An Evaluation of Wireless Power Transfer Systemwith Plural Repeater Coils for Moving Objects
Tatsuya Yamamoto
Graduate school of Science and Engineering
Saitama University
Saitama, Japan
Email: grgrstar@gmail.com

Kenji Nara
Graduate school of Science and Engineering.
Saitama University
Saitama, Japan
Email: k.nara.495@ms.saitama-u.ac.jp

Abstract— In this paper, we study the use of Wireless Power
Transfer (WPT) for feeding Electric Vehicles (EV) and otherconveyance machines. We researched circuit topologies that canbe extended to a bidirectional feed and are suitable as feeds formoving objects, and proposed two systems; a two-repeater coils
system and a Parallel-Parallel compensation capacitor system(PP system), which are symmetrical circuit configurations on the
primary and secondary side transfer. The results show that theimmittance converter characteristics can be obtained by optimal
design of the capacitor. Based on the power feeding experimental
result, it was confirmed that the input power can be suppressedby increasing the input impedance at the time of shifting theposition of the secondary side. We demonstrate the usefulness ofthe two-repeater coils system and PP system, assuming the use ofmultiple ground coils.
Keywords—Wireless power transfer, Repeater coil, Plural
repeater coils, Compensation capacitor

I. INTRODUCTION
Recently, Plug-in Hybrid Vehicles (PHVs) and Electric
Vehicles (EVs) are being promoted as new vehicles replacing
those powered by gasoline due to considerations of global
environmental problems and effective use of energy. A
conductive type of connection using electric cables andconnectors is used for charging EVs at present. However, withthis method, there are the problems that wear can occur when
attaching and detaching the connector, or that spontaneouselectric shocks can occur if it is raining. It is therefore expectedthat establishing a charging method based on Wireless Power
Transfer (WPT) [1] will be superior to the conductive method
in terms of convenience, safety, and maintainability throughcordless technology. WPT is adopted not only for EVs but also
for equipment used in factories. For cleanrooms and buildings
which require painting work, WPT is utilized for charging anddriving Automated Guided Vehicles (AGVs) and conveyancemachines used for transporting parts and the like.
For supplying power to the functional EV, multiple coils
are arranged on the ground side [2] that are switched on to beenergized depending on the presence or absence of the vehicle.
Using a one-repeater coil system, which has a third coilbetween the primary and secondary coil, or a Parallel-Series
compensation capacitor (PS) system, which has acompensation capacitor in parallel on the primary side and inseries on the secondary side, there is a possibility that the

Yasuyoshi Kaneko
Graduate school of Science and Engineering.
Saitama University
Saitama, Japan
Email: kaneko@ees.saitama-u.ac.jp

Fig. 1 Circuit of Two-Repeater Coils WPT System
ground side coils connected in parallel can be switched without
a control mechanism when driving at constant voltage [3].
However, in these systems, it is necessary to increase thenumber of turns of the coil on the secondary side with respect
to that on the primary side, which may be difficult to design.
Furthermore, because the circuit configuration is asymmetricalbetween the primary and secondary side, it is difficult to extend
to bidirectional feeding [4].
Research on the practical application of bidirectional power
supply to allow electrical power to be interchanged for houses
is also being conducted, as is research for EVs incorporating
their own mobile battery. When the battery capacity decreases,
it is charged to the EV from the house or electric power system,
whereas on the contrary, electricity is supplied to the house in
the case of emergency when the power system is down. In
addition, to return the power to the power supply side byregenerative braking with WPT while the conveyor is moving,a mechanism such as bidirectional feeding is required.
Therefore, in this research, we propose a design guidelineby systematically summarizing characteristics of circuit
topology which can be extended to bidirectional feed and issuitable for a feed to moving objects. We perform a theoreticalanalysis of the two-repeater coils system, in which the repeater
coil is wound in close contact with the coils of both theprimary and secondary side, and the Parallel-Parallel
compensation capacitor (PP) system [5], which is considered tohave characteristics similar to the two-repeater coils system.
The validity of the theoretical equation is verified by a power
feeding experiment using real equipment.
II. TWO-REPEATER COILS WPT SYSTEM
A. Circuit of Two-Repeater Coils WPT System
The circuit configuration of the two-repeater coils system isshown in Fig. 1. In this system, there are two windings of therepeater coil between the primary and secondary side, andcompensation capacitors are connected in series to all coils.
Subsequently, the winding (coil) resistance and iron loss are
assumed to be sufficiently smaller than the impedance of thecoil at high frequencies. The relationship between the voltage
and the current of each coil is represented by (1) using theimpedance matrix.
1æç jwL1 +jwC1çæV IN ö çç÷
jwM 12
ç 0 ÷ çç 0 ÷=ç
ç
jwM 1rç÷
ç 0 ÷ çèø ç
ççj wM 1 s
è

