General Analytical Model for Inductive Power
Transfer System with EMF Canceling Coils
Keita Furukawa, Keisuke Kusaka, and Jun-ichi Itoh
Department of Electrical Engineering, Nagaoka University of Technology, NUT
Niigata, Japan*E-mail: itoh@vos.nagaokaut.ac.jp, kusaka@vos.nagaokaut.ac.jp, archer_FK@stn.nagaokaut.ac.jp
Abstract- This paper provides an analytical model anddesign criteria of additional windings for reducing
electromagnetic field (EMF) generated from inductive powertransfer (IPT) systems. In particular, the canceling coils areconnected to the main transmission coils with common-mode
connection or differential-mode connection. Otherwise, thecanceling coils are short-circuited. Parameter variation,
which may degrade the system efficiency, occurs in the IPT
system due to the unwanted coupling between the maintransmission coils and the canceling coils. Therefore,
theoretical analysis of the IPT system with the canceling coils
is conducted in order to evaluate the effects of the EMF
shielding methods on the system parameter variation. The
calculation results of the system parameters agree to themeasurement results in the prototype of the four-windingtransformer with the error of lower than 5%.
Keywords— active shielding, electromagnetic
inductive power transfer, multiple magnetic couplingI.

field,INTRODUCTION

In recent years, inductive power transfer (IPT) systems
have attracted much attention in terms of safety andconvenient battery chargers for electrical vehicles (EVs)[1–5]. The IPT systems achieve power transmission usinga magnetic coupling without electrical contacts.
Electromagnetic field (EMF) should be considered
because EMF may cause health impairment or malfunctionof electrical equipment [5–7]. In particular, high-power
IPT systems such as quick battery chargers for EVs
generate higher level of EMF. Therefore, it is necessary to
reduce EMI noise to widespread use of the IPT system.
In order to reduce EMF, many studies have been
conducted on circuit topologies, modulation methods andconfigurations of transmission coils [5–13]. In particular,
non-resonant reactive shield and active shield, which arefocused on the configurations of the transmission coils,
have been proposed [11–13].
Non-resonant reactive shielding methods require
additional short-circuited coils in order to reduce EMF[11]. The magnetic flux induces a current which cancels
the leakage magnetic field in the short-circuited coils whena leakage magnetic flux crosses the short-circuited coils.
However, the EMF-reduction effectiveness is low at theplace far from the canceling coils because themagnetomotive force of the canceling coil is limited by theinterlinkage magnetic flux [11].
On the other hand, the active shielding method employs
canceling coils which are connected to the maintransmission coils or additional power sources [11–13]. In
this method, the current flowing in the canceling coils is
controllable with the main coils or the power sources.
Therefore, the cancellation of the magnetic field becomes
more effective compared to the non-resonant reactive
shielding method because the magnetic field generated by
the canceling coils are controllable [11].
The reduction effect of EMF by adding coils has beenreported in several papers [11–13]. Nevertheless, theinfluences on parameter variations of the transmission coil
due to the additional coils have not been analytically
discussed. In particular, the magnetic flux generated by thecanceling coils not only reduces the EMF but also crosses
the main coils as an interlinkage flux. Thus, the selfinductance and the mutual inductance of the entire
transmission coil are changed due to the additional coils.
This variation of the self-inductance changes the resonant
frequency. Thus, the transmission power or the efficiency
might be decreased compared that of the non-cancelingcoils. This problem in the past work is that the influencesof attaching the canceling coils to the entire IPT systems
are not discussed enough.
In this paper, the effect of the canceling coils is revealed
as focusing on the variations of the equivalent selfinductance and the equivalent mutual inductance of theentire transmission coil, which is theoretically analyzed
using a model of a four-winding transformer. The newcontribution of this paper is providing a general analyticalmodel and design criteria in order to reduce the parameter
verification for the EMF canceling coils. In particular, thecanceling coils are connected in parallel to the maintransmission coils when the non-resonant reactive
shielding method or the active shielding method are
introduced in order to reduce EMF of transmission coils
system. The equivalent self-inductances and theequivalent coupling coefficient taking into account the
influence of the canceling coils are calculated from a viewof the entire transmission system. Then, the calculation
results are confirmed with measurement of the equivalent
self-inductances and the equivalent coupling coefficient inWinding #1
Main coil

Path of leakage magnetic flux
Winding #2
Winding #3
Main magnetic path

Canceling coil
Outside of coil
Winding #4

Path of leakage magnetic flux

Inside of coil(a) Outline of transmission coil.
(b) Front view with magnetic paths.
(c) Configuration of coil at one side.
Fig. 1. Investigated model of transmission coil as example. The solenoid-type transmission coil with the canceling coils (winding #2 andwinding #4). EMF upper and under cores is reduced by the canceling coils.

prototypes of the four-winding transformer. Moreover, theeffect of EMF reduction is simulated when the prototypes
are installed to the 1-kW IPT systems.
II.

