Zero Phase Difference Capacitance Control (ZPDCC) for
Magnetically Resonant Wireless Power Transmission
Shunta Iguchi, Pyungwoo Yeon, Hiroshi Fuketa, Koichi Ishida, Takayasu Sakurai, and Makato Takamiya
University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
Abstract- In a magnetically resonant wireless power transmission
system, a DC-DC power transmission efficiency (ηTOTAL) at an
inherent resonant frequency (fRES) is degraded when the distance
between a transmitter (TX) coil and a receiver (RX) coil is short,because the frequency dependence of ηTOTAL has two peaks. In
order to solve the efficiency degradation, a zero phase difference
capacitance control (ZPDCC) is proposed, which is suitable forthe integration to LSI’s. In ZPDCC, either of the two peaks isshifted to fRES and ηTOTAL is increased by tuning the capacitance(C) of the resonator in TX and RX to keep the zero phasedifference (θ = 0) between the voltage and the current in TX at
Δθ / ΔC > 0. Both TX and RX circuits are fabricated in a 3.3V,
180nm CMOS. By introducing ZPDCC, the measured ηTOTAL at
fRES of 13.56MHz increases 1.7 times from 16% to 27% at the
distance of 2.5mm between the TX and RX coils with a diameterof 40mm.

P2 [mW]

120

CAPACITANCE

P2P1Z IN = Z IN ∠θ

C

In
PA
(13.56MHz)

k

P2
P1

L

ηCOIL =

ηPA [%]

P4
P1

ηRECTIFIER =

P4
P3

(c)

(d)

100
k=0.1
80
k=0.2
k=0.5
60
A
C
40
20
B
0
10 12 14 16 18 20
Frequency [MHz]ηTOTAL [%]

=

P3
P2

RL

100
k=0.1
k=0.2
80
A
k=0.5
60
C
40
B
20
0
10 12 14 16 18 20
Frequency [MHz](b)

ηTOTAL = ηPA × ηCOIL × ηRECTIFIER

CL

100
80 A B k=0.5 C
60
k=0.2
40
k=0.1
20
0
10 12 14 16 18 20
Frequency [MHz]ηCOIL [%]

100
80
C
A
60
B
40
k=0.1
k=0.2
20
k=0.5
0
10 12 14 16 18 20
Frequency [MHz]Out

Rectifier

ηRECTIFIER [%]

ηPA =

P4

P3

C

L

(e)
Fig. 1. Schematic of magnetically resonant wireless power transmission
system. Simulated frequency dependence of (a) P2, (b) ηPA, (c) ηCOIL, (d)ηRECTIFIER, and (e) ηTOTAL. Coupling coefficient (k) is varied.

power transmission system including PA and a rectifier. The
details of the circuits of a class-D PA and the rectifier will beshown in Fig. 4. P1 is an input power to TX, P2 is an output
power of PA, P3 is an input power to the rectifier, and P4 is aload power. P1, P2, P3, and P4 are effective powers. The
definitions of a PA efficiency (ηPA), a coil efficiency (ηCOIL), a
rectifier efficiency (ηRECTIFIER), and ηTOTAL are shown in Fig. 1.
Fig. 1 (a) shows a simulated frequency dependence of P2.
Figs. 1 (b) - (e) show simulated frequency dependence of ηPA,
ηCOIL, ηRECTIFIER, and ηTOTAL, respectively. A coupling
coefficient (k) is varied to emulate the change of d. In the
SPICE simulation, a 3.3V, 180nm CMOS is used with theparameters in the table in Fig. 1. In this work, the target
frequency is fixed to 13.56MHz.
The frequency dependence of the efficiency, one peak or
two peaks, is discussed in the followings. The frequency

CONTROL

In order to analyze the frequency dependence of ηTOTAL,
Fig. 1 shows a schematic of a magnetically resonant wireless978-1-4673-5010-5/13/$31.00 ©2013 IEEEAC
B
0
10 12 14 16 18 20
Frequency [MHz]