jwM 12

jwM 1r1+ RD
j wL 2 +jwC 2

jwM 2 rjwM 2 r1
jwLr +
jwC r

j wM 2 s

jwM rsö÷÷÷æç I 1 ö÷
jwM 2 s÷ç I ÷
÷ç 2 ÷
÷ç I r ÷
jwM rs÷ç I ÷
è sø1 ÷÷jwLs +
jwC s ÷øj wM 1 s

C1 =

(1)

These values are the voltage V, current I, compensation
capacitance C, self-inductance L, as shown in Fig.1, mutual
inductance Mij (i,j = 1,2,r,s) between the primary andsecondary coil and repeater coils (r coil and s coil,respectively), and angular frequency ω (= 2πf0) of the power
supply.
First, the capacitor values are determined as shown in (2),so as to resonate with the self-inductance of the repeater coil asin the conventional one-repeater coil system.
Cr =

1
1
C =
w 2 Lr , s w 2 Ls

(2)From (1) and (2), it is possible to obtain the immittanceconverter characteristics and set the input power factor to 1 bysetting the values of the primary and secondary side capacitor
as shown in (3).
1
C1 =
C2 =
ö
æ
æ
2
k
k
2k k ö
w 2 L1 çç1 - 1r 1s ÷÷ ,w 2 L2 çç1 - 2 r 2 s ÷÷kk rs ø
rsøè
è

B. Circuit Characteristics during Capacitor Correction
In order to prevent the primary and secondary capacitorsfrom taking a negative value, it suffices that the denominator of
the capacitance formula becomes 0 when they come into close
contact with the repeater coil. We therefore modify it, asshown in (7), and proceed with the analysis based on this.

Cr =k1r = k2 s = 1(4)

In addition, it is assumed that all other coupling coefficients
between the coils are equal to k.

k12 = k rs = k1s = k 2 r = kæ0çæVIN ö ç
çç
÷÷ =
k
ç
1
I
rs
è IN ø ç è jw k1r k 2 s - k12 k rs

C1 =

1

w 2 (- L1 ) ,

C2 =

1

w 2 (- L2 )

(6)

(8)

jw

k1r k 2 s - k12 k rs
k rs

1

0

L1 L2

ö
L1 L2 ÷÷æçVD ö÷÷ç I D ÷
÷è ø
ø

(9)

From (9), the self-inductance (and the number of turns) of the
two-repeater coils is irrelevant to the input/output
characteristics of the WPT circuit. The input impedance ZIN isthen obtained as shown in (10).
2æ k k - k12 k rs ö1
÷÷ L1 L2Z IN = çç w 1r 2 s
k
R
rs
D
ø
è

(10)

Here, when the coupling coefficient satisfies the conditions of(4) and (5), (10) can be rewritten as (11).
2

ì æ1
1
öü
Z IN = íw ç - k ÷ý L1 L2
k
R
øþ
î è
D

(11)

Equation (11) shows that the input impedance increases as thecoupling coefficient decreases (such that the position shift
increases), and that the input current can be suppressed whendriving with constant input voltage.
Next, ignoring the iron loss, the transformer efficiency isgiven by following (12).
hTR =

(5)

In this situation, the primary and secondary side capacitances
are represented by the expressions show in (6), which take anegative value. This causes problems for practical use.