CONFIGURATION OF TRANSMISSION COILSIn this section, the equivalent self-inductance and theequivalent coupling coefficient are formulated by a modelof the multi-winding transformer when the canceling coils
are connected to the main coils in parallel or shortcircuited. The equivalent self-inductance is defined as selfinductances from a view of a primary side or secondaryside of the entire transmission coil. The equivalent
coupling coefficient is defined as a coupling coefficient
between the primary side and the secondary side. Both ofthe equivalent values are essential to design a resonant
frequency and a transmission power for IPT systems.
A. Analytical Model with Four-winding Transformer
Figure 1 shows the schematic of the analyzed
transmission coils. Although following analysis is possible
to be applied to general transmission coils, which fulfill
some conditions as mentioned later, the solenoid-typetransmission coil is analyzed as an example. The
transmission coil behaves as the four-winding transformer.
In order to avoid the additional core, the canceling coil is
wired on the same core of the main coil. The main coils,e.g., winding #1 and winding #3, are wired on the cores tothe form of the solenoid coils, whereas the canceling coils,e.g., winding #2 and winding #4, form a pair of the serial
rectangular coil. As shown in Fig. 1(a), the canceling coils
are placed on the outside of the primary and secondarycores in order to reduce EMF which emits in the directionof the upper and below the transmission coils.
Due to the placement of the canceling coils, the mutual
inductances between following windings, e.g., winding #2
and winding #3, winding #2 and winding #4, and winding#4 and winding #1, are negligibly weak. Thus, therelationship between current and voltage of each coil in
Fig. 1 is expressed by the four-order inductance matrix as v1   L11 L12 L13 0   i1 
  
  
0  d  i2  v2   L12 L22 0
v    L
0 L11 L12  dt  i3 
 3   13  
v   0
0 L12 L22   i4  4 

 1
kc 
kM
0   i1   kc 00  d  i2  L   (1),01k c   dt  i3 
 kM
 0
0
kc 
   i4 where vm and im (m = 1, 2, 3, and 4) are the input voltage
and the current of the winding m , Lmm is the selfinductance of the winding m, and Lmn (m ≠ n,n = 1, 2, 3, or 4) is the mutual inductance between thewinding m and the winding n, respectively. Here, L isequal to L11. Note that kM and kc are the coupling
coefficients between the main-coil to the main-coil or thecanceling-coil, respectively. Moreover,  is the inductanceratio L13 / L.
Figure 2 shows the connection diagrams of the nonresonant reactive shielding method and the active
shielding method. In the active shielding method, both ofthe cases, where the canceling coils are connected as thecommon-mode coils and the differential-mode coils, areconsidered. In particular, the common mode coils result in
the positive mutual inductance between the parallelconnected coils, whereas the negative mutual inductance
between the parallel-connected coils occurs in the
differential mode coils.

III.

CALCULATION OF EQUIVALENT PARAMETERS

A. Inverse Matrix of Inductance Matrix
In order to clarify the equivalent self-inductance and theequivalent coupling coefficients, the inductance matrix is
calculated. It is convenient to calculate the current of thecoils from the input voltage with the inverse matrix of theinductance matrix when conditions of the input voltage isdecided as shown in Fig. 2. The relationship between
current and voltage of each coil in Fig. 1 is also expressedby a four-order inverse matrix in (2) (bottom of next page)and (3)

det L   L 1  kc  1  kc   kM 2 .................... (3).
22where detL is the determinant of the four-order inductancematrix in (1).

