Wireless Power Transfer System
whose Input / Output Ratio is Determined
Only by Self-InductanceKenji Nara
Graduate School of Science and Engineering
Saitama University
Saitama, Japan
Email: pistasuper921@gmail.com

Naofumi Madoiwa
School Engineering
Tokyo Institute of Technology
Tokyo, Japan
Email: madoiwa.n.aa@m.titech.ac.jp

Abstract—Wireless power transfer (WPT) technology is a
power transmission system that does not necessitate an electricalcontact. This study focuses on a simple design for WPT products
through an analysis of a series/series-parallel (S/SP) WPT circuit
scheme that exhibits the same input/output (I/O) characteristics
as ideal transformers. S/SP is a circuit topology characterized bycapacitors connected in series to a primary coil and in seriesparallel to a secondary coil. Moreover, even with the inductorcapacitor-capacitor/series (LCC/S) scheme, determining a
specific value for the compensation coil results in idealtransformer characteristics. To validate the theoretical results ofthe study, an experiment and a simulation are conducted, where
solenoid type coils of the same shape and external dimension forthe primary and secondary sides are applied for the S/SP and
LCC/S WPT systems. Specifically, the experimental andsimulated findings confirm that the winding number ratio of thecoils and the I/O voltage ratio of the WPT system are inagreement.
Keywords—wireless power transfer, compensation capacitor,
input/output characteristics, ideal transformer characteristics, S/SP
system, LCC/S system

I. INTRODUCTION
From the point of view of environmental problems andefficient energy utilization, plug-in hybrid vehicles and electricvehicles (EVs) have recently been attracting attention.
Nevertheless, such vehicles may be characterized bysignificant mechanical drawbacks. For instance, EVs operate
on electricity supplied via electric cables and connectors, a
conductive method that invites the danger of electric shock
during recharge in rainy weather. Needless to say, the charging
cable needs to be connected to the car body daily, which cancreate a sense of annoyance for the EV user. In addition, themomentum of motorization is increasing in all markets, as
shown by the spread of electric-assisted bicycles and the
expansive distribution of automated guided vehicles infactories, as well as the palpable rise in the demand forelectronic appliances, such as smart phones and wearable
devices. In other words, expectations for wireless powertransfer (WPT) technology are increasing. This study aims topromote the introduction of WPT products to the market byfocusing on the ease of design.

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

In contrast to the conductive charging method, WPT is atransmission system that does not need an electrical contact,
thereby preventing the danger of electric shock. It is aconvenient charging method in which power is supplied to avehicle simply by parking the vehicle, and to a device only byplacing it on the wireless charger. In a WPT based on amagnetic field coupling system (which is also called inductive
power transfer), the method of connecting inductors andcapacitors in series or in parallel to the transmitting andreceiving coils, respectively, is commonly observed [1-3].
Moreover, through the application of compensation circuits,
devices can be designed to achieve specific characteristics,
such as efficiency improvement and power factor
compensation. The S/SP method [4-6], in which compensation
capacitors are connected in series to the primary coil and inseries-parallel to the secondary coil, provides constant voltage(CV) output during CV driving, so the output voltage can be
kept constant against load fluctuation. Moreover, it is also
reported that the CV output can be maintained even if thecoupling coefficient fluctuates due to positional deviation [4,5],
indicating the superiority of the topology.
In this study, by newly analyzing the circuit using an Fmatrix, the method for deciding the compensation capacitors isclearly presented, and it is shown that the input/output (I/O)
relation of the circuit is equivalent to the ideal transformer.
Theoretical formulas are also derived for maximum efficiency
and optimum load, which takes maximum efficiency. In
addition, under limited conditions, as with the generaltransformer, it is possible to determine the I/O voltage/current
ratio using only the turn ratio of the coils, demonstrating that it
is an advantageous circuit system in product design.
Moreover, we show that the ideal transformer
characteristics can likewise be obtained by the inductorcapacitor-capacitor/series (LCC/S) method [7,8]. WPT by LCC
compensation has been regarded as an effective circuit
topology for dynamic wireless power transfer in EVs [7-9]. In
particular, the LCC/S scheme has been reported to haveexcellent characteristics as well as CV output [2,7,8]. The
compensation inductor used for the LCC method is not in acoupled state with the transmitting and receiving coils but isdetermined to have an arbitrary value. In addition, because it isa parameter contributing to the I/O ratio, by taking a certain