1
1
Cs =
æ
ö
æ
k k ö
k
k
w 2 Ls çç1 - 1s rs ÷÷w 2 Lr çç1 - 2 r rs ÷÷ ,
k1r ø
k
è
2s ø
è

The input/output characteristics are expressed by (9).

(3)

In real situations, when winding the two repeater coils inclose contact with the primary and secondary side coil, thefollowing problem arises with this method of determining
capacitance. Assuming that the primary side and r coil and thesecondary side and s coil are tightly coupled, the coupling
coefficient is expressed by (4).

(7)

From (1) and (7), the compensation capacitor value of therepeater section with input/output power characteristics
matching the immittance converter characteristics and an input
power factor that becomes 1 is as follows.

1

Here, kij (i,j = 1,2,r,s) is the coupling coefficient between thecoils.

1
1
C2 =
æ
ö
æ
k k ö
k
k
w 2 L2 çç1 - 2 r 2 s ÷÷w 2 L1 çç1 - 1r 1s ÷÷ ,k rs ø
k rs ø
è
è

=

RD
2
2
æM ö
r1M rs + rs M 1r
2
RD + RD + r2 + rr çç 2 s ÷÷w 2 (M 1r M 2 s - M 12 M rs )2
è M rs ø

2

(12)

RD
æ
k rs Qs + k1r Q1
k Q ö
2
RD + RD + r2 çç1 + 2 s2 2 ÷÷2
r2Q1Q2Qs (k1r k2 s - k12krs )k rs Qr ø
è
2

2

2

Q (= ωL/r) is an index representing the performance of the coil.
For ∂ηTR/∂RD = 0, the maximum efficiency ηTRmax and the load
resistance value RDmax at the maximum efficiency (optimumload) are obtained as follows.
2

RD max =2

k1r k 2 s - k12 k rs
k Q + k 2 s Q2 Q1Qs
r2 Q2 rs 2 r
2k rs
k rs Qs + k1r Q1 Q2 Qr
1h TR max =1+

2(k1r k 2 s - k12 k rs )k rs Qr Qs(k Q + k Q )(k Q + k Q ) QQ QQ
2

rs

2

r

2s

2

2

rs

2

s

1r

(13)

r

s

1

2

1

C. Comparison with Magnetic Resonant Coupling System
A magnetic resonant coupling system [6] proposed by MIT
is cited as a WPT method with four coils from the power
supply to the load configured like the two-repeater coils system.
Fig. 2 shows a diagram of WPT by the magnetic resonant
coupling system. It is said that the magnetic resonant couplingsystem is equivalent to the SS system in terms of its electric
circuit [7] [8]. In this section, based on the description insection Ⅱ-B, we show that both methods are equivalent in theirmathematical equations with regards to the input/output
characteristics and power supply efficiency.
When mutual coupling exists only between adjacent coils(primary side and r coil, r and s coil, s and secondary side coil),the coupling coefficients other than k1r, krs, and k2s are all 0. In
this case, the capacitor values take the form shown in (14), and
it is found that they are determined the values to resonancewith each associated self-inductance value.
C1 =1

w 2 L1 ,C2 =1

w 2 L2 ,Cr =1w 2 Lr ,Cs =Fig. 2 Pattern Diagram of WPT by Magnetic Resonant
Coupling System
Table Ⅰ. Comparison between Magnetic Resonant Coupling
and SS method
Magnetic Resonant
SS
Coupling
C1 =

C

(14)

when

M rs
k
k = rs
M1r M 2 s ,k1r k2 s , the equation is rewritten as (16).