B. Short-circuited CoilWhen the canceling coils are shorted as shown in Fig.
2(a), the input voltage is v1 = vp, v3 = vs and v2 = v4 = 0.
Hence, the input current is expressed by
 1  kc 2  v p dt   kM  vs dt
 i1    k 1  k 2 v dt   k k v dt 
 
i
c
c
p
c
M
s

 
 2 1 2

 i3  det L  kM  v p dt   1  kc  vs dt


 


 i4 
2
 kc kM  v p dt   kc 1  kc  vs dt .................................................................................... (4).
In addition, the conditions of the input current i1 = ip,
i3 = is are considered. The relationship between thevoltage and the current of the entire transmission coils isshown as
 i p   i1  1  kc 2 kM    v p dt ...... (5),     
2 
 is   i3  det L  k M 1  kc    vs dt Winding #1

ip






Leq _ short

L12

L13

Winding #1

ip

L22

0

0
0

L11
L12

1









Leq_com



















Winding #4

keq_shortPrimary side

Secondary side Winding #3
i3

kM

is
vs

L

kc

kc

L

Winding #1

ip

i4

L

CommonWinding #4

keq_comPrimary side

Secondary side Winding #3

i1

vp

i3

kM

L
i2

L

kc

kc

L

Leq_dif

Leq_com

is
vs

i4

L
Differential

Winding #2

Leq_dif

Winding #4

keq_dif(c) Canceling coils connected as differential-mode coils.
Fig. 2. Connection diagrams of main coils and canceling coils.

v3 = v4 = vs. Hence, when the canceling coils are connectedto the main coils as the common-mode coils as shown in
Fig. 2 (b), the input current is expressed by (9).
In addition, the conditions of the input current ip = i1 + i2,
is = i3 + i4 are considered. The relationship between thevoltage and the current of the entire transmission coils isshown in (10) and (11) (next page), where Lpeq_com is theequivalent self-inductance of the primary side, Lseq_com isthe equivalent self-inductance of the secondary side, andMeq_com is the equivalent mutual inductances between the
primary side and the secondary side. The equivalent selfinductance Leq_com (= Lpeq_com = Lseq_com) and the equivalent 1  k   k
  kc 1  kc 2

 k M2

 kc k M

2cM

 kc k M 1  kc 2  kc k M  kc 1  kc

2








Leq_short(b) Canceling coils connected as common-mode coils.






i4

L

Winding #2

    k 1  k 2 v dt     k k v dt 
c
c
c
M  s
 p


 i1 
22
 
 1   kc 1  kc  k M  v p dt    kc kc k M  vs dt  i2   1 
 i3  det L      k k v dt     k 1  k 2 v dt 
c
M  p
c
c
s 
 

 i4 
22
   kc kc k M  v p dt  1   kc 1  kc  k M  vs dt 





kc

L
i2

  1  kc 2
 v1dt    k 1 k 2
 v dt 
2
c
c

1



 v dt  det L  kM 3 



v dt
 kc k M
 4 




vs

L

kc

i1

vp

kM
.................................. (8)1  kc 2

0 

0 
L12 

L22 

i2kMis(a) Short-circuited canceling coils.

C. Commom-mode CoilThe conditions of the input voltage is v1 = v2 = vp and i1   L11
  
 i2    L12
 i3   L13
   i4   0

Leq_short







L

L

Leq _ short  L 1  kc 2 ............................................... (7)M eq _ shortvp

Winding #2

 v p   Lpeq _ short M eq _ short  d  i p      
 vs   M eq _ short Lseq _ short  dt  is 
 1  kc 2
kM  d  i p  L    ........................ (6),
1  kc 2  dt  is  kM
where Lpeq_short is the equivalent self-inductance of the
primary side, Lseq_short is the equivalent self-inductance ofthe secondary side, and Meq_short is the equivalent mutual
inductances between the primary side and the secondaryside.
Through the calculation, the self-inductance and thecoupling coefficient of the entire transmission coil arechanged from the original values L and kM, respectively.
Theequivalent
self-inductance
Leq-short(= Lpeq_short = Lseq_short) and the equivalent coupling
coefficient keq_short are expressed in (7) and (8).

keq _ short 

Secondary side Winding #3
i3







Primary side

i1









 v1dt   v dt kc k M
2


 (2)
2 
v dt   kc 1  kc
  3 
1  kc 2  kM 2    v4 dt 

 kc k M
2

2

 






(9)

coupling coefficient keq_com are expressed in (12) and (13).

