Low-EMF Wireless Power Transfer Systems of FourWinding Coils with Injected ReactanceCompensation Current as Active Shielding
Keita Furukawa, Keisuke Kusaka, and Jun-ichi Itoh
Department of Electrical, Electronics and Information Engineering,
Nagaoka University of Technology, NUT
Nagaoka, Niigata, Japanarcher_FK@stn.nagaokaut.ac.jp, kusaka@vos.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp

Abstract—This paper proposes and analyzes low-radiationnoise wireless power transfer (WPT) systems with active shielding.
Current flowing on the additional windings around the WPT coils
is compensated with additional power supplies to cancel themagnetic field generated by the WPT coils. The current of theadditional windings is controled with the additional power
supplies to achieve zero magnetic field at rated power. The
additional power supplies increase in the RMS current of theadditional windings to inject reactance-compensation current. As
a result, a transmission power of 1 kW and a reduction in radiationnoise by 39.5 dB are achieved with the proposed active shielding.
In addition, it is revealed that the transmission power with theproposed method is increased by the magnetic field reduction.
Keywords—active shielding, multiple
radiation noise, wireless power transfer

magnetic

coupling,

I. INTRODUCTION
Wireless power transfer (WPT) systems have been attracted
as battery charging systems of electric vehicles (EVs) to avoid
electric shocks for safety [1–4]. Large radiation noise isgenerated by the WPT coils when batteries on EVs arecharged [1]. The radiation noise negatively affects electric
devices or human bodies near the WPT system [1]. Thus, theradiation noise is limited by several regulations, such as theInternational Commission on Non-Ionizing Radiation Protection(ICNIRP) 2010 guidelines and International Special Committeeon Radio Interference (CISPR) guidelines [5–8].
Many studies have been conducted on modulations,
topologies of converters, and configurations of the WPT coils to
reduce the magnetic field generated by the WPT coils [9–19].
Conductive plates are used to cancel the magnetic field ingeneral [12, 14]. However, a reduction in the magnetic field withthe conductive plates is small, and eddy current loss is generated
on the conductive plates [14]. Resonant shielding has been
proposed to reduce the magnetic field drastically [13, 15]. The
resonant shielding uses resonant capacitors connected to theadditional windings around the WPT coils to increase RMS
current of the additional windings [13, 15]. However, theeffective frequency band is limited by resonant frequency [13].
Active shielding has been proposed to solve the problems

with the conductive plates and resonant shielding [14–19].
Additional windings (canceling windings), which are connectedto additional power supplies or the main windings, are woundaround the WPT coils [14–19]. The canceling windings cancel
the magnetic field [14–19]. The advantage of the active shieldingis that radiation noise is decreased significantly because thephase and RMS values of the current are controllable [14, 15, 18,19]. However, the influence on the power transmission has notbeen discussed in detail. Moreover, a voltage or current rating of
the additional power supplies has not been discussed.
This paper proposes a novel design method for a lowradiation-noise WPT system with the active shielding. The
current of the canceling windings is designed with the operating
current when the WPT system is operated with the shortcircuited canceling windings. The RMS current of the cancelingwindings is increased with the additional power supplies such as
capacitive loads to inject reactance-compensation current.
Moreover, the influence of the electrical and magnetic
characteristics is clarified in a simulation and experiment of the
WPT system designed under the condition of the short-circuited
canceling windings. The advantage of the proposed method isthat the loss and capacity of the additional power supplies are
smaller than those of converters connected to the main windings
because the additional power supplies do not contribute to powertransmission. In addition, the magnetic field is adjustable withthe change of the RMS current of the canceling windings. As aresult, the reduction effects and influence on the transmission
power are revealed according to the injected current.
II. ACTIVE SHIELDING
A. Outline of Active Shielding
Figure 1 shows the schematic diagram of the active shielding.
The WPT coils are constructed with the same two circular coils
which the canceling windings (winding #2 or #4) are woundaround the main windings (winding #1 or #3). The cancelingwindings are connected to the additional power supplies tocompensate for the current of the canceling windings.
Magnetic field is generated by the current of the windings.
The magnetic field is proportional to the current of the windingTransmitting coil
Main windings:
Winding #1
Winding #3