æ0çæ VIN ö ç=ç÷
è I IN ø ç - 1 krs
çè jw k1r k2 s
æ 0
æ VIN ö ç1ç÷=ç
è I IN ø ç è jw M

k k
jw 1r 2 s
krs
1
L1 L2

0

æ
0
jw M ö
÷ æ VD ö ç
=
1
1
ç
÷
ç
0 ÷÷ è I D øç jw k L L
ø
1 2
è

ö
L1 L2 ÷÷ æ VD ö÷ çè I D ø÷÷ø
jw k L1 L2 ö÷ æ VD ö÷ç I ÷
0
÷è D ø
øìVIN = jw k L1 L2 I D
ï
1
1
í
VD
ï I IN = - jw k
L1 L2
î

ZIN

~ 2 1
Z IN = wMRDhTR =ηTR max

RD

(17)

RD

(w M )RD 2 + RD + r2
2

RD
1
2
R
D + RD + r2
k 2 r2 Q1Q2

RD max = kr2 Q1Q2

1

1

hTR max =

2

1+

1
RD

1+

2
k Q1Q2efficiency ηTRmax are obtained as shown in (19) with Q1 = r1 ,
Q2 =

2

r1

hTR =

k Q1Q2w L2
r2.
RD max = w M

hTR max =

hTR =

2

RD
1
2
R
D + RD + r2
k 2 r2 Q1Q2

hTR max =1

w 2 L2

w L1

(16)

2

æM ö
r1 + rs ç 1r ÷
2
è M rs ø R 2 + R + r + r æ M 2 s ö
÷
D
D
r ç
2
2
æ M 1r M 2 s öè M rs ø
çw
÷
M
rs
è
ø

Z IN = (wM )RD max = krr2 Q1Q2

RDmax

, C2 =

ìVIN = - jw k L1 L2 I D
ï
1
1
í
VD
ï I IN = jw k
L1 L2
î

( )

ηTR

1

w 2 L1

From this, the optimum load RDmax and the maximum

æM ö
æM ö
r1 = r1 + rs ç 1r ÷ r2 = r2 + rr ç 2 s ÷,, the equation is rewritten as (18).
è M rs øè M rs ø

hTR =

C1 =

(15)

Power supply efficiency is given by (17), and when21

w 2 L2

Input /
Outputchar

The input/output characteristics are expressed by (15), andM =, C2 =

1
1
Cr = 2 , Cs = 2
w Lr
w Ls

1

w 2 Ls

1

w 2 L1(18)

r2= kr2 Q1Q2
r1

1
2
1+
wM

1

=
r1r2

1+

(19)
2

k Q1Q2

Table Ⅰ compares the respective values of the magnetic
resonant coupling system and the SS system [9]. Although thepositive and negative signs of the input/output characteristics
are reversed, it can be confirmed that the circuit characteristics
in the two schemes. From the above, it can be seen that themagnetic resonant coupling system is also equivalent to the SS
system with respect to the mathematical description, exceptthat the sign of the input/output characteristics differs.

III. PARALLEL-PARALLEL WPT SYSTEM
A. Circuit of Parallel-Parallel WPT System
The circuit configuration of the PP system is shown in Fig.
3. In the PP system, capacitors are connected in parallel to thecoils on both the primary and secondary sides. Because there is
only one mutual coupling, and because it can be regarded as atransformer with a gap, it is represented by the T-type
equivalent circuit shown in Fig. 4. We calculate the F-matrix of
the T-type equivalent circuit and obtain the capacitor values
such that its diagonal component is 0 as shown in (20). Unlike
the conventional design method [10], it is determined
independently of the load resistance.
C1 =1

w 2 L1 (1 - k 2 ) ,

C2 =

1

w 2 L2 (1 - k 2 )(20)

The input/output characteristics are obtained by substituting(20) into the F-matrix and are expressed by (21).
jw

(21)

400

0

Winding

80

1
L1 L2

ö
L1 L2 ÷÷æçVD ö÷÷çè I D ÷ø
÷
ø

1- k2
k

Fig. 4 T-type Equivalent Circuit of PP System

120

æ
ç
0
æVIN ö ç
çç I ÷÷ = ç 1kè IN ø
ç - jw 1 - k 2
èFig. 3 Circuit of Parallel-Parallel WPT System

Ferrite20

As for the two-repeater coils system, the immittance converter
characteristics are obtained and the input power factor is also 1.
The input impedance is given by (22), which shows that it
increases as the coupling coefficient decreases (corresponding
to increasing position shift).

