A Large Air Gap 3 kW Wireless Power Transfer
System for Electric Vehicles
Hiroya Takanashi*, Yukiya Sato*, Yasuyoshi Kaneko*, Shigeru Abe*, Tomio Yasuda***Saitama University, Saitama, Japan** Technova Inc., Tokyo, Japans11mm222@mail.saitama-u.ac.jp
Abstract— A wireless power transfer system for electricvehicles is required to have high efficiency, a large air gap, andgood tolerance for misalignment in the lateral direction and to
be compact and lightweight. A new 3 kW transformer has beendeveloped to satisfy these criteria using a novel H-shaped coreand split primary capacitors. The design procedure based on
the coupling factor k, the winding's Q, and the core loss is
described. An efficiency of 90% was achieved across a 200 mm
air gap.

I.

INTRODUCTION

The development and commercialization of plug-in
hybrid electric vehicles (PHVs) and electric vehicles (EVs)are actively being realized due to environmental concerns
and rising oil prices. PHVs and EVs currently need to beconnected to power supplies by electrical wires to charge
their batteries. A wireless power transfer system for electricvehicles (such as that depicted in Fig. 1) would have many
advantages, such as having the convenience of being
wireless and enabling high-power charging to be performed
safely [1, 2]. Therefore, wireless power transfer systems arebeing studied around the world. Wireless power transfer
systems for electric vehicles must have high efficiency, alarge air gap, and good tolerance for misalignment in thelateral direction and be compact and lightweight [3].
There are two types of methods used in wireless powertransfer systems: inductive coupling methods [1, 2, 3] andmagnetic resonance methods [4, 5]. The inductive coupling
methods use a frequency lower than 200 kHz, use ferrite
cores, and have coupling factors above 0.1. On the other
hand, the magnetic resonance methods use a frequency
higher than 1 MHz, do not use ferrite cores, and havecoupling factors below 0.1.
Recently, research on the inductive coupling methods
used for PHVs and EVs has adopted rectangular cores
instead of the conventional circular cores. For example,
these include Flux pipes [1], Double-D-Quadrature (DDQ)
structures [2], and H-shaped cores [3].
To compensate for leakage inductance, the inductive
coupling methods usually adopt the series and parallel
capacitor methods (SP methods) [3] or parallel and parallel
capacitor methods (PP methods) [1, 2]. It is known that themagnetic resonance methods can be represented by anequivalent circuit of the series and series capacitor methods(SS methods) [5].
Inductive coupling methods and magnetic resonancemethods have not been compared in terms of their efficiency
because they use different frequencies and differ in their useof ferrite cores. In this paper, we compare the efficiencies of
the two methods using the coupling factor k and thewinding's Q values when considering the copper loss only.
The results show that the maximum efficiencies of the SP
methods and SS methods are given by the same simple
equations of k and Q, and those equations indicate that k and
Q must be increased in order to increase the efficiency.
A large air gap 3 kW transformer of the inductive
coupling type is developed using this efficiency equation.
To increase the coupling factor k, we adopt an H-shaped
core and a wide winding width. To increase the winding's Q,
we increase the input frequency.
The experimental results show that this large air gap 3
kW transformer has an efficiency of over 90% for a gap
length of 200 mm. The results for the gap changes (160 mm± 40 mm) and misalignments (forward ± 100 mm, lateral ±z : Vertical direction
x : Forward direction
y : Lateral direction

Wireless
Power Transfer

Figure 1. Wireless power transfer system of an EV.
VDC IDC

VIN IIN

V1

I2

V2 ID

VL IL

CS1
Regulated DC
Power Supply

+
－

+

CP

CS2

－

RL

+
－

η

Figure 2. Wireless power transfer system configuration.

POUT

200 mm) are also presented. Adopting the H-shaped core,
the transformer is small in size (320 × 300 × 40 mm) andlightweight (5.5 kg).
The purpose of this paper is to introduce the maximum
efficiencies of the inductive coupling methods and magnetic
resonance methods using the same simple equations when
considering the copper loss only, to propose the design
procedure for the inductive coupling type using thisequation, and to present a newly designed 3 kW transformer.
This transformer has high efficiency, a large air gap, andgood tolerance for misalignments in the lateral direction andis compact and lightweight.
II.