Central axis of circular WPT coils

Power s upply forI 2 power trans mission

I1
V1

Ferrite core

V2

z

Load
V3

H ( r , , z )Canceling windings:
Ferrite core
Winding #2
Winding #4
r Receiving coil
Reference axis: central axis of circular WPT coils

I3

V4
I4

Additional
power supply

Fig. 1. WPT coils and active shielding.
I 2 L
Winding #2

Figure 2 shows the cross-section of the WPT coils, the selfinductance L and L of each winding, and the coupling
coefficients kc, kM, kad, and ksub between each pair of the windings.
The transmitting coils and the receiving coils are the same
configurations
for simplification.
The relationship between the．
．
current Im and voltage Vm of the winding #m is given by (2) with
the inductance matrix L when parasitic capacitance andresistance of the WPT coils is negligible.

Central axis of circular WPT coils
kc

Ferrite core

L

V1 
 I1 
 L11
 
 

V2  = j L  I 2  = j  L21
V 
I 
 L31
 3
 3

 L41
V4 
 I 4 

I1 Winding #1

ksub

coils. The equivalent self-inductance Leq and coupling
coefficient keq from the view of the main windings areformulated when the canceling windings are shorted.

kad

kM

z

I 3 Winding #3

Winding #4
LFerrite core
kc
I4
L
r
Reference axis: central axis of circular WPT coils
Fig. 2. Self-inductance and coupling coefficients of each winding.

L12

L13

L22

L23

L14   I1  
L24   I 2 
L34   I 3  
L44   I 4 

L32

L33

L42

L43

 kc

kM



 kad

 kad

1

 ksub

 kc

 kad   I 
 1 ksub   I 2  kc   I 3     I 4 when the magnetic field is the near field at the operational．
frequency of the WPT coils [16, 18, 19]. The magnetic field H(r,, z) at any measurement point (r, , z) is given by
4

4

m =1

m =1

(2)

Here  is the angular frequency, Lmm is the self-inductance of thewinding #m, and Lmn (m ≠ n, n = 1, 2, 3, and 4) is the mutual
inductance between the winding #m and the winding #n. The
diagonal component of L is the same.

H ( r , , z ) =  H m ( r , , z ) =  N m I m hm ( r , , z )4=  N m I m ( hrm er + h m eθ + hzm ez ) 1  kc= j L  kM  kad(1)

The coupling coefficient kmn is given by

m =1．
where H m (r, , z) is the magnetic field generated by the current Imof the winding #m (m = 1, 2, 3, and 4), Nm is the number of turnsof winding #m, hm (r, , z) is the vectorial transfer function, hrm,hm and hzm are the field components, and er, e, and ez are theunit vectors of the cylindrical coordinate system.
The active shielding reduces H(r, , z) with control of thecurrent of the canceling windings. The advantage of the active
shielding is that H(r, , z) is decreased significantly. However, it isgenerally difficult to design the whole WPT system. The numberof parameters, such as the current of the canceling windings andthe size of the components of the WPT coils, is larger than aconventional two-winding WPT system. Moreover, the selfinductance and the coupling coefficient of the WPT coils fromthe view of the main windings are changed due to magnetic flux
generated by the current of the canceling windings [13, 17]. The
parameter variation of the WPT coils changes the electriccharacteristics of the WPT system, such as the transmission
power and the whole efficiency. Thus, a design considering theparameter variation is necessary to achieve power transmission
and effective reduction of the magnetic field.
B. Parameter Variation
This section analyzes the parameter variation of the WPT

kmn =

Lmn
Lmm Lnn

(k

mn

 1)

(3).