Leq _ com 







 L 1  kc  1    2kc   kM
22

 .... (12)  2  k  1  kk   k 1  k  1    2k    k22c

Leq _ dif 

keq _ com M

Leq _ com

keq _ dif c  2  k  1  k

c

2



k M   kc

D. Differential-mode CoilThe conditions of the input voltage is v1 = -v2 = vp andv3 = -v4 = vs when the canceling coils are connected to themain coils as the differential-mode coils as shown in Fig.
2 (c). Hence, the input current is expressed by (14).
In addition, the conditions on the input current ip = i1 - i2,
is = i3 - i4 are considered. The relationship between thevoltage and the current of the entire transmission coils isshown in (15) and (16), where Lpeq_dif is the equivalent selfinductance of the primary side, Lseq_dif is the equivalent
self-inductance of the secondary side, and Meq_dif is theequivalent mutual inductances between the primary sideand the secondary side. The equivalent self-inductance
Leq_dif (= Lpeq_dif = Lseq_dif) and the equivalent coupling
coefficient keq_dif are expressed in (17) and (18).





2
M

2

1  k 1    2k   k2c2................ (18)

M







2


2
2

   kc k M
 i p   i1  i2    v p dt 
1    2  kc  1 1  kc  k M
   



2

 is   i3  i4  det L    kc k M
  2  kc  1 1  kc 2  kM 2    vs dt 
 v p   Lpeq _ com M eq _ com  d  i p      
 vs   M eq _ com Lseq _ com  dt  is 2   2  k 1 1 k 2  k 2  kc k M c Mc d  ip L  
22
  2  kc  1  k M 2   kc k M
  2  kc  1 1  kc 2   kM 2  dt  is 














































   kc 1  kc 2  v p dt     kc k M  vs dt 
 i1 22
 
  1   kc 1  kc  k M  v p dt    kc kc k M  vs dt 
i
1
2
 


 i3  det L      k k v dt     k 1  k 2 v dt 
c
M  p
c
c
s

 


 i4 
22
   kc kc k M  v p dt   1   kc 1  kc  k M  vs dt 2   2  k 1 1 k 2  k 2   kc k M
ccM i p   i1  i2    v p dt 1   2 is   i3  i4  det L    kc k M
  2  kc  1 1  kc 2  kM 2    vs dt 
 v p   Lpeq _ dif M eq _ dif  d  i p      
 vs   M eq _ dif Lseq _ dif  dt  is 2   2  k 1 1 k 2  k 2



k
kM
c
c
M
c

 d  ip L  
22
  2  kc  1  k M 2   kc k M
  2  kc  1 1  kc 2  kM 2  dt  is 






























(10)

(11)

(14)































 .... (17)E. Design Criteria of Canceling Coils
Figures 3 and 4 show the contour diagrams of theequivalent coupling coefficients and the equivalent selfinductances derived from Eqs. (7–8, 12–13, 17–18),
respectively. It is noted that the coupling coefficient kM isfixed at 0.2, whereas the coupling coefficient kc and theself-inductance ratio  are variables. In particular, kc isadjusted by changing installation location andconfiguration of the canceling coils, whereas  is also
adjusted by changing the number of the turns of thecanceling coils.
Figure 3(a) shows that keq_short is improved by increasingkc, whereas keq_short is not varied by . Meanwhile, Fig. 4(a)shows that the Leq_short is decreased by increase kc, and
Leq_short is not also varied by . Hence, the parametervariation with the short-circuited canceling coils is not
influenced by the number of the turns of the cancelingcoils.

M................................................................................... (13)



c

c

2

c



2

M

2

M eq _ com L 1  kc 2  1    2kc   kM 2

















(15)

(16)

keq_short = 0.3

Coupling coefficient kc

0.5
0.4
0.3
0.2
0.1
2

4

6

keq_c

om =

0.3
0.2

0.0
0

10

8

0.5
0.4

Self-inductance ratio 

2

4

6

0.2

keq_dif = 0.6
keq_dif = 0.5
keq_dif = 0.4

0.6

keq_dif = 0.3

0.5
0.4
0.3

keq_dif = 0.2

0.2
0.1

0.0
0

10

8

0.7

0.8

keq_com = 0.3

0.6

0.1

keq_short = 0.2

0.0
0

0.7

= 0.1

0.6

keq_com = 0.6
keq_com = 0.5
keq_com = 0.4

0.8

keq_dif = 0.7

keq_dif = 0.8

Coupling coefficient kc

keq_short = 0.6
keq_short = 0.5
keq_short = 0.4

keq_com = 0.1

0.7

0.8

keq_com = 0.7

keq_com = 0.8

k eq_dif

keq_short = 0.7

keq_short = 0.8

Coupling coefficient kc

keq_short = 0.9

2

Self-inductance ratio 

4

6

10

8

Self-inductance ratio 

0.8

0.7

0.5

0.7

0.5
0.6
0.7
0.8

0.6

0.9

0.6

0.6

0.7
0.5
0.8

0.4

0.9

0.3

4

6

Self-inductance ratio 

8

0.2
0.1

L
2

0.3

10

0.0
0

2
0.1 0.2 0.3

L eq _ com

8
0.

