Analysis of Wireless Power Transfer System
Employing Active Shielding with Virtual Inductanceand Two-port Equivalent Circuit
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 an activeshielding method to reduce EMF of wireless power transfer (WPT)
systems. Additional power supplies and two windings cancel
magnetic field generated by the WPT coils with only reactive
power. The advantage of the proposed method is that the capacityof the additional power supplies are small. The parametervariation of the WPT coils and the magnetic field are calculatedwith a two-port equivalent circuit which the additional power
supplies are replaced to virtual inductance in. As a result, themagnetic field decreases by 27.2dB with the proposed method. In
addition, the transmitting power is increased as the magnetic field
becomes smaller because the equivalent mutual inductance isreduced.
Keywords—active shielding, equivalent circuit, leakage magnetic
field , wireless power transfer

I. INTRODUCTION
Electric vehicles (EVs), which do not emit CO2 duringrunning, are becoming increasingly popular [1]. Battery chargers
with cables are mainly used to charge batteries in EVs when EVs
are parked in parking places [1]. Howerver, the battery charging
process is a burden to users [1]. In addition, electric shock is oneof serious risks when the users touch metallic contacts [1].
Wireless power transfer (WPT) systems have been attracted
as battery charging systems of EVs to solve the issues [1–4]. The
WPT coils generate large radiation noise during the charging
operation of the WPT [1]. Electric devices or human bodies near
the WPT system are harmed by the radiation noise [1]. Thus, thepermissible level of the radiation noise is regulated by various
regulations, e.g. the International Commission on Non-Ionizing
Radiation Protection 2010 guidelines and International Special
Committee on Radio Interference guidelines [5–8].
Many methods conducted on modulations, topologies of
converters, and configurations of the WPT coils have beensuggested to reduce the magnetic field [9–19]. Metallic plates orrings are used to cancel the magnetic field with eddy current ingeneral [12, 14]. However, a reduction in the magnetic field issmall, and the tempreture of the metallic plates or rings is rised
due to eddy current loss. Resonant shielding has been proposed
as a method to further reduce the magnetic field [13, 15]. The

resonant shielding uses capacitors and additional windings. The
capacitors are connected to the additional windings around the
WPT coils. The RMS current flowing on the additional windings
is increased with resonance between inductance of the additional
windings and capacitance of the capacitiors [13, 15]. However,
the effective frequency band is limited by design of the resonant
frequency [13].
Active shielding has been proposed to solve the issues withthe metallic plates or rings, and resonant shielding [14–20]. The
active shielding uses additional windings (canceling windings)
and power supplies. The canceling windings wound around the
WPT coils, are connected to the additional power supplies or themain windings [14–20]. The additional power supplies control
the current of the canceling windings to reduce the magnetic
field with effect [14–20]. Thus, the advantage of the active
shielding is not only that radiation noise is decreased
significantly but also that the magnetic field is adjustabledepending on the load [14, 15, 18, 19].
The design method of the active shielding using injectedreactance-compensation current has been suggested [20].
Moreover, electrical and magnetic characteristics are clarified
with the design method [20]. The current flowing on thecanceling windings and the output voltage of the additional
power supplies are calculated with the operational current when
the canceling windings are short [20]. The features of the design
method are that the loss and capacity of the additional power
supplies are small, and that how to adjust the magnetic field isdemonstrated [20]. However, the operational condition atminimum leakage magnetic field and transmitting power does
not agreed with the designed values, because influence of thechange in the current of the canceling winidngs is not considered.
This paper proposes an active shielding method based on theresonant shielding. In addition, the electrical and magnetic
characteristics are shown with a two-port equivalent circuit of
the WPT coils. The additional power supplies output only
reactive power to cancel the magnetic field. The advantage ofthe proposed method is that the small-capacity additional power
supplies are available because the canceling windings do not
donate the power transmission. Moreover, suitable operating
condition at zero leakage magnetic field at a measurement point

Canceling winding(Ncancel = 15 turn)

Receiving coil
18

Winding #4
Winding #3
Winding #1
Winding #2
Transmitting coil

20 GapFerrite core (TDK, PC40)

18

Main winding(Nmain = 55 turn)
Groove for main winding
Width: 15, Depth: 13(a) Side view of WPT coils.
Fig. 1. Prototype of WPT coils.