MAXIMUM EFFICIENCY OF WIRELESS POWER
TRANSFER SYSTEM USING k AND Q

A. Series and Parallel Resonant Capacitor Methods(Inductive Coupling Method)
Fig. 2 shows a schematic diagram of the wireless powertransfer system with series and parallel resonant capacitor(SP methods). A full-bridge inverter is used as a highfrequency power supply. A double-voltage rectifier is used
as a rectifier circuit on the second side to raise theefficiency. The cores are made of ferrite, and litz wires areused for the windings.
1) Equivalent Circuit
Fig. 3 (a) shows a detailed equivalent circuit. It consistsof a T-shaped equivalent circuit to which the primary seriescapacitor CS, secondary parallel capacitor CP, and load
resistance RL have been added. The primary values areconverted into secondary equivalent values using the turnratio a = N1/N2. Since the winding resistances r'1 and r2 and
VIN’ IIN’ V1’ r1’
C S’
-jxS’

jx1’ V0’ jx2

r2 V2=VL

ID

r0’

CP
-jxP

RL

η=

RL I L2=2+ r2′I 22
RL I L2 + r1′I IN

jx1’ V0’ jx2
I0’
r0’

RL
⎧⎪ ⎛ R ⎞ 2 ⎫⎪r′
RL + 12 + r2 ⎨1 + ⎜⎜ L ⎟⎟ ⎬b⎪⎩ ⎝ xP ⎠ ⎪⎭(4)

The maximum efficiency ηmax SP is obtained when RL =RLmax SP.
RLmax SP = xP

1 r1′
+ 1 , η max SP =b 2 r2

1
2r
1+ 2
xP

1 r1′
+1
b 2 r2(5)

If these characteristics are used, it is possible to design atransformer that has a maximum efficiency when the output
power is equal to the rated power.
3) Maximum Efficiency of Series and Parallel Resonant
Capacitor Methods using k and Q
The coupling factor k, the primary winding's Q1, and thesecondary winding's Q2 are represented by:
M
ωL
ωL
(6)
k=
, Q1 = 1 , Q2 = 2(a) SP method

CS1’-jxS1’

2) Characteristics of Series and Parallel Resonant
Capacitor Methods
To achieve resonance of the input frequency f0 (=ω0/2π)
with the self-inductance of the secondary winding L2, whichis equivalent to adding a mutual reactance x'0 and a leakage
reactance x2, the secondary parallel capacitor CP is given by:1(1)= ω 0 L2 = xP = x0′ + x2
ω 0C P
The primary series capacitor CS (C'S denotes its secondary
equivalent) is determined as:
x′ x
1
(2)
= x S′ = x1′ + 0 2
ω 0 C S′x 0′ + x 2
V'IN and I'IN can be expressed as:x0′(3)′ = VIN / a = bV2 , I IN
′ = ID b , b =VINx0′ + x2
These equations suggest that the equivalent circuit of atransformer with these capacitors is the same as an idealtransformer at the resonant frequency.
Ignoring the ferrite core loss (r0 = 0), the efficiency canbe approximated by:

I0’

jx0’

VIN’ IIN’ V1’ r1’

the ferrite core loss r'0 are considerably lower than theleakage reactance x'1 and x2 and the mutual reactance x'0 at
the resonant frequency, the winding resistances. The ferrite
core loss is ignored. Here, M is the mutual inductance (x'0=ω0M/a). The rectifier is also omitted, and a secondary
circuit for analysis consists of CP and the load resistance RL.

r2 V2 -jxS2 VL

L1L2

CS2
I2=IL
RL

jx0’

(b) SS method
Figure 3. Detailed equivalent circuit of wireless power transfer systems.

r1

r2

Here, L1 is the self-inductance of the primary winding (L1 =a2(x'1+x'0)/ω0).
If k is lower than 0.3 and Q1 ≅ Q2,
1 Q2>>1
k 2 Q1

Then, these equations can be expressed using k and Q.

(7)

η

max

100

AND RL max FOR EACH METHOD.

Copper loss

98

Resonant
capacitor

RLmax

ηmax

Efficiency [%]TABLE I.

r2Q2 Q2
k
Q1

SP
1

PP

1+

r2Q2 Q2kQ1

2
k Q1Q2

SS

96
Iron loss

94
92
90
88

kr2 Q1Q2

ηmax (w = 190 mm)

New Trans.