The coupling coefficient kmn is determined by theconfiguration of the WPT coils. The number of turns of thewindings does not change kmn.
The self-inductance L is given by
L = Pmain N main 2(4),where Pmain and Nmain are the permeance and the number of turnsof the main windings, respectively.
The ratio  is given by=

Pcancel N cancel 2
Pmain N main 2(5),where Pcancel and Ncancel are the permeance and the number ofturns of the canceling windings, respectively.
The equivalent parameters Leq and keq are calculated with the

． ．
voltage condition (V2 = V4 = 0) and (2). The relationship of thevoltage and current of the main windings are expressed in (6)when the canceling windings are short [17].

V1 
 Leq
  = j V3 
 Leq keq

Leq keq   I1  
Leq   I 3 
 

(6)

．
the center of the gap of．
the WPT
coils.
The
z-axiscomponentHz．
and r-axis component H r of H are H z   hz1 N1 = H r   hr1 N1

hz2 N 2hz3 N 3hr2 N 2hr3 N 3(())

The equivalent self-inductance Leq is shown in ( kad + kc )2 − 2 (1 + k sub ) kc kad 
Leq = L 1 −

1 − k sub 2



(7).

The equivalent coupling coefficient keq is shown in

keq =

(

)

(

)

k M 1 − k sub 2 + k sub kad 2 + kc 2 − 2kc k ad

(1 − k ) − ( k
2

sub

2
ad

+ kc

2

) + 2k k k(8).

c sub adEquations (7) and (8) show that the current of the cancelingwindings decreases Leq from L, and changes keq from kM. Thus,
the WPT system should be designed with Leq and keq [17].
III. PROPOSED METHOD AND DESIGNING WPT SYSTEMS
A. Design Process used Proposed Method
Figure 3 shows the flowchart diagram of the proposed design
method. The proposed method focuses on the processes todetermine the current of the canceling windings after the processof making the WPT coils. The injected reactance-compensation
current is determined with the phase and RMS of the current
measured or calculated under the condition of powertransmission
when the canceling windings are short． ．
(V2 = V4 = 0). First, Leq and keq are calculated with measured L,
, kc, kM, kad, and ksub of the WPT coils. Second, the WPT system
is designed with Leq and keq. Next, the current phase and RMS ofeach winding are measured when the WPT system transmits
rated power. Then, the injected reactance-compensation current
is determined with the following equations.
The proposed method requires the．WPT coils．satisfing with
(2) and a linear relationship between H(r, , z) and Im. In particular,H(r, , z) is reduced by the WPT coils with windings of highquality factor significantly. The proposed method is useful toestimate whether the fundamental harmonics component of themagnetic field satisfies regulations of CISPR and ICNIRP
guidelines.
B. Injected Reactance-compensate Current of Canceling
Windings
This section describes how to decide the injected reactancecompensate current in the box． of red dashed enclosing line in
Fig. 3. The magnetic field H on the horizontal plane through at

 I1  
hz4 N 4   I 2 
hr4 N 4   I 3   I 4 

(
(

)
)

 hzmain N main I1 + I 3 + hzcancel N cancel I 2 + I 4 = hr N

I
−
I
+
hr
N
I
−
I
cancel cancel
24  main main 1 3(9),where Nmain is the number of turns of the main windings, Ncancel
is the number of turns of the main windings, hzmain and hrmain are
the field components of the main windings, and hzcancel andhrcancel are the field components of the canceling windings
because of the symmetry of the WPT coils in Fig. 2.
． When the canceling windings are short, the components of
H are expressed byPmain kc + kad 
N main I1 + I 3  hzmain − hzcancel
Pcancel 1 + ksub  H z  

=
  
 (10).
Pmain kc − kad  H r  
 N main I1 − I 3  hrmain − hrcancel P
cancel 1 − k sub 



(

)

(

)

Start
Making four-winding WPT coils as prototype or simulation model
Measuring L, , kM, kc, kad, and ksub
Calculating Leq and keq by (7) and (8)Designing overall WPT system with Leq and keq
Experiment or simulation of WPT system with short-circuited
canceling windings
Measuring or calculating current Im of each winding
Calculating vector components of hm (ex. hZmain and hZcancel )between magnetic field and current with experiment or simulation
Calculation of injectedreactance-compensate
current for proposed method
Calculating ratio Kamp_z and Kamp_r by (12)Calculating voltage V2 and V4 of canceling windingsby (13) to inject reactance-compensation current
FinishFig. 3. Flowchart diagram of design processes include proposed method.