Cs1 6.30 nF (Open canceling windings) Cs2 6.30 nF (Open canceling windings)
6.68 nF (Proposed method)
Po ut
6.69 nF (Proposed method)
Rated power: 600 W
Prototype of WPT coils+

Winding #1
Switching frequency f: 83.3 kHz( = 5.24×105 rad/s )Dead time: 250 ns
MOSFET: SCH2080KEC (ROHM)
Winding #2
A.C. power supply

i2
v2

L

L

kad
kc

kc

L

ksu b

v3 vsec

+

v4

i4

Leqs

kM

Cs1

i1
v1

vpri

177 V
(Proposed
method)Winding #3 Diode: SCS220AE (ROHM )Parameters of WPT coils:
L = 595 mH,  = 0.112, kM =0.282,
kc = 0.231, ka d = 0.186, ksub = 0.254
Winding #4

L

Meq

Leqp

kM

i3

Unit: mm(b) Top view of transmitting coil.

300 V

i1
vpri v1

40 80

Winding #1
Winding #2

2L

Cs2

i3
L

L

ka d

kc

i
v2 2

L

v3

vsec

Req

Winding #3

kc

Winding #4

i4v4

L

4L

ksu b

Prototype of WPT coils

A.C. power supply(a) Equivalent circuit using virtual inductance.

Fig. 2. Experient circuit and conditions.

ip = i1
vpri
vp = v1

Figure 2 shows the circuit diagram and the conditions of theexperiment. The input DC voltage is 300 V. The resonantcapacitors are connected to the main windings in series for
power factor compensation. The load is the 177-V DC power
supply because of the battery load. The parameters of the WPTcoils in Fig. 1 (the self-inductance of each winding and thecoupling coefficients between each windings) are also shown in
Fig. 2. Note that the parameters of the circuit in Fig. 2 aredesigned to achieve 600-W transmitting power and the resonantcondition when the canceling windings are short.
B. Equivalent Circuit of WPT Coils and EquivalentInductance
Figure 3 shows the equivalent circuit of the WPT coils andthe two-port equivalent circuit. The additional power supplies
are replaced to the virtual inductance in the equivalent circuit.

Leqp

Cs2
is = i3

Leqs

vsec
vs = v3

Req

Equivalent two-winding WPT coils(b) Equivalent two-port circuit of WPT coils.
Fig. 3. Equivalent circuit of WPT circuit.

II. CONFIGURATION OF WPT SYSTEM WITH ACTIVESHIELDING METHOD
A. Configuration of WPT Circuit
Figure 1 shows the prototype of the four-winding WPT coils.
The configuration of the transmitting and receiving coils are
identical. The main windings (windings #1 and #3) are woundin the grooves on the cores. The canceling windings (windings#2 and #4) are wound on the side of the cores.

Meq

Cs1

is caliculated. The originality of the proposed method is that afour-winding WPT coils and the operation of the proposed
method are converted to the two-port equivalent circuit tosimplify analysis.

The virtual inductance representes the operation of theadditional power supplies as passive elements from the terminal
voltage and output current. The virtual inductance provides thecanceling windings with the reactive power to reduce theleakage magnetic field. The coefficients 2 and 4 of the virtual
inductance are defined as
V2
 2 = −j LI 2
2 = 0( = 2 f sw )(  2 f sw )

(1),

and


V4
 4 = −
j

LI 4


4 = 0( = 2 f sw )(  2 f sw )(2),

where fsw is the switching frequency of the inverter．in Fig. 2, Lis the self-inductance of the canceling．
windings, Im is current ofwinding #m (m = 1, 2, 3, 4), and Vm is induced voltage ofwinding #m. The range of 2 and 4 is a real number. The
coefficients 2 and 4 are infinity when the canceling windings
are open. Whereas, 2 and 4 are zero when the cancelingwinding are short.
Representing operation of the additional power supplies as
the virtual inductance offers several benefits:⚫ The operation of the additional power supplies islimited not to donate the power transmission.
⚫ The replacement helps conversion of the four-winding
WPT coils and the additional power supplies to thetwo-port network.
⚫ Required apparent power of the additional power
supplies is normalized.
⚫ Frequency dependance of the additional power
supplies is avoided on later analyses.
The relationship between the current and voltage of thewindings is shown in (3) with the inductance matrix L.

The relationship between the current and voltage of the main
windings is given by I1 
V1 
 
 
 0  = j L  I 2 
I 
V 
 3
 3
 0 
 I 4 ( 2 +  2 +  4 ) kc kad − ksub kc 2 + kad 2 M eq = L kM −
(1 +  2 )(1 +  4 ) − ksub 2





 1

  kc= j L  kM  kad kckM (1 +  2 )

 kad

 kad

1

 ksub

 kc

Hz

Hr

Measurement point ofmagnetic field500

 kad   I 
 1
 ksub   I 2  kc   I 3   (1 +  4 )   I 4 

(3).

z



r

hrmai n = 3.04×10-5 /mhzmai n = -2.18×10-3 /mCentral axis of circular WPT coils
Receiving coil
Ferrite core

Winding #4

Winding #3

Winding #2

Winding #1

10
18

Ferrite core
6

15

20

40
Transmitting coilhrcancel = 6.30×10-4 /mhzcancel = -6.00×10-3 /m

Fig. 4. Measurement point of magnetic field.