100

20
Al sheet400yInside: Primary or Secondary Coil
Outside: Repeater Coil(a) Appearancex  (b) Dimensions

Fig. 5 Transformer Used in the Experiment

2

ì æ1
1
öü
Z IN = íw ç - k ÷ý L1 L2
k
R
ø
è
þ
î
D

(22)

The transformer efficiency (ignoring iron loss) is calculated
and expressed by (23), and the optimum load RDmax and the
maximum efficiency ηTRmax are obtained as shown in (24).
hTR =

RD
r1M 2 + r2 L1

2

2

2 2

w (L1 L2 - M )
=

æL ö
2
RD + RD + r2 + r1 ç 2 ÷
èM ø

2

RD
k Q2 + Q1 21
1
k 2Q1 + Q2
RD + RD + r2
2
2 2
Q1
k 2Q1
r2Q2 1 - k

(

)

Cr =

1- k
k Q1 + Q2
r2Q2
kk 2Q2 + Q1
2

RD max =

(23)

2

1+

1

w 2 Lr (1 - k 2 ) ,

Cs =

1

w 2 Ls (1 - k 2 )

(25)

2

1

hTR max =B. Comparison between PP and Two-Repeater Coils System
In the two-repeater coils system, as described above, when
two repeater coils are wound in close contact with the primaryand secondary side coil (in consideration of the real situation),
it is assumed that the coupling coefficient satisfies theconditions of (4) and (5). We also consider using coils with thesame performance (equal Q values). Under this condition, theprimary and secondary capacitances C1 → ∞, C2 → ∞ (andreactance is 0) according to (7). In addition, the capacitance ofthe repeater section is given by (25), and has the same form as(20) which determines the capacitor values of the PP system.

2

(24)

(1 - k )kQ Q (k Q + Q )(k Q + Q )
2

2

1

2

1

2

2

2

1

Furthermore, calculation of the input/output characteristics,
input impedance, and power supply efficiency is also
analogous to (21) to (24) in the PP system. From theseobservations, it was found that the two-repeater coils system is
equivalent to the PP system depending on how the repeater
coils are wound.
IV. POWER FEEDING EXPERIMENT OF THE TWO SYSTEMSIn order to verify whether the results of the two-repeater
coils system and the PP system from theoretical analysis canalso be realized in an actual machine, we fabricatedtransformers and measured constants corresponding to bothmethods. The appearance and dimensions of the transformer
used are shown in Fig. 5. The coil shape was solenoidal. In theWe conducted power feeding experiments of the tworepeater coils system and the PP system using the specificallyfabricated transformers. Table Ⅲ displays the conditions
during power supply and Fig. 6 shows the experimental circuit.
A square wave inverter was used as the power supply. In order
to confirm the characteristics at the fundamental frequency f0 =85.0 kHz, a band pass filter was inserted into the power output
section with a sine wave input. The load resistance RL after therectification was set to a value at which the transformer
efficiency ηTR was maximized. The DC input voltage VDC was
adjusted so that the output power PL after the rectification
reached 1.5 kW in the standard state for each method.
Input waveforms at the time of power supply in thestandard state are shown in Fig. 7. The voltage and current
waveforms of both methods were almost identical. Also, due tocapacitor compensation, the input power factor was almost 1 inFig. 6 Experimental Circuit

0

0

−150

−300
0

25

10

20

50
VIN
IIN

150

VIN [V]

VIN [V]

150

300

0

−25

−150

−50
30

−300
0

25

0

IIN [A]

50
VIN
IIN

IIN [A]

300

−25

10

Time [ms]