Equations (10) shows that the magnetomotive force of thecanceling windings is the opposite phase to the magnetomotive
force of the main windings. The number Ncancel is not related toH. The z-axis component Hz is zero when the item of hzmain isequal to the item of hzcancel. However, Hz is not reduced enoughwith the short-circuited canceling windings because the item ofhzcancel is generally smaller than the item of hzmain. Reducing Hr
is also the same mechanism. The proposed method increases thecurrent RMS of the canceling windings in phase with theadditional power supplies to reduce H.
Ratio Kamp of the current RMS is given by

K amp =

I 2a
I
= 4a
I2s
I4s

(11)

．
．
where I2s and I4s are the currents of windings #2．
and #4．
when thecanceling windings are short, respectively, and I2a and I4a are thecurrents of windings #2 and #4 with the active shielding,respectively.
．
．
When the variations of I1 and I3 are negligible with theproposed method, zero Hr or Hz are achieved with proper Kamp.
The ratio Kamp_z and Kamp_r, which achieve zero Hr and Hz,
respectively, are shown inPcancel hzmain (1 + ksub ) K amp _ z Pmain hzcancel ( kc + kad )Pcancel hrmain (1 − ksub ) K amp _ r  Pmain hrcancel ( kc − k ad )


(12).

The ratio Kamp_z and Kamp_r are also evaluation criteria of theconfiguration of the WPT coils focused on H; the WPT coilswith Kamp_z and Kamp_r of around one should be designed. Large

Canceling winding

Main winding
Groove for main winding
Width: 15, Depth: 13(a) Top view of transmitting coil.

18

40 80

Unit: mm

Winding #4
Winding #3
Winding #1
Winding #2

Gap 2018

Unit: mm(b) Side view of overall WPT coils.
Fig. 4. Prototype of WPT coils.

Kamp_z or Kamp_r requires the large apparent power of theadditional power supplies to cancel H because the volume andloss of a power supply become larger as the larger capacity ingeneral. In particular, the additional power supplies are notneeded to achieve zero H at Kamp_z = Kamp_r = 1.
．
．
The voltage V2 and V4 of winding #2 and #4 are shown inksub   I 2 s 
(13).
 
1   I 4 s ．
．
The imaginary equivalent impedance Z2a and Z4a of theadditional power supplies are shown in
V2 
 1
  = j L K amp − 1  ksub
V4 

(

)



I  K amp − 1
V Z 2 a = − 2 = − j L 1 + k sub 4 s 
I 2a
I 2 s  K ampI 2 s  K amp − 1
V4
 Z 4 a = − I = − j L 1 + k sub I  K
amp
4a
4s 



(14).

．
．
Negative inductance is dominant in Z2a and Z4a because
active power for ksub is much smaller than reactive power of selfinductance in general WPT systems (|ksub| << 1). The additional
power supplies contribute to not the power transmission but the
reduction of the magnetic field around the WPT coils.
IV. EXPERIMENT AND ANALYSIS WITH PROTOTYPE
A. Equivalent Values Leq and keq of WPT Coils
Figure 4 shows the prototype of the WPT coils. The
prototype is made as the miniature model for WPT coils for thebattery charger in order to evaluate the proposed method. The
pot cores are made with ferrite (TDK, PC40). The main winding
is wound into the groove. The canceling winding is wound on
the outside of the pot core. The gap between the transmitting coiland the receiving coil is 20 mm. The number of turns Ncancel is
20 turns to increase the quality factor of the canceling windings.
Table I shows the parameters of the prototype. The
inductance, ESR, and coupling coefficients are measured with
the LCR meter (HIOKI, 3532-50). Measured and calculated Leq
and keq are also shown in Table I. The validity of (7) and (8) is
confirmed from an error of less than 0.5%.
B. Designing Circuit
Figure 5 shows the experiment circuit as the miniature modelof the WPT systems. Table II shows the experiment condition
with the experiment circuit. The input DC voltage Vin is 300 V,
the operational frequency fsw is 83.3 kHz, and the rated output
power Pn is 1 kW as the miniature model. The experiment circuit
is operated as the conventinal WPT system when the cancelingwindings are open (I2 = I4 = 0). Whereas, the experiment circuit
is operated with the active sheildng when the canceling windings
are short (V2 = V4 = 0) or connected to the additional power
supplies (Kamp ≠ 1). The operational frequency fsw, Vin and theoutput DC voltage Vout refer to WPT battery charging systems