0.0
0

0.4

0.6
0.5 0.4

L eq _ short

0.1

0.5

0.7

0.2

0.8

Coupling coefficient kc

0.3
0.4

Coupling coefficient kc

0.8

9
0.

Coupling coefficient kc(a) Short-circuited.
(b) Common mode.
(c) Differential mode.
Fig. 3. Relationship among equivalent coupling coefficients, coupling coefficient between main coil and canceling coil, and self-inductanceratio. The coupling coefficient kM is 0.2. Variation range of the coupling coefficient between the main coil and the canceling coil kc is from 0 to
0.89, whereas range of the self-inductance ratio is from 0 to 10.

6

Self-inductance ratio 

8

0.2

0.7

0.3

0.6

0.4

0.5

0.5

0.4

0.6

0.3

0.7

0.2

0.8

L eq _ dif

0.1

L
4

0.1

10

0.0
0

L
2

4

6

8

10

Self-inductance ratio (a) Short-circuited.
(b) Common mode.
(c) Differential mode.
Fig. 4. Relationship among ratio of equivalent self-inductances to self-inductance of main windings, coupling coefficient between main coils
and canceling coils, and self-inductance ratio. Conditions of kM, kc, and  are same as in Fig. 3.

Figure 3(b) shows that keq_com is improved by increasing
kc or . Figure 4(b) shows that Leq_com is decreasing due tothe increase in kc or the decrease in . Thus, in order toavoid the parameter variation which is caused by thecommon-mode-connected canceling coils, not only the
number of the turns of the canceling coils should bedesigned larger than the number of the turns of the main
coils, but also the canceling coils have to be placed close
to the main coils.
Figure 3(c) shows that keq_dif is improved in the range ofhigh kc and high . Meanwhile, Fig. 4(c) shows that Leq_dif
is decreasing due to the high kc and the decrease in .
Therefore, not only the winding turn should be muchlarger than the main coils, but also the canceling coils haveto be installed apart from the main coil in order to avoid
the parameter variation which is caused by the differentialmode-connected canceling coils.
However, setting the canceling coils apart from themain coils degrades a canceling performance of EMF.
There is the trade-off between the parameter variation(decreasing of the equivalent self-inductance) and thecanceling performance. Thus, an operation frequency or
the construction of a transmission coil should beredesigned, when the canceling coils are installed in orderto reduce EMF.
As a conclusion, it is shown that the design criteria forthe three connection methods of the canceling coils at theview point of avoiding the parameter variations as follows:
1) the short-circuited connection (non-resonant
reactive shield) the long distance between the main coils and thecanceling coils.
 the low self-inductance of the canceling coils.
2) the common-mode connection
 installation of the canceling coils by the main coils.
 twice times or more the number of the turn of thecanceling coils compared with the main coils.
3) the differential-mode connection
 the long distance between the main coils and thecanceling coils.
 twice or more the number of the turn of thecanceling coils compared with the main coils.
The advantage of avoiding the parameter variations is
reducing the mismatch between the operation frequency
and the resonant frequency, which is necessary to operate
IPT systems under the conditions of the high efficiency
and the high power transmission.
IV.

EXPERIMENTAL VERIFICATION WITH PROTOTYPE
TRANSMISSION COIL

The self-inductances and the mutual inductances of thewired coils are measured in order to confirm Eqs. (7–8,
12–13, 17–18) with the prototype four-windingtransmission coil.