30

3.3μH
300
42pF
1μF
80Ω
3.3V

(a)

Ambient or ubiquitous charging of electronic devices suchas smartphones is increasingly needed, because thesmartphone requires a frequent charging due to the increased
power consumption. A magnetically resonant wireless powertransmission board (MR-WPTB) [1] on a printed-circuit board(PCB) with a transmitter (TX) coil array and a selectively
activation of a TX coil based on the position detection of areceiver (RX) coil is one of a possible solution for the ambient
charging.
In MR-WPTB, however, a DC-DC power transmission
efficiency (ηTOTAL) at an inherent resonant frequency (fRES)
including a power amplifier (PA) in TX and a rectifier in RX
reaches its maximum at a certain distance (dX) between a TX
coil and a RX coil. When the distance (d) between a TX coiland a RX coil is shorter than dX, ηTOTAL at fRES is reduced,
which is a unique phenomenon in the magnetic resonance [1]and is not observed in the conventional electromagnetic
induction.
In order to solve the efficiency reduction in the magnetic
resonance, a zero phase difference capacitance control(ZPDCC) is proposed in this paper, which is suitable for the
integration to LSI’s. By introducing ZPDCC, ηTOTAL at fRES isincreased.
DIFFERENCE

L
Q (Coil)C
CL
RL
VDD (PA)60

VDD

I. INTRODUCTION

II. ZERO PHASE(ZPDCC)

k=0.1
k=0.2
k=0.5

90

25

Phase of ZIN (θ) [degree]dependence of ηCOIL has the one peak [2]. In contrast, thefrequency dependences of ηPA, ηRECTIFIER, and ηTOTAL have thetwo peaks. The origin of the two peaks derives from the two
peaks of P2 shown in Fig. 1 (a). The reason is explained in thenext paragraph. The frequency dependence of ηPA has the two
peaks, because ηPA increases with increasing P2. Similarly, thefrequency dependence of ηRECTIFIER has the two peaks, because
ηRECTIFIER increases with increasing P3. Therefore, thefrequency dependence of ηTOTAL ( = ηPA x ηCOIL x ηRECTIFIER)
has the two peaks.
The reason why the frequency dependence of P2 has thetwo peaks is explained in the following. P2 of class-D PA isgiven by [3]22V
cos 2 (θ )(1)P2 = DD2
π Re(Z IN )where VDD is a power supply voltage of PA, ZIN is an input
impedance at the coil as shown in Fig. 1, θ is a phase of ZIN,
and π is a circular constant. P2 is determined by θ and Re(ZIN),
because VDD is fixed to 3.3V in this work. P2 is maximized,
when θ = 0 and Re(ZIN) is minimum. Figs. 2 (a) and (b) show
simulated frequency dependence of θ and Re(ZIN),
respectively. k and the capacitance (C) of the resonator in TX
and RX shown in Fig. 1 are varied. In Fig. 2 (a) at k = 0.1, thefrequency at θ = 0 is only 13.56MHz, which corresponds tothe one peak in Fig. 1 (a). In contrast, in Fig. 2 (a) at k = 0.5
and C = 42pF, the frequencies at θ = 0 are Point A, Point B,
Point C shown in Fig. 2 (a). Point B is 13.56MHz. Point A andPoint C corresponds to the two peaks in Fig. 1 (a) and Point B
corresponds to a bottom of a valley in Fig. 1 (a), because
Re(ZIN) of Point A and Point C is smaller than Re(ZIN) of
Point B. In this way, the frequency dependence of P2 has thetwo peaks in Fig. 1 (a).
In this paper, in order to increase ηTOTAL at k = 0.5 and13.56MHz shown as Point B in Fig. 1 (e), Point A or Point C
is moved to 13.56MHz by changing C. In order to determine
an optimum C, ZPDCC is proposed. In ZPDCC, C is tuned tokeep θ = 0 at Δθ / ΔC > 0, thereby shifting either of Point A or
Point C to 13.56MHz and increasing ηTOTAL. For example,
when C is changed from 42pF to 31pF at k = 0.5, Point A
moves to Point D (= 13.56MHz) as shown in Fig. 2 (a) andRe(ZIN) at 13.56MHz decreases from Point B to Point D as
shown in Fig. 2 (b), thereby increasing P2 and ηTOTAL.
The reason why θ = 0 at Δθ / ΔC > 0 is required in ZPDCC
is explained in the following. Figs. 3 (a) and (b) show
simulated capacitance (C) dependence of θ and Re(ZIN) at k =0.5 and 13.56MHz, respectively. In Fig. 3 (a), C at θ = 0 are
Point B, Point D, and Point E. In Fig. 3 (b), Re(ZIN) at Point D
and Point E is smaller than Re(ZIN) at Point B. Therefore, P2and ηTOTAL at Point D and Point E is larger than those at Point
B. For ZPDCC, Point D and Point E are right points, while
Point B is a wrong point. In order to distinguish Point D andPoint E from Point B, ” Δθ / ΔC > 0” condition is required. In
this work, Point B is moved to Point D by changing C from
42pF to 31pF.