for EVs. Output DC voltages Vout of 390 V and 295 V are
adjusted at I2 = I4 = 0 and V2 = V4 = 0 to transmit Pn, respectively.
Bipolar power supplies are used as the additional power supplies.
The resonant capacitors Cs1 and Cs2 are connected to the main
windings in serial to improve the power factor. The capacitanceof Cs1 and Cs2 is given by

Cs1 = Cs 2 =

1
 Leq

(15)

2

from the resonant condition.
TABLE I.

ELECTRIC AND MAGNETIC PARAMETERS OF PROTOTYPEParameter
Self-inductance of main windings L
Inductance ratio 
Coupling coefficient kM
Coupling coefficient kc
Coupling coefficient kad
Coupling coefficient ksub
ESR of main windings rmain
ESR of canceling windings rcancel
Number of turns of main windings Nmain
Number of turns of canceling windings Ncancel
Permeance of main windings Pmain
Permeance of canceling windings Pcancel
Measured
Equivalent self-inductance Leq
Calculated
Error
Measured
Equivalent coupling
Calculated
coefficient keq
Error
P1

Cs1
S1

Vin

S3

+

S2

Prototype of WPT coils
Cs2

i1
vpri v1

i3
v3 vsec

S4

Winding #1
Winding #2
P2

Value
580 H
0.187
0.275
0.229
0.185
0.267
1.03 
0.192 51 turn
20 turn
2.23×10-7 H
2.71×10-7 H
537 H
540 H
0.5%
0.224
0.224
< 0.2%

i2
v2

D1

D2

D3

+

Vout

D4

P4

Figure 8 shows the distribution of the magnetic field． ．aroundthe．
simulation
model
of
the
prototype.
The
current
Im (I1 = 3.91．
．
-j93.6°A, I2 = 0 A, I3 = 2.80 eA, and I4 = 0 A) in Fig. 7 (a) with theopen canceling windings are measured with the experiment. The
magnetic field is decreased by approximately 40 dB with theproposed method not only at the measurement point but also at
a distance from the simulation model of the prototype.
Central axis of circular WPT coils
Receiving coil
Ferrite core

Hz

EXPERIMENT CONDITIONS
SymbolVin
Vout

Rated output power
Switching frequency
Angular frequency
Dead time
Resonant capacitors

Pn
fsw
Tdead
Cs1, Cs2

MOSFETs
Diodes

S1 – S4
D1 – D4

Winding #4

Value / model number
300 V
295 V
Open (I2 = I4 = 0): 390 V
1 kW
83.3 kHz
5.24×105 rad/s
250 ns6.30 nF
Open (I2 = I4 = 0): 6.69 nF
SCH2080KEC (ROHM)
SCS220AE (ROHM)

Winding #3

Hr
Measurement pointof magnetic field

20
Winding #2

Winding #1

13

10

18
Ferrite core

z

6



15

20
40

r
Transmitting coil Unit: mm
Fig. 6. Simulation model and measurement point.

TABLE III.

Fig. 5. Experiment circuit.