Winding #1 (main coil) Winding #2 (canceling coil)

145

200

65

65

190

190

16

Gap 120

16
Winding #3 (main coil) Winding #4 (canceling coil)

195
280

Prop of primary-side core

Unit: mm(a) Front view.
(b) Top view.
(c) Side view.
Fig. 5. Outline of prototype four-winding transmission coils. The main coils are wired on center of the cores (winding #1 and winding #3). The
canceling coils are put on top of the primary core and bottom of the secondary core (winding #2 and winding #4). The canceling coils construct
the serial two coils. The four props support the primary-side core.
Table I. Experimental results: equivalent coupling coefficient and inductances of prototype four-winding transformer.
Connection of canceling coils
Short-circuited
Common mode
Differential mode

 399 432 70.4 12.2  432 3120 12.8 6.7  [H]
 70.5 12.8 393 422  12.2 6.7 422 3010 

Inductance matrix as 4-winding transformer

Measured value
Measured value
Measured value
Measured value
Measured value
Equivalent primary self-inductanceCalculated value
Error of calculated equivalent primary self-inductance
Measured value
Equivalent secondary self-inductanceCalculated value
Error of calculated equivalent secondary self-inductance
Measured value
Equivalent mutual inductanceCalculated value
Measured value
Equivalent coupling coefficient
Calculated value
Error of calculated coupling coefficient

396 H
7.94
0.382
0.178
396 H394H
0.6%
391 H394H0.7%
73.0 H
72.1H
0.185
0.183
1.2%

Self-inductance of main winding L
Self-inductance ratio 
Coupling coefficient kc
Coupling coefficient kM

Figure 5 shows the prototype of the transmission coil.
In order to shield EMF on the top and below, the cancelingcoils shaped double-D are put on the outside cores. The
core material is ferrite (TDK Corp., N87). The number ofturns of the main coils is 30 with 3.5-mm2 insulated wires,
whereas the number of turn of the canceling coils is 130
with enameled wires. Note that the number of turns of the
primary side and the secondary side are the same.
Table I shows the measurement results of the four-orderinductance matrix, the equivalent self-inductances and theequivalent coupling coefficients in the each connection. In
order to compare the equivalent self-inductance, theequivalent mutual inductance, and the equivalent coupling
coefficient, both the measured values and the calculated
values are shown.
In particular, the calculated values of the equivalent
self-inductances correspond to the measured values with amaximum error of 2.7%. The self-inductance is theimportant factor because the IPT system should bedesigned to resonate at the transmission frequency. Thus,a precise calculation is crucial for the design of the IPT
system. Besides, the maximum error of the equivalent
coupling coefficients is 4.9%, which is larger than the errorof the equivalent self-inductance because of the influenceof the ignored magnetic coupling between following

334 H
338H
1.3%
332 H
338H
1.9%
67.5 H
70.4H
0.203
0.208
2.7%

236 H
241H
2.3%
235 H
241H
2.7%
43.3 H
46.6H
0.184
0.193
4.9%

windings, i.e., winding #2 to winding #3, winding #2 towinding #4, and winding #4 to winding #1.
V.

EMF REDUCTION WITH CANCELING COILS

A. Circuit and Model Configuration
In order to confirm the effect of the EMF reduction, theprototype transmission coil is simulated with JMAG
(JSOL Corporation). JMAG is a software for theelectromagnetic field analysis with a finite element
method.
Figure 6 shows the circuit configuration in thesimulation model, whereas Table II shows the
specification of the circuit. The IPT system is constructedwith S/S topology, which has the resonant capacitors
connected to both of the primary side and secondary sideof the transmission coil in series. The input voltage is thesinusoidal wave for focusing on fundamental frequency.
The capacitances of the resonant capacitors Cs1, Cs2 aredecided in order to resonate with the considered L at aresonance frequency of 84.75 kHz. Noted that operating
frequency is decided by the resonant conditions of theresonance capacitances and the equivalent self-inductancesuch as Leq_short, Leq_com, or Leq_dif. The output power is 1
kW by adjusting the value of the equivalent load resistancekM ,keq_short ,keq_com ,keq_dif
ffshort
fcom
fdif

Cs1
Vin
cos inL
Leq_short
Leq_com
Leq_difL
Leq_short
Leq_com
Leq_dif

Cs2
Req

Equivalent circuit of prototype four-winding transmission coilFig. 6. Circuit configuration of simulation model. The prototype four-winding transformer is equivalent to the two-winding transformer when thecanceling coils are shorted or connected to the main coils in parallel. For individual connection such as when the canceling coils are shorted, theequivalent self-inductance, the equivalent coupling coefficient and the operation frequency are chosen Leq_short, keq_short and fshort differently.
Winding #2 (canceling coil)
10