ηmax (w = 230 mm)

Trans.Ⅰη(w = 150 mm)

Trans.Ⅱη(w = 190 mm)

η(w = 230 mm)

2

1.4

Winding w／Magnetic gap g

100

Figure 5. Relationship between η and w/g.

95
Efficiency [%]Trans.Ⅱ

New Trans.

1

primary series capacitor CS1 and the secondary seriescapacitor CS2 are given by:

90
85

1

11
1
+
/ kQ
1 + 2 /2kQ

ηη
max==
max

80

′ = − jx0′ I L
VIN

10

50

20

100

Figure 4. Relationship between ηmax and kQ.

Q2, η max SP =Q1
1+

= xS2 = x0′ + x2

12
k Q1Q2

′ =−j
I IN

1
VL
x0′

(9)

(10)

These equations suggest that the equivalent circuit for atransformer with these capacitors has the samecharacteristics as the immittance converter at the resonant
frequency.

kQ = k Q1 Q2

rQ
RLmax SP = 2 2
k1= x′ = x′ + x′

S1
0
1
′
ω0 CS1
ω0 CS2and V'IN and I'IN can be expressed as:

75
70
5

ηmax (w = 150 mm)

Trans.Ⅰ(8)

By following the same steps, the RLmax PP and ηmax PP of the
PP methods can be derived. Table I lists the equations forthe maximum efficiency ηmax and RLmax of the SP methods,
PP methods, and SS methods. From Table I, the equation
for the maximum efficiency of the PP methods is the sameas that of the SP methods [6].
B. Series and Series Resonant Capacitor Methods(Magnetic Resonance Methods)
1) Equivalent Circuit
The magnetic resonance methods can be represented byan equivalent circuit of the series capacitors methods. Fig. 3(b) shows a typical detailed equivalent circuit with seriescapacitors (SS methods). It consists of a T-shaped
equivalent circuit to which the primary series capacitor CS1,
the secondary series capacitor CS2, and the load resistance
RL have been added.
2) Characteristics of Series and Series Resonant
Capacitor Methods
To achieve resonance with the self-inductance of the
primary winding L1 and the secondary winding L2, the3) Maximum Efficiency of Series and Series Resonant
Capacitor Methods using k and Q
The equation for the maximum efficiency of the SS
methods is given by:
1r(11)
RLmax SS = x '0 2 , η max SS =
r1′

1+

2r2
x '0

r1′
r2

Then, these equations can be expressed using k and Q.
1(12)
RLmax SS = kr2 Q1Q2 , η=
max SS1+

2
k Q1Q2The ηmax SS in (12) is equal to the ηmax SP in (8).
Fig. 4 shows the relationship between the maximum
efficiency ηmax and kQ (= k Q1Q2 )of (8) and (12). Larger
values of k and Q realize a higher maximum efficiency ηmax.
III.

DESIGN OF A LARGE AIR GAP TRANSFORMER

A. Decision on the Winding Width
The coupling factor k decreases with an increase in the
gap length. In the design of a large air gap transformer, it isnecessary to increase the winding width to prevent a
decrease in the coupling factor k. The coupling factor kdepends on the ratio w/g, where w is the winding width, andg is the air gap length between the primary core and thesecondary core. A larger value of w/g implies a larger value

TABLE III.

TRANSFORMER PARAMETERS.

f0 [kHz]50

gap [mm]

160

200

k

0.18

0.12

RLmax [Ω]

12.8

15.7

ηmax [%]

97.1

95.5

Q1

345

329

Q2

462

357
C

(a) Picture

B

Ferrite core

C

V1

x
Windingw

VCSyunit : mm

A

VIN B

A

Al sheet(a) Without split windings and capacitor

C2(b) Dimensions
Figure 6. Photograph and schematic of the 3 kW transformer.
TABLE II.