value, the ideal transformer characteristics can also be obtainedin the LCC/S system.
The remainder of this paper is organized as follows.
Section II analyzes the series/series (S/S) topology which is themost basic circuit of WPT, briefly describes the characteristics,
and showed the problems of the system. Section III presents ananalysis of the WPT circuit, which takes on ideal transformer
characteristics. Section Ⅳ discusses the simulation and theexperimental results verifying the analysis. Finally, Section V
emphasizes specific conclusions and states the direction of our
future work.

II. S/S WPT SYSTEM(1)

A. Constant Current Output of S/S System
In (2), capacitances C1 and C2 on the primary andsecondary sides, respectively, are determined to resonate with
L1 and L2 at the resonant frequency ω = 2πf:1
1
C1 = 2 , C2 = 2 .
ω L1
ω L2

(2)

If, with respect to the reactance component, the winding
resistances r1 and r2 are sufficiently small that they can beignored, then the I/O characteristics of the circuit can be
expressed by (3) using the F-matrix. Here, VIN, Vd, IIN, and Id
represent the input and output voltage, and the input and output
current, respectively:
VIN   0  =1
 I IN   − j ωM

− jωM V 
 d 
0  I d  .
,

Fig. 1 WPT circuit with S/S method,,

Fig. 2 WPT circuit with S/SP method

The S/S method has been widely studied and used because
it has excellent circuit characteristics, such as a simple circuit
structure, as well as a theoretical maximum efficiency and an
input power factor of 1. Fig. 1 shows a simplified S/S type
WPT circuit. L1, L2, and M indicate the self-inductance andmutual inductance of the primary and secondary side coils,
respectively, which follows relationship (1) via the coupling
coefficient k:
M = k L1 L2 .

,(3)

In a two-port network, by expressing the I/O relationship of thecircuit by the F-matrix, the output characteristics when driven
by a CV (or Constant Current (CC)) can be easily confirmed.
In addition, if the diagonal elements (or non-diagonal
elements) of the matrix are all 0, it can be determined that the
input power factor is 1, and zero-voltage switching (ZVS) is
possible. When the capacitances are determined by (2), theoutput becomes CC with CV driving, as shown in (3).
Therefore, it is difficult to keep the output voltage constantagainst load fluctuation and to obtain I/O voltage and powerwith the desired values.
In practice, a DC–DC converter is applied to the output of
the WPT circuit to control the voltage and power applied to theload [10, 11]. On the contrary, a circuit design that considers
the output eliminates feedback control. This makes it possible

to use a general-purpose DC–DC converter, which isadvantageous in mass production and cost reduction.
B. Constant Voltage Output of S/S System
Contrary to the discussion in Section II-A, it has beenreported that by driving the power supply at offset frequencies
with respect to f, the output characteristics can be changed, anda CV output is obtained at certain frequencies [2,12,13]. In[12,13], it is shown that by driving at the frequency ω1 = 2πf1
represented by (4), the I/O relationship of CV can be obtainedeven in an S/S system:
f1 =

1
f
1± k .

(4)

Shifting the power supply frequency is equivalent to shifting
the resonant frequency of the compensation capacitors. That is,when the power supply is driven at f in the S/S system, a CV
output can be obtained by determining the compensation
capacitors as in (5):1
C1 = ω 2 (1 ± k )L

1

.
1
C =
2
2

ω (1 ± k )L2(5)

Consequently, the I/O characteristics of the circuit are given
by:

L1
m
VIN  
L2  = I
 IN   − j 1

ωM


0
m



Vd 
 
L2  I d  .

L1 

(6)

Specifically, (6) shows CV output under CV driving. Moreover,as the non-diagonal components are not all 0, the input power
factor is not 1.