90
60
30
0

B,D

A

C

-30

k=0.1(C=42pF)
k=0.5(C=42pF)
k=0.5(C=31pF)

-60
-90
10

12

14

16

18

20

Frequency [MHz](a)300

Re(ZIN) [Ω]

B
200
C

A
D

100

0
10

k=0.1(C=42pF)
k=0.5(C=42pF)
k=0.5(C=31pF)
12

14

16

18

20

Frequency [MHz]Phase of ZIN (θ) [degree](b)
Fig. 2. Simulated frequency dependence of (a) θ and (b) Re(ZIN). k and C arevaried.
90
60
30
0

D

-30
-60
-90
20

E

B

Proposed

Conventional
k=0.5, 13.56MHz

30

50

40

60

70

80

Capacitance [pF](a)

Re(ZIN) [Ω]

300

B

200

Conventional

D

E

100
Proposed
0
20

30

40

k=0.5, 13.56MHz
50

60

70

80

Capacitance [pF](b)
Fig. 3. Simulated capacitance dependence of (a) θ and (b) Re(ZIN) at k = 0.5
and 13.56MHz.

26

III. EXPERIMENTAL RESULTS

ZPDCC is achieved by TX, which is important for MRWPTB, because RX in electronic devices such as smartphones
should be simple. Compared with conventional capacitancecontrol methods using a vector network analyzer [4] and a
directional coupler and a power meter [5], ZPDCC is suitable
for the integration to LSI’s, because the current monitor andthe capacitance controller are easily implemented into theintegrated circuits.
Fig. 5 shows photographs of TX PCB, TX LSI (PA), RX
PCB, and RX LSI (rectifier). The size of coils fabricated on
TX and RX PCB is 40mm x 40mm. The core size of PA andrectifier is 684μm x 661μm and 320μm x 450μm, respectively.
Fig. 6 shows the measured frequency dependence ofηTOTAL, which corresponds to Fig. 1 (e). d is varied. When d =15mm and 25mm, the frequency dependence of ηTOTAL has a
one peak at 13.56MHz. In contrast, at d = 5mm, the frequency
dependence of ηTOTAL has the two peaks. In order to increase
ηTOTAL at d = 5mm and 13.56MHz, ZPDCC is applied.
Fig. 7 shows the measured capacitance (C) dependence ofθ at 13.56MHz, which corresponds to Fig. 3 (a). d is varied. θ
is measured with an oscilloscope. When d = 15mm and 25mm,
θ = 0 is at only one capacitance, which corresponds to the one
peak in Fig. 6. In contrast, at d = 5mm, θ = 0 is at Point B andPoint D. Point D is the right point for ZPDCC because Point D
satisfies θ = 0 at Δθ / ΔC > 0. Therefore, C should be changed
from Point B (C = 37pF) to Point D (C = 25pF).