H-shaped core

Litz wire

0.1 mmφ × 800

Weight of secondary transformer

5.5kg

Size

320 × 300 × 40 mm

WindingPrimary

20 T (3 parallel)

Secondary

4 T (15 parallel)

Aluminum sheet

600 × 600 × 1 mmof k. Fig. 5 shows the relationship among the maximum
efficiency ηmax, the experimental efficiency η, and w/g forthree existing transformers. Here, the horizontal axis is w/g,
and the vertical axis is the efficiency. The winding widths ofthe small gap transformers are 150 mm and 190 mm. Fig. 5
shows that a larger w/g ratio can achieve a higher efficiency.
In addition, the ηmax curves of the small gap transformers
show the same characteristics, and the η curves also show
the same characteristics. The difference in efficiency
between ηmax and η is considered an effect of the ferrite coreloss. We designed the new large air gap transformer using
the efficiency curves in Fig. 5.
In the design of a small air gap (70 mm) transformer, we
set the target of the transformer efficiency η to be above
96%, and the w/g ratio is set to 2, as shown in Fig. 5.
However, for a large air gap transformer, it is difficult to set

V1

D1

SPECIFICATIONS OF THE 3 KW TRANSFORMER.

Type

C2

C1

B

V12

Vcs1

C1

V11
Vcs2

A

A

D1

B

(b) With split windings and capacitors
Figure 7. Split winding voltage vector.

the w/g ratio to 2 because the secondary transformer must becompact in order to be installed in cars. We decided on a
w/g ratio of 1.4 to get an efficiency above 92% at the normal
air gap of 160 mm. Consequently, the winding width w is
230 mm.
B. Specifications of a Large Air Gap Transformer
Table II lists the specifications of a 3 kW double-sided
winding transformer using an H-shaped core. Fig. 6 (a)shows a photograph of the transformer, and Fig. 6 (b) showsa schematic of the transformer with dimensions. Table III
lists the transformer parameters for the normal position(mechanical gap length of 160 mm). The coupling factor kof the 160 mm air gap is approximately 0.18. The turn ratio
is determined by (3) and is found to be 20 / 4 = 5, which isalmost equal to the reciprocal of k [3]. Then, the output
voltage V2 is almost equal to the input voltage VIN.

250

3

V2 2

150

VIN

100

k 1

η

0
120

L2
140

160
gap [mm]

x [mm]

1.5

0.5

200

V2

150

VIN

100

k

50

η

0
0

L2
50
x[mm]

3
2.5
2
1.5
1
0.5

VIN [V], V2 [V], L2 [μH]

POUT

POUT [kW], η, k × 10

VIN [V], V2 [V], L2 [μH]

Figure 8. Transformer values with change in air gap.

250

3000

gap [mm]

0
200

180

EXPERIMENTAL RESULTS.

POUT [W]

2.5

200

50

TABLE IV.

160
0

100

200
0

0

y [mm]

0

0

200

0

VIN [V]

217

168

162

167

V1 [V]

501

621

676

643

V2 [V]

213

213

213

213

VL [V]

547

547

547

547

η [%]

92.9

90.1

88.9

90.0

250

POUT

200

V2

150

VIN

100

k

50

η

0
100

Figure 9. Transformer values with change in x position.

C. Increasing of the Winding’s Q Values
As the winding's Q values are represented by (6), theeasiest way to increase Q is to increase the frequency. Table
III shows the winding's Q values for a 3 kW double-sided
winding transformer using an H-shaped core at 30 kHz and
50 kHz. The winding's Q values at 50 kHz are about 20%
higher than those at 30 kHz. To achieve a high efficiency,
we chose to use 50 kHz.
D. Avoidance of Primary Terminal Overvoltage
The coupling factor k decreases with an increase in gap
length, and the overvoltage of the primary terminal voltage
V1 (in Fig. 2) becomes a problem. The primary terminal
voltage V1 is represented by:
2(13)
V1 = V IN2 + (x S I IN )In (13), xs IIN becomes larger than VIN, and the value of V1
is mainly determined by xs IIN. The coupling factor k isequivalent to the value of b shown in (3). Thus, the primary
current IIN increases as the coupling factor k gets smaller.
The primary terminal voltage V1 increases with an increasein air gap length. The overvoltage of V1 is not good for theseries capacitor and the primary winding. To avoid highprimary terminal voltage, the primary winding and the seriescapacitor are severally split into two, and the split windings
and capacitors are alternately connected in series [7]. Fig. 7(a) depicts the voltage vectors when the primary winding
and the series capacitor are not split, and Fig. 7 (b) depicts

0
0

L2
50

100
y [mm]

150

3
2.5
2
1.5
1
0.5

POUT [kW], η, k × 10

POUT

POUT [kW], η, k × 10

VIN [V], V2 [V], L2 [μH]

300

0
200

Figure 10. Transformer values with change in y position.

those when they are split. Fig. 7 (b) shows the reduction in
the capacitor voltage and the primary terminal overvoltage.
IV.