Unit: mm

(4).

The equivalent self-inductance Leqp and Leqs and theequivalent mutual inductance Meq at the view point of the main
windings in Fig. 3(b) are formulated in (1 +  4 ) kc 2 + (1 +  2 ) kad 2 − 2kc ksub kad 
Leqp = L 1 −
(1 +  2 )(1 +  4 ) − ksub 2



(5),

 (1 +  2 ) kc 2 + (1 +  4 ) kad 2 − 2kc ksub kad 
Leqs = L 1 −
(1 +  2 )(1 +  4 ) − ksub 2



(6),

)

(7).

The equivalent inductances Leqp, Leqs and Meq are changed by
the operation of the additional power supplies. The variation of
Leqp, Leqs and Meq brings errors of the designed transmitting
power and resonant frequency of the WPT system. Thus, theparameter variations should be considered in the process of thedesign or analysis.
B. Leakage Magnetic field
Figure 4 shows the sectional view of the WPT coils and themeasurement point of the magnetic field. The measurement
point is at the 50-cm horizontal distance from the center．of the
gap as the representative example. The magnetic field H at themeasurement point is shown in (8) from Biot-Savart law.
4

4

m =1

m =1

H ( r , , z ) =  H m ( r , , z ) =  N m I m hm

=

20

13
Winding #1:(N1 = 55 turn，h1 = hrmai ner + hzmai nez)
Winding #2:(N2 = 15 turn，h2 = hrcanceler + hzca n celez)

M eq   I1  
Leqs   I 3  (

Here, kc, kM, kad and ksub are the coupling coefficient between
two windings. Equation (3) shows that the equivalent circuit inFig. 3(a) is also the two-port network such as Fig. 3(b) because
degree of freedom is two.

Winding #3:(N3 = 55 turn，h3 = -hrmai ner + hzmai nez)
Winding #4:(N4 = 15 turn，h4 = -hrcancel er + hzcancelez)

V1  Leqp  = j 
 M eqV3 

4
1  4

V
l
N
h
+
V
 p  1m m m s  l3m N m hm 
det L  m =1
m =1


(8)

Here, det L is the determinant of L, lnm (n = 1, 2, 3, 4) is the．
cofactor of the component (m, n) of L, Hm(r, , z) is the magnetic．
field generated by Im, hm is the vector expressing relationship．
．
between Hm(r, , z) and Im, and Nm is the turn of winding #m. The
vector hm is determined by the construction of the WPT coils
and the relative distance from the WPT coils to themeasurement point. Note that values of hm at the measurement
point are calculated with electromagnetic field simulation(JSOL, JMAG-Designer). ．
Equation (8) shows that H is determined by the voltage ofInductance ratio
Leqp / L

1.0

1.5

1.2

0.0

1.1
-0.5

1.0
0.9

-1.0

0.8
0.7

-1.5

1.5
1.4

0.5

1.3

Coefficient 2

Coefficient 2

1.0

1.4

0.5

Inductance ratio
Meq / (LkM)
1.3

1.2

0.0

1.1
-0.5

1.0
0.9

-1.0

0.8
0.7

-1.5

0.6
-2.0

-1.5

-1.0

-0.5

0.0

Coefficient 4

0.5

1.0

0.6

0.5

-2.0

(a) Equivalent self-inductance Leqp.
Fig. 5. Parameter variation of equivalent self-inductance and mutual inductance.

-1.5

Inverter output voltage vpri 500 V/div
ZCS

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

I1 = 2.40 A00

4 ms/div

Current of winding #3 i3 10 A/div
V2 = V4 = 0 V

0.5

1.0

0.5

Current of winding #1 i1 10 A/div

I1 = 2.55 A

Current of winding #2 i2 10 A/div

I2 = 2.66 A

Current of winding #3 i3 10 A/div

I3 = 4.00 A

0Current of winding #2 i2 10 A/div

I2 = 1.78 A

Current of winding #3 i3 10 A/div

I3 = 3.71 A

0

0

0.0

0
Current of winding #1 i1 10 A/div

0

0

-0.5

Coefficient 4(b) Equivalent mutual inductance Meq.