Input DC voltage
Output DC voltage

Figure 7 showsHr, and H when Kamp and the phase． Hz, ．
difference  of I2s and I4s are changed. The magnetic field Hz
and H reach a minimum at Kamp_z and  = 0 deg. Whereas, Hrreaches a minimum at a Kamp of 1.00 and  = 10 deg. The error
between Kamp = 1.00 and Kamp_r occurs due to dimensional error.
In addition, H approaches to Hz because |hzmain| and |hzcancel| aremuch larger than hrmain and hrcancel at the measurement point.

500

Additional power supply

TABLE II.

Figure 6 shows the simulation model．as the prototype and themeasurement point. Table III shows Im, hm, Kamp_z and Kamp_r.
The measurement point is at a horizontal distance of 50 cm fromthe
． center of the gap as the representative. The standard current
Im is the measured values from the experiment when thecanceling windings are shorted.

P3

Winding #3
Winding #4
i4
v4

C. Simulation of Magnetic Field with Proposed Method
In this section, H is estimated with electromagnetic field
simulation (JSOL, JMAG-Designer) when the proposed method
is applied to the experiment circuit.

VECTORAL TRANSFER FUNCTIONS AND CONDITION
Parameter．
Current ．
I1 of winding #1
Current I．
2s of winding #2
Current ．
I3 of winding #3
Current I4s of winding #4
Vectoral transfer function h1 of winding #1
Vectoral transfer function h2 of winding #2
Vectoral transfer function h3 of winding #3
Vectoral transfer function h4 of winding #4

Value
3.96 A
2.10Kamp ej(144 + )° A
3.75 e-j92.3° A
2.00Kamp ej(126 + )° A
hrmainer + hzmainez
hrcanceler + hzcancelez-hrmainer + hzmainez-hrcanceler + hzcancelez

Vector component hzmain-2.43×10-3 /m-6.70×10-3 /m
Vector component hzcancel
Ratio Kamp_z
1.22
3.04×10-5 /m
Vector component hrmain
Vector component hrcancel
6.30×10-4 /mRatio Kamp_r
0.886*The measurement point of the magnetic field is shown in Fig. 5

RMS ratio Kamp

1.3
1.2

0.40

1.1

0.35

1.0

0.30

30

40

Phase difference  deg.

(a) Z-axis component Hz.

-3

5.0×10

1.0

-3

1.2

0.40

1.1

0.35

1.0

0.30

0.9

0.25

0.8

0.20

2.0×10-3

0.7

0.05

0.6

-3

1.0×100.6

00.5-40 -30 -20 -10

00.5-40 -30 -20 -10

0.10
20

6.0×10

1.1

1.3

0.7

0.15

10

-3

3.0×10-3

0.20

0

1.2

RMS valueof magnetic
field (A/m)
0.45

1.4

0.8

0.8

0.5
-40 -30 -20 -10

1.3

1.5

4.0×100.25

0.6

RMS valueof magnetic
field (A/m)
7.0×10-3

1.4

0.9

0.9

0.7

1.5

RMS ratio Kamp

RMS valueof magnetic
field (A/m)
0.45

1.4

RMS ratio Kamp

1.5

0

10

20

30

Phase difference  deg.

40

0.15

0.10
0.05
0

10

20

30

40

Phase difference  deg.

0(b) R-axis component Hr.
(c) Magnetic field H.
Fig. 7. Estimation of Magnetic field with electromagnetic field simulation.

Central axis of circular WPT coils

Central axis of circular WPT coils
Receiving coil

Central axis of circular WPT coils
RMS value ofmagnetic field (A/m)
1000
100
10
1
0.1
0.01

(a) Open canceling windings.

0Transmitting coil(b) Kamp = 1.0 and  = 0 deg.
(c) Minimum H (Kamp = 1.22,  = 0 deg.).
Fig. 8. Magnetic field around WPT coils.