EXPERIMENTAL RESULTS

When using wireless power transfer systems for EVs,misalignment due to the driver's skill and gap changes dueto the car weight cannot be avoided. A mechanical gap
length of 160 mm with no misalignment is taken to be thenormal position. The transformer characteristics were
measured for gap lengths in the range of 160 mm ± 40 mm,
misalignments in the forward direction x of ± 100 mm, andmisalignments in the lateral direction y of ± 200 mm.
Misalignments in the x direction can be minimized using
wheel stops, but a large misalignment tolerance in the y
direction is required to allow for easy parking. Experiments
were performed in the circuit shown in Fig. 2. The operating
frequency f0 was 50 kHz and was constant during theexperiments. A double-voltage rectifier was used as arectifier circuit on the second side to increase the efficiency.
In the experiments, the capacitances of CS and CP remained
constant during the experiments, and the load resistance RL
was kept constant at 100 Ω. A thick aluminum sheet (600mm × 600 mm × 1 mm) was attached to the back of thetransformer to shield the leakage flux.
A. Characteristics with a Wide Gap
Figs. 8 to 10 and Table IV show the transformer values
when the gap length or position was changed. The mutual
inductance M and the coupling factor k decreased with anincrease in gap length or misalignment because the160 mm x
160 mm y
200 mm x
200 mm yflux density [μT]

1000
500
100
50

27

large air gaps. Fig. 11 also shows the leakages flux densitiesof the 3 kW transformer at gap lengths of 160 mm and 200
mm. The electromagnetic flux leakages for the 160 mm and
200 mm air gaps were less than the reference levels for
exposure to the general public given in ICNIRP2010 about
700 mm and 800 mm away from the center of thetransformer, respectively. If the transformer is attached tothe center of the car, it is safe for humans near the vehicle.
V.

10
5
1
0.5
100

200
400
1000
distance from center [mm]2000

Figure 11. Leakages flux measurement (50 kHz).

magnetic reluctance of the main flux path became larger.
However, the secondary self-inductance L2 was almost
constant; consequently, the capacitance of the parallel
capacitor CP given by (1) can be constant.
As shown in Figs. 8 to 10, the coupling factor k
decreased when the gap length or the misalignment
increased, and the ideal transformer turn ratio b decreased
and the voltage ratio (V2/VIN) increased according to (3).
The output power POUT remained constant at 3 kW when the
input voltage VIN was varied. The transformer experimental
efficiency η at the normal position was 92.9% at 3 kW of
output power, and the efficiency was 90% at a 200 mm air
gap. From Fig. 5, the characteristics of the prototypetransformer were similar to those of the conventionaltransformers.
B. Characteristics with a Large Misalignment
Figs. 9 and 10 show the transformer values when theposition was changed. The efficiency η was 89% at
maximum misalignment in the lateral y direction, and theoutput power was 3 kW. The 3 kW transformer wascomparable to the conventional transformer in its positional
deviation characteristics. Therefore, a large air gap 3 kWtransformer was achieved.
C. Characteristics of Leakage Flux
Since the wireless power transformer has small coupling,
the leakage flux is distributed around the transformer. In
practical applications, the effects of leakage flux poseserious problems to human health. The leakage flux aroundhumans must fall below the value specified by safety
standards. Fig. 11 shows the criteria for exposure toelectromagnetic lines; the 27 μT line represents thereference level for exposure to the general public given in
ICNIRP2010 [8]. The coupling factor k decreased with anincrease in gap length. Therefore, the influence of external
electromagnetic flux leakage is a significant concern for

CONCLUSION

The maximum efficiencies of the inductive coupling
methods and magnetic resonance methods are expressed by
the same simple equations using the coupling factor k andthe winding's Q if considering the copper loss only. The
design procedure for the transformer of the inductive
coupling type using this equation is proposed. The
experimental results for the newly developed 3 kWtransformer with an H-shaped core has a high efficiency(90%), a large air gap (200 mm), and good tolerance formisalignments in the lateral direction (± 200 mm) and issmall in size (320 × 300 × 40 mm) and lightweight (5.5 kg).
ACKOWLEDGMENT
This research was sponsored by the New Energy andIndustrial Technology Development Organization (NEDO)
of Japan.
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