In order to demonstrate the improvement of ηTOTAL by the
proposed ZPDCC, a magnetically resonant wireless powertransmission system with ZPDCC is implemented. Fig. 4
shows a circuit schematic of the magnetically resonant
wireless power transmission system with ZPDCC. The class-D
PA in TX and the rectifier in RX are designed and fabricatedin a 3.3V, 180nm CMOS process. The coils are fabricated on
FR4 PCB and the layout of the coils are the same as [1]. The
capacitors are implemented by ceramic capacitors on PCB.
In the circuit implementation of ZPDCC, θ is measured by
the phase difference between the voltage (V1) and the current(I1) in TX. The proposed ZPDCC includes a current monitor
and a capacitance controller. I1 is converted to a voltage by a
non-inverting amplifier and the θ is measured in thecapacitance controller. The capacitance controller tunes C in
TX and RX to keep θ = 0 at Δθ / ΔC > 0. The non-inverting
amplifier is implemented by an operational amplifier(OPA847ID) and two resisters. The gain of amplifier is 1 +(10kΩ / 100Ω) = 40dB.
180nm CMOS LSI
RectifierClass-D PA
3.3V
In

Out

Distance(d)

V1

C

2C

80Ω
1μF

13.56MHz
I1

60
2C

d=5mm
d=15mmd=25mm50

ηTOTAL [%]OPA847ID
10kΩ
0.1Ω
100Ω
Current monitor

30
20
10

Capacitance controller
I1 V1
V1
θ
I1 Tune C for θ=0

0
10

12

14

16

18

20

Frequency [MHz]Fig. 6. Measured frequency dependence of ηTOTAL, which corresponds to Fig.

Proposed ZPDCC

Fig. 4.
Circuit schematic of magnetically resonant wireless powertransmission system with ZPDCC.

1 (e). d is varied.

Receiver50mm

Phase (θ) between V1 and I1 [degree]

Transmitter
50mm

40

40mm
40mm
Current
monitor
93mm

104mm

320μm
684μm
450μm
661μm

90

d=5mm
d=15mmd=25mm60

13.56MHz
Conventional

30
D

0

B

-30
Proposed

-60
-90
15

20

25

30

35

40

45

Capacitance [pF]

Fig. 7. Measured capacitance dependence of θ at 13.56MHz, whichcorresponds to Fig. 3 (a). d is varied.

Fig. 5. Photographs of TX PCB, TX LSI (PA), RX PCB, and RX LSI(rectifier).

27

IV. CONCLUSION
60

ηTOTAL [%]40

For the magnetically resonant wireless power transmission
system, ZPDCC is proposed to increase ηTOTAL at fRES, when
the d is short and ηTOTAL at fRES is reduced due to the two
peaks. In ZPDCC, C of the resonator is tuned to keep the zero
phase difference (θ = 0) between the voltage and the current in
TX at Δθ / ΔC > 0, thereby shifting either of the two peaks to
fRES and increasing ηTOTAL. Compared with the conventional
monitoring methods for the capacitance control, the proposed
ZPDCC is suitable for the integration to LSI’s, because thedirectional coupler is not required. Both TX circuits and RX
circuits are fabricated in a 3.3V, 180nm CMOS. By
introducing ZPDCC, the measured ηTOTAL at fRES of 13.56MHz
increases 1.7 times from 16% to 27% at d = 2.5mm.