0

Inverter output voltage vpri 500 V/div000

Current i1 of winding #1 10 A/div

0

0

0

Current i1 of winding #1 10 A/div

I1 = 3.96 A

Current i1 of winding #1 10 A/div
Rectifier input voltage vsec 500 V/div

Rectifier input voltage vsec 500 V/div

0

Current i1 of winding #1 10 A/div

Inverter output voltage vpri 500 V/div

I1 = 4.18 A

0Current i2 of winding #2 10 A/div

Current i2 of winding #2 10 A/div

Current i3 of winding #3 10 A/div

Current i3 of winding #3 10 A/div

I2s = 2.10 A

0

I2a = 2.73 A

0

I3 = 3.75 A
00Current i3 of winding #3 10 A/div

4 s/div0

Current i3 of winding #3 10 A/div

4 s/div(a) Open canceling windings. (b) Short-circuited canceling windings.
Fig. 9. Operating waveforms.

D. Operational Waveforms
Figure 9 shows the voltage and current vpri, vsec, i1, and i3 ofthe inverter and rectifier at Pn when the canceling windings areopen or short. The validity of designing Cs1 and Cs2 with Leq is
confirmed because the power factor of vpri and i1 is unity. The
DC output voltage Vout decreases as the equivalent mutual
inductance decreases to keqLeq.
Figure 10 shows the current im at Kamp = 1.00 and 1.30. The
RMS current I2 and I4 are increased by 1.30 times with the

0.001

I3 = 4.01 A
0Current i4 of winding #4 10 A/div

4 s/div

I4s = 2.00 A

Current i4 of winding #4 10 A/div

4 s/div

I4a = 2.61 A(a) Ratio Kamp = 1.00.
(b) Ratio Kamp = 1.30.
Fig. 10. Current of each winding.

additional power supplies.
E. Leakage Magnetic field
Figure 11 shows the fundamental component of Hz at themeasurement point when Kamp changes from 0.75 to 1.33. The zaxis component Hz is measured with the magnetic probe(Electro-Metrics Corporation, EM-6993). Only Hz in themagnetic field is measured because Hz is dominant in H at themeasurement point. The z-axis component Hz is 25.7 dBA
when the canceling windings are open. The fundamental

component of Hz is decreased by 39.5 dB at most with theproposed method. An error between Kamp_z and measurement
Kamp of minimum Hz is 6.2% because of an increase in I1 and I3
for the proposed method. Figure 10 (b) shows that a 5.6%
increase in I1 and a 6.9% increase in I3 with the proposed method.
The ratio Kamp at minimum Hz is changed to cancel the increased
magnetic field of the main windings.

Z-axis component Hz (dBA)

F. Variation of Electrical Characteristic
Figure 12 shows the input/output power P1 and P3, and active
30
25
20
15
10
5
Short (V2 = V4 = 0)
0 Calculated condition of zero magnetic field(Kamp_z = 1.22)
-5
-10
-15
0.6
0.8
1
1.2
1.4
Ratio Kamp of RMS current of winding #2 and #4
1400
Input power P1

Power (W)

1000
600
400
200
0

Input power P2 of winding #2 (green curve)
Input power P4 of winding #4 (blue curve)

-200
0.6
0.8
1
1.2
1.4
Ratio Kamp of RMS current of winding #2 and #4
Fig. 12. Input/output power of each winding.

Imaginary equivalent resistanceand reactance ()

30
20
10

.
Reactance Im (Z.2a): black line
Reactance Im (Z4a): red line.
Resistance Re (Z2a. ): black dashed line
Resistance Re (Z4a): red dashed line

0
-10
-20
-30
0.6

Imaginary equivalent impedance is given by (14)

0.8

1.0

1.2

P3 − P4
P1 + P2(16).

Note that the canceling windings are connected to the bipolar
power supplies at Kamp = 1.00 to compare  with the same circuit
configuration. The efficiency  is decreased as Kamp increases.
Thus, efficiency  is deteriorated by the injected reactancecompensated current to achieve the minimum H.

Output power P3

800

Figure 14 shows the efficiency  versus Kamp. The efficiency

 is given by=

Fig. 11. Fundamental component of Magnetic field Hz.

