conducted research in the ﬁeld of VLSICAD. From 1996, he has been a Professor at the University of Tokyo, working
on low-power high-speed VLSI, memory design, interconnects, ubiquitouselectronics, organic ICs, and large-area electronics. He has published morethan 600 technical publications including 100 invited presentations and several
books and ﬁled more than 200 patents.
He is the executive committee chair for VLSI Symposia and a steering committee chair for the IEEE A-SSCC. He served as a conference chair for the
Symp. on VLSI Circuits, and ICICDT, a vice chair for ASPDAC, a TPC chairfor the A-SSCC, and VLSI symp., an executive committee member for ISLPEDand a program committee member for ISSCC, CICC, A-SSCC, DAC, ESSCIRC, ICCAD, ISLPED, and other international conferences. He is a recipient of 2010 IEEE Donald O. Pederson Award in Solid-State Circuits, 2009
and 2010 IEEE Paul Rappaport award, 2010 IEICE Electronics Society award,
2009 IEICE achievement award, 2005 IEEE ICICDT award, 2004 IEEE Takuo
Sugano award, and 2005 P&I patent of the year award and four product awards.
He delivered keynote speech at more than 50 conferences including ISSCC, ESSCIRC and ISLPED. He was an elected AdCom member for the IEEE SolidState Circuits Society and an IEEE CAS and SSCS distinguished lecturer. He
is also a domain research supervisor for nano-electronics area in Japan Scienceand Technology Agency. He is an IEICE Fellow.

Makoto Takamiya (S'98–M'00–SM'14) received
the B.S., M.S., and Ph.D. degrees in electronicengineering from the University of Tokyo, Tokyo,
Japan, in 1995, 1997, and 2000, respectively. In
2000, he joined NEC Corporation, Japan, where
he was engaged in the circuit design of high speed
digital LSIs. In 2005, he joined University of Tokyo,
Japan, where he is an associate professor of VLSI
Design and Education Center. From 2013 to 2014,
he stayed at University of California, Berkeley, as
a visiting scholar. His research interests include thecircuit design of the low-power RF circuits, the ultra low-voltage logic circuits,
the low-voltage power management circuits, and the large area and ﬂexible
electronics with organic transistors.
He is a member of the technical program committee of IEEE International
Solid-State Circuits Conference and IEEE Symposium on VLSI Circuits. He
received 2009 and 2010 IEEE Paul Rappaport Awards and the best paper award
in 2013 IEEE Wireless Power Transfer Conference.