13.56MHz

d=5mm
d=15mmd=25mm

50

D

30
20

B

Proposed10

Conventional

0
15

20

25

30

35

40

45

Capacitance [pF]
Fig. 8. Measured capacitance dependence of ηTOTAL at 13.56MHz. d is varied.
60
50

ηTOTAL [%]ACKNOWLEDGMENT
This work is partly supported by Renesas Electronics
Corporation. The authors thank Masayuki Mizuno, Koichi
Yamaguchi, Haruya Ishizaki, Hideki Sasaki, Tatsuaki Tsukuda,
Hiroki Sugimoto, Yuji Shinohara, and Tomotoshi Nureki ofRenesas Electronics Corporation for encouragement anddiscussions.
The VLSI chips in this study have been fabricated in thechip fabrication program of VLSI Design and Education
Center (VDEC), the University of Tokyo in collaboration with
Rohm Corporation and Toppan Printing Corporation.

Constant capacitance (Conv.)ZPDCC (Proposed)

40
30
x1.7

20
10
0

13.56MHz
0

10

20

30

40

Distance (d) [mm]

REFERENCES

Fig. 9. Measured distance dependence of ηTOTAL in conventional constantcapacitance and proposed ZPDCC at 13.56MHz.

[1]

Fig. 8 shows the measured capacitance (C) dependence ofηTOTAL at 13.56MHz. d is varied. When d = 15mm and 25mm,
ηTOTAL is a maximum at an original C of 37pF. In contrast, at
d = 5mm, ηTOTAL is a maximum at a modified C of 25pF.
ηTOTAL is increased from 25% to 34% by changing from Point[2]

B (C = 37pF) to Point D (C = 25pF) using ZPDCC. The
measured load power (P4) is 8.4mW at Point D.
Fig. 9 shows the measured distance (d) dependence ofηTOTAL at 13.56MHz. The conventional constant C and the
proposed ZPDCC are compared.
When d is longer than 10mm, ZPDCC is not activated andC is constant. Therefore, ideally, ηTOTAL of ZPDCC and theconventional constant are the same. In the measurement,
however, ηTOTAL of ZPDCC is 1-7% lower than that of theconventional constant C, because of the resistive loss in 0.1Ωfor the current monitor shown in Fig. 4. In contrast, when d isshorter than 10mm, ηTOTAL of ZPDCC is higher than that of
the conventional constant C, which indicates the increase of
ηTOTAL by ZPDCC exceeds the decrease of ηTOTAL by theresistive loss. For example, ηTOTAL increases 1.7 times from
16% to 27% at d = 2.5mm by tuning C from 37pF to 20pF. In
ZPDCC, the maximum ηTOTAL is 49% at d = 15mm.

[3]
[4]

[5]

28

H. Lim, K. Ishida, M. Takamiya, and T. Sakurai, “Positioning-Free
Magnetically Resonant Wireless Power Transmission Board with
Staggered Repeater Coil Array (SRCA),” IEEE MTT-S International
Microwave Workshop Series on Innovative Wireless Power
Transmission: Technologies, Systems, Applications (IMWS-IWPT), pp.
93-96, May 2012.
I. Awai and T. Ishizaki, “Transferred Power and Efficiency of a
Coupled-resonator WPT System,” IEEE MTT-S International
Microwave Workshop Series on Innovative Wireless Power
Transmission: Technologies, Systems, Applications (IMWS-IWPT), pp.
105-108, May 2012.
M. K. Kazimierczuk, RF Power Amplifiers, Wiley, 2008.
K. Ogawa, N. Oodachi, S. Obayashi, and H. Shoki, “A Study of
Efficiency Improvement of Wireless Power Transfer by ImpedanceMatching,” IEEE MTT-S International Microwave Workshop Series on
Innovative Wireless Power Transmission: Technologies, Systems,
Applications (IMWS-IWPT), pp. 155-157, May 2012.
Y. Moriwaki, T. Imura, and U. Hori, “Basic Study on Reduciton ofReflected Power Using DC/DC Converters in Wireless Power Transfer
System via Magnetic Resonant Coupling,” IEEE 33rd International
Telecommunications Energy Conference (INTELEC), pp 1-5, Oct.
2011.