−50
30

20
Time [ms](a) Two-Repeater Coils System (b) PP System

Fig. 7 Input Waveforms in Standard State

0

300

25

0

150

0

−150

−25

−150

−300
0

−50
30

−300
0

10

20

50
VIN
IIN

Time [ms](a) Two-Repeater Coils System 

25

0

−25

10

20

−50
30

Time [ms](b) PP System

Fig. 8 Input Waveforms Secondary Side Absenceboth cases. Comparing the circulating currents, in the PP
system I1 = 41.3 A and I2 = 53.8 A, which are larger than the
input/output currents (IIN = 13.1 A, ID = 12.9 A), but in the tworepeater coils system, Ir = 12.1 A and Is = 18.8 A, which isabout a third of the PP system currents. It was confirmed thatthe circulating current could be drastically reduced using a
repeater coil with many more turns than the primary andsecondary side coils. In addition, by using the split capacitor
method, the voltage across the terminals of the coil reached amaximum of 255 V, which was only 1.5 times as much as thehighest alternating voltage VD = 165 V in the PP system.
In the case of secondary side absence, input waveforms areshown in Fig. 8. By comparing these results with those of the

IIN [A]

50
VIN
IIN

150

VIN [V]300

IIN [A]

two-repeater coils system, repeater coils were wound so as to
be closely contacted from above the coils of the primary andsecondary side. In order to reduce the current flowing throughthe repeater coil, the number of turns was set to 4.5 times thenumber of turns of the primary and secondary side coil. In
addition, in order to prevent excessive voltage [11], the split
capacitor method was adopted with the coil divided into 2 forevery 9 turns. Aluminum plates were installed on the back of
the primary and secondary coils for both methods. Table Ⅱshows the measured results when the gap of the transformers is
60 mm and in the standard state without position shift. In the
two-repeater coils system, k1r and k2s were 0.9 or greater, whichmeans that there was stronger coupling than for the other coils.

Table Ⅲ. Experimental Conditions
Two-Repeater
TopologyPPCoils
f0 [kHz]
85.0
RL [Ω]
25.0
30.0
C1 [μH]4.90
0.587
Cr [μH]
0.0629Cs [μH]
0.0696C2 [μH]
4.34
0.629
Lf [μH]104
Cf [μF]
0.0336

VIN [V]

Table Ⅱ. Transformer Parameter
Two-Repeater
TopologyPP
Coils
Gap length [mm]60.0N1 [Turn]
44
Nr [Turn]
18
Ns [Turn]
18
N2 [Turn]
4
4
r1 [mΩ]9.79
12.8
rr [mΩ]105
rs [mΩ]105
r2 [mΩ]10.5
11.6
L1 [μH]
6.78
5.83
Lr [μH]54.0
Ls [μH]55.5
L2 [μH]
6.71
6.03
k12
0.201
0.226
krs
0.245
k1s
0.237
k2r
0.229
k1r
0.924
k2s
0.930
|Zin| [Ω]11.8
12.3
RDmax [Ω]12.1
14.4
ηTRmax [%]
96.8
96.4

90

standard state shown in Fig. 7, it was confirmed that the peakvalue of the input current IIN and the input power factor weregreatly reduced in both systems. Variations of the input
impedance | ZIN | and the input power PIN in the case of
misalignment are shown in Fig. 9 and 10. We confirmed that
| ZIN | increases and PIN decreases in the case of misalignment
in both systems when VDC is constant.