200

20

16

Winding #1 (main coil)
Case

Core

230

Gap: 120

Winding #3 (main coil)

Winding #4 (canceling coil)

195
280

350
Unit: mm105(a) Front view.
(b) Top view.
(c) Side view.
Fig. 7. Outline of CAD model of prototype four-winding transmission coil. The size of the cores and the cases matches the prototype fourwinding transformer; the coils are constructed as the solid model, and the material of the cores is PC40. The cases are treated as air, whereas the
thickness of the cases and the main coils is 5 mm.
Table II. Simulation conditions.
Parameter
SymbolValue
Input AC voltage
Vin
252 Vrms
Rated powerP
1.0 kW
Operation frequency
f84.75 kHz
without canceling coils
Operation frequency offshort95.00 kHz
short-circuited operation
Operation frequency offcom
85.40 kHz
common-mode operation
Operation frequency of
fdif
115.5 kHz
differential-mode operation
Resonant capacitors
Cs1 ,Cs2
8.56 nF

Req because the output current of the S/S resonant circuit
is inversely proportional to the equivalent mutual
inductance of the transmission coil at the LC resonance.
Figure 7 shows the computer-aided-design (CAD)
model of the transmission coil on JMAG. The structure
and the size of the CAD model are based on the prtototype
four-winding transmission coil as shown in Fig. 5. The
wires are expressed as the colored solid models. Noted thatthe eddy current and hysteresis loss are not considered.
B. EMF Reduction Effect with Canceling Coils
Figure 8 shows the simulation results of the magnetic
flux distribution under the each condition. The result isobtained on the cross-section of the center of thetransmission coil as a representative case. Note that the
input power factor cos in is unity when the operation
frequencies of Fig. 8(a)–(d) are 84.75 kHz, 95.00 kHz,85.40 kHz, 115.5 kHz, respectively.
The flux distributions on the top and bottom of thetransmission coils decreases with the short-circuitedconnection and differential-mode connection incomparison with the flux distribution without thecanceling coils. The magnetic flux distribution of Fig.
8(a)–(d) are 13.8 T, 9.41 T, 12.6 T, and 8.06 T at the
50-cm bottom of the secondary core as the representativevalues, respectively. In addition, the magnetic density at
the outside of the canceling coil decreases by the cancelingcoils. Moreover, the effect of EMF reduction is more
effective with the differential operation than that with theshort-circuited connection.
VI.

CONCLUSION

In this paper, the effect of the canceling coils on theparameter variation of the IPT system was consideredregarding to the equivalent self-inductance and theequivalent coupling coefficient. Three connection
methods of the canceling coils, i.e. the short-circuitedconnection, the common-mode connection and thedifferential-mode connection, were evaluated.
The calculated equivalent values agreed with themeasured values through the inductance measurement
using the prototype transmission coil attached thecanceling coils. The relative error between the calculated
values and measured values was 4.9%.
In addition, EMF reduction near the canceling coils
were confirmed with the short-circuit connection (by 32%)
and the differential-mode connection (by 41%) in thesimulation using JMAG.
Above of the results, the design criteria focusing on
avoiding the parameter verifications are as follows: the canceling coils far from the main coils at the
short-circuited connection.
 the canceling coils closed to the main coils with

Magnetic
flex density
T
10-1
10-2
10-3
50 cm

10-4

50 cm

13.8 T

9.41 T

10-5
10-6(a) Without canceling coil.

(b) Short-circuited coil.
Magnetic
flex density
T
10-1
10-2
10-3
10-4

50 cm

50 cm

12.6 T

8.06 T

10-5
10-6(c) Common-mode coil.
(d) Differential-mode coil.
Fig. 8. Magnetic flux distribution of prototype transmission coil. The transmission coils are placed at the center of the contour plots (orange or
yellow area). The upper-side core is the primary side. The bottom-side core is the secondary side. Note that the operation frequency is different
for each the simulation conditions, which are shown in Table II. Transmission powers of without-canceling coil, short-circuited connection,common-mode connection and differential-mode connection are 991 W, 1.16 kW, 1.03 kW and 1.27 kW, respectively.

the large number of the turn at the common-mode
connection.
 the canceling coils far from the main coils with thelarge number of the turn at the differential-mode
connection.
Future plans are considerations of the parameter
verifications introduced cross couplings between
canceling coils.
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