1200

power P2 and P4 of the canceling windings. The transmission
power (P3 - P4) increases as Kamp becomes large. The increase in
the transmission power should be given by decreasing in keqLeq
with the proposed method because the transmission power isinverse proportion to the equivalent mutual inductance in theseries-series compensated WPT system. In addition, the active
power P2 and P4 of the canceling windings are much lower than
the transmission power. Thus, it is verified that the main
windings transmit power, and that the canceling windings
cancels H with the proposed method.
．
Figure．13 shows the imaginary
equivalent
resistance
Re
(Z
2a)
．
．
．
．
and Re (Z4a) and reactance ．
Im (Z2a) and Im
(Z
)
of
Z
and
Z
4a
2a
4a
．
versus Kamp. Note that Re (Z2a) and Re (Z4a) are negative when
the bipolar power supplies are operated
generation mode. The． in．
imaginary equivalent． ． impedance Z2a and Z4a are calculated withthe measured Im, Vm and Pm of the canceling windings. The
additional power supplies are operated as the capacitive load
when．Kamp is morereactance． than 1. The imaginary equivalent．
．
Im (Z2a) and Im (Z4a) are much larger than Re (Z2a) and Re (Z4a).

1.4

Ratio Kamp of RMS current of winding #2 and #4．
．
Fig. 13. Imaginary equivalent impedance Z2a and Z4a versus ratio Kamp.

Figure 15 shows the estimated losses on the prototype of the
WPT coils. The copper losses of the windings are calculatedwith measured RMS values of im and ESR in Table I. The． ironloss is calculated with JMAG-Designer from measured Im. The
copper losses of the main windings are dominant. The copper
losses of the canceling windings are lower than the copper lossesof the main windings by 7.7% at Kamp = 1.30. Thus, the copper
loss of the main windings is clearly increased with the proposed
method, although the increase in the copper losses of thecanceling windings are negligible.
V. CONCLUSIONSThis paper proposed the low-radiation-noise WPT systemwith the injected reactance-compensation current as the active
shielding. In addition, the changes of the electrical and magnetic
characteristics are clarified when the proposed method is
employed. The RMS current of the canceling windings isincreased with the additional power supplies to inject thereactance-compensation current designed with the operation of
rated power transmission when the canceling windings are short.
The advantage is that the loss and capacity of the additional
power supplies are smaller than those of the converters
connected to the main windings. The experiment circuit
parameters are designed with the equivalent self-inductance and[3]Total efficiency  %

93.0
92.5
92.0
91.5
91.0
0.6

0.8

1.0

1.2

1.4

Ratio Kamp of RMS current of winding #2 and #4
Fig. 14. Efficiency of overall WPT system.
D: Copper loss of winding #4
E: Iron loss of ferrite cores

Loss (W)

20
20
18
18
16
16
14
14
12
12
10
10
88
66
44
22
00

A: Copper loss of winding #1
B: Copper loss of winding #2
C: Copper loss of winding #3

A B C D E

A B C D E

A B C D E

(I = I = 0)(V
field (K2 = V4 = 0)巻線4銅損
amp = 1.30)
巻線3銅損
鉄損Sim.よりキャンセルコイル開放
キャンセルコイル短絡
漏洩磁界最小Open
Short
Minimummagnetic
2
4
巻線1銅損
巻線2銅損

Fig. 15. Loss analysis of copper loss on each winding.

coupling coefficient of the prototype of the WPT coils when thecanceling windings are short.
As a result, the transmission power of 1 kW and radiationnoise reduction of 39.5 dB are achieved with the proposed
method. The calculated and measured RMS current of the lowest
magnetic field agreed with the error of 6.2%. The transmission
power of the WPT systems is increased as the decrease in themagnetic field with the injected reactance-compensation current.
The efficiency of the WPT systems is deteriorated by theincrease of the copper loss on the main windings due to theequivalent parameter variation of the WPT coils with theproposed method.
In the future, a current-compensation method will be
evaluated when position misalignments of the WPT coils occur.
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