0

0

-1.0

0

Current of winding #4 i4 10 A/div
4 ms/div

I4 = 2.02 A
V2 = V4 = 0 V

0I4 = 3.04 A
Current of winding #4 i4 10 A/div
4 ms/div
V2 = 32.8 V, V4 = 33.1 V(a) Input and output waveforms.
(b) Current waveforms.
(c) Lowest magnetic field.
Fig. 6. Waveforms of WPT system. The waveforms (a) and (b) are measured at the short-circuited canceling windings (2 = 4 = 0). The waveforms (c)are measured at 1.50 Kamp.

the main windings, the construction of the WPT coils, 2 and 4.
The coefficients 2 andshould be adjusted to achieve． 4 ．
minimum H because Vp and Vs are not zero． during． the powertransmission. When the z-axis component Hz of H(r, , z) is zero,
the coefficients 2 and 4 are given by 2 =  4 = ( kc + kad )Pmain hzcancel− ( ksub + 1)
Pcancel hzmain(9).

III. ANALYSIS AND EXPERIMENTAL RESULTS
A. Equivalent Inductance
Figure 5 shows maps of Leqp and Meq with the proposed
method. The vertical and horizonal axes are 2 and 4,
respectively. The equivalent inductances Leqp and Meq arenormalized by L or LkM. The coefficients 2 and 4 are decreased
when the current RMS of the canceling windings is increased
with the active shielding. The equivalent inductances Leqp, Leqs
and Meq are decreased with the proposed method.
B. Operational Waveforms and Transmitting Power
Figure 6 shows the 600-W operation waveforms. It is notedthat the additional power supplies adjust the current RMS of thecanceling windings for simplification. The ratio Kamp of thecurrent RNS is defined as

K amp =

I2I
= 4
I2s I4s(10),

where, I2s and I4s are the current RMS of windings #2 and #4 at
the short-circuited canceling windings, respectively.
The circuit is operated under the resonant condition because
the phases of the inverter output voltage and the current of thewinding #1 are matched. In addition, not only I2 and I4 but also
I1 and I3 are in phase, respectively, at 1.50 Kamp because of thevariation of Meq.
Figure 7 shows the relationship between Kamp, 2 and 4.
The coefficients 2 and 4 become smaller as Kamp becomeslarger.
Figure 8 shows the output power Pout when Kamp is changed
from 0.5 to 1.5. The output power becomes larger as Kamp
becomes larger because the transmitting power of the S/Scompensated WPT system is inverse proportion to Meq. Thus,
the variation of the equivalent inductance with the proposed
method is demonstrated.
C. Measured and calculated Leakage Magnetic Field
Figure 9 shows the measured and calculated magnetic field
Hz. The magnetic field Hz is calculated under two conditions
which are the proposed method and disregarding the variation of
I1 and I3. The measured magnetic field is more decreasing byCoefficient 2 and 4

1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
0.4

parameter variation of the WPT coils and the magnetic field are
calculated with the two-port equivalent circuit with the virtual
inductance. As a result, the magnetic field decreases by 27.2dB
with the proposed method. In addition, the transmitting power
is increased as the magnetic field becomes smaller because theequivalent mutual inductance is reduced.
n the future, a current-compensation method will be
evaluated when position misalignments of the WPT coils occur.

4 (blue curve)2 (red curve)

0.6

0.8

1.0

1.2

1.4

1.6

Ratio Kamp of current RMS of winding #2 and #4

Output power Pout

Fig. 7. Variation of 2 and 4 with proposed method.

800
700 Calculated power (dashed curve)
600
500
Measured power
400(plots and curve)
300
200
100
0
0.4
0.6
0.8
1.0
1.2
1.4

1.6

Ratio Kamp of current RMS of winding #2 and #4

Magnetic field Hz

Fig. 8. Measured and calculated output power.

0.40
Open canceling winding (Pout = 600 W)
0.35 Calculated
magnetic field ignored
0.30
variation of I1 and I3
0.25
Calculated magnetic field
0.20
with proposed method
0.15
0.10 Measured magnetic field
0.05
0.00
0.4
0.6
0.8
1.0
1.2
1.4

1.6

Ratio Kamp of current RMS of winding #2 and #4

Fig. 9. Magnetic field at measurement point.

27.2dB than Hz of the open canceling windings. Calculated Hz
does not match to the measured Hz expecting 1.0 Kamp when thevariation of I1 and I3 is disregarded. Whereas, the trend of Hz
with the proposed method agrees with the trend of measured Hz.
The error of Hz with the proposed method is probably caused by
the parameter mismatch of the WPT coils and calculated errorof 2 or 4.
IV. CONCLUSIONSThis paper proposed and analyzed an active-shielding
method to reduce EMF of WPT systems. The advantage of the
proposed method is that the small-capacity power supplies areavailable. The magnetic field around the WPT coils is canceledwith the additional power supplies and the two canceling. The
feature of the proposed method is that the additional power
supplies outputs only reactive power such as capacitance. The

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