|ZIN| [W]6030

V. CONCLUSION

00

In this research, we studied two types of circuit topologies
that can suppress the input power for the case of secondary side
misalignment or absence when driven with constant input
voltage. We conducted a circuit analysis of the two-repeater
coils system, in which a repeater coil was added to each of two
windings to make a transmitting and receiving coil. We
analyzed the case where capacitor compensation was carriedout by the same determination method as for the conventional
one-repeater coil system and outlined an immediate practicalproblem that arises. In order to solve this problem, the methodof capacitor compensation was modified to obtain adequate
circuit characteristics, power supply efficiency, etc.
Furthermore, applying the condition of no coupling between
non-adjacent coils, we analyzed the magnetic resonancecoupling system using four coils as in the two-repeater coils
system and proved that it is equivalent to the SS system.
Next, we conducted a circuit analysis on the PP system,
which is considered to have characteristics similar to the tworepeater coils system. Comparing the two systems, theinput/output characteristics and the power supply efficiency
were similar, depending on the conditions.
We also verified the validity of the theory behind the tworepeater coils and PP systems through a power supply
experiment using real equipment. It was confirmed that the
input power is reduced by changing the input impedance andthe input power factor in the case of secondary side
misalignment or absence.
As described above, the two-repeater coils and PP systems,
which have symmetrical circuit configurations on the primaryand secondary side, exhibit immittance converter
characteristics useful for batteries that require charging with aconstant current. This, and the findings that the input power
can be suppressed in the case of secondary side misalignment
are useful characteristics for power supplies of moving objects,
and we have shown the usefulness of the method proposed here.

REFERENCES
[1]

[2]

G. A. Covic and J. T. Boys, “Modern trends in inductive power transfer
for transportation application”, IEEE J. Emerg. Sel. Topics PowerElectron., vol. 1, no. 1, pp. 28–41, 2013.
J. M. Miller, P.T. Jones, J-M. Li, and O. C. Onar, “ORNL Experience
and Challenges Facing Dynamic Wireless Power Charging of EV’s”,
IEEE Circuits and Systems Magazine, pp. 40-53, 2015.

2 Repeater Coils (x)PP (x)
2 Repeater Coils (y)PP (y)

30

60

90

120

150

Misalignment [mm]Fig.9 |ZIN| in Secondary Side Misalignment
2500
2 Repeater Coils (x)PP (x)
2 Repeater Coils (y)PP (y)PIN [W]

2000
1500
1000
500
0
0

30

60

90

120

150

Misalignment [mm]Fig.10 PIN in Secondary Side Misalignment[3]

J. Yamada, K. Tsuda, R. Kobayashi, and Y. Kaneko, “Circuit Analysis
and Characterization of Contactless Power Transfer System with
Variable Impedance”, IEEJ Transactions on Industry Applications, vol.
137, no. 11, pp. 815-826, 2017.
[4] S. Nakadachi, S. Mochizuki, S. Sakaino, Y. Kaneko, S. Abe, and T.
Yasuda, “Bidirectional Contactless Power Transfer System Expandablefrom Unidirectional System”, ECCE2013, Denver, P505, 2013.
[5] T. Yamamoto and Y. Kaneko, “An Evaluation of Wireless Power
Transfer System with Plural Repeater Coils for Moving Objects”, IEEJ,
2018.
[6] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M.
Soljacic, “Wireless Power Transfer via Strongly Coupled Magnetic
Resonances”, Science Express on 7 June 2007, vol. 317, no. 5834, pp.
83-86, 2007.
[7] N. Hagiwara, “Study on the Principle of Contactless Electric Power
Transfer via Electromagnetic Coupling”, IEEJ Transactions on Industry
Applications, vol. 131, issue. 5, pp. 708-713, 2011.
[8] T. Imura and Y. Hori, “Unified theory of electromagnetic and magnetic
resonant coupling”, IEEE Transactions on Industry Applications, vol.
135, no. 6, pp. 697-710, 2015.
[9] T. Tohi, Y. Kaneko, and S. Abe, “Maximum Efficiency of Contactless
Power Transfer Systems using k and Q”, IEEJ The papers of Technical
Meeting on SPC-11-179, 2011.
[10] Chewi-Sen Wang, O. H. Stielau, and G. A. Covic, “Design
Considerations for a Contactless Electric Vehicle Battery Charger”,
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, vol. 52,
no. 5, pp. 1308-1324, 2005.
[11] T. Yamamoto and Y. Kaneko, “A Study of the Common Use of
Wireless Power Transfer System Which Has a Difference in the
Magnetic Field Structure”, IEEJ Transactions on Industry Applications,
1-94, pp. 327-332, 2015.