III. WPT SYSTEMS WITH IDEAL TRANSFORMER
CHARACTERISTICS,

A. Analysis of S/SP System
Fig. 2 shows the WPT circuit of the S/SP system. When C1and C2 are determined as in (5), the I/O relationships of thesystem can be obtained through:
L1
mVIN  
L2  = L2
 I IN   − j 1 m jωC
p2

L1
ωM


0
m



Vd 
 
L2  I d  .

L1 

(7)

(8)

and the I/O characteristics are expressed by: L1
VIN   L2

 = 
 I IN   0




0 
Vd 
 
L2  I d  .
L1 

(9)

Equation (9) shows that the I/O characteristics of the S/SP
system are determined only by the self-inductances of the coils.
Because it does not include parameters that are determined by
the positional relationship of the coils, such as the coupling
coefficient (or mutual inductance), this topology is simpler
than the previously proposed WPT topologies in terms of
product design and production.
Next, we show the power transfer efficiency of the S/SP
method. By the loss generated in the coils and the power
consumed by the load resistance, the efficiency is expressed as:

ηTR =
=

Rd I d2
r I + r2 I 22 + Rd I d2
2
1 1

Rd
2

 Q 
1 1  2
 Rd + Rd + r2 1 + 2 r2  kQ2 
Q1 


.

(10)

Here, I1 and I2 are the current flowing through the primary andsecondary coils, respectively, and Q (= ωL / r) is the index that
represents the performance of the coil. From ∂ηTR / ∂Rd = 0, theoptimal load Rdopt and the maximum efficiency ηTRmax are,respectively:
Rdopt = kQ2 r2 1 +Q2
Q1

Fig. 3 WPT circuit with LCC/S method

andCorrespondingly, Cp2 is determined so that the non-diagonalcomponent becomes 0. Considering Cp2 > 0, each capacitanceis respectively determined by:1C1 = 2(
1− k )L1
ω
1
C 2 = 2(
1k )L2 ,−
ω
1
C p 2 = 2
ω kL2


,

(11)

ηTR max =1
2
Q
1+
1+ 2 .
kQ2
Q1

(12)

B. Analysis of LCC/S System
Fig. 3 displays a simplified WPT circuit diagram of the
LCC/S system, where C0, L0, and r0 are the compensation
capacitor, inductor, and its winding resistance on the primaryside, respectively. Based on [7,8], each capacitance isdetermined by:
1
C 0 = 2ω L01
C1 = 2
ω (L1 − L0 ) .

1
C 2 = 2
ω
L2


(13)

At this stage, the I/O relationships of the circuit are expressed
by:
 L0

V IN   k L1 L2 = 
 I IN  
0





Vd 
 
k L1 L2  I d  .

L0 
0

(14)

The compensating inductor L0 does not couple with thetransmitting and receiving coils via a toroidal core or the like.
That is, as its value can be arbitrarily determined, the I/O
voltage (/current) ratio has a high design freedom. Specifically,
determining L0 as in (15), transforms the I/O relationships, asin (9), and provides the ideal transformer characteristics, evenin the LCC/S system:
L0 = kL1 .

(15)

IV. VERIFICATION BY EXPERIMENT AND SIMULATION
Guided by the theory proposed in Section Ⅲ, we conducteda power feeding experiment to validate the SS/P scheme, alongwith a power feeding simulation for the LCC/S method via thecircuit simulation software PSIM. Solenoid coils as shown in
Fig. 4 (a) were created. The relationship between the selfinductance of the solenoid coil and the number of turns of thecoil is expressed as:

(a) Coils(b) Ferrite coreFig. 4 Solenoid-type coil and core

3.56

Table II. Experimental/simulation conditions
MethodSS/P
LCC/Sf [kHz]85.0
RL [Ω]
4.83
7.49
L0 [μH]112
r0 [Ω]
0.567
C0 [μF]
0.0314C1 [μF]0.02970.0283C2 [μF]
0.373
0.192
Cp2 [μF]0.403-(i ∈ 1,2 )Fig. 5 Experimental/simulation circuit

20

20

10

0

(16)

0

-20

-10

2

50
0

0

-50

-2

-100
-150 0

-40

VIN
I IN
5

(17)

10
15
20
Time [ µsec]

25

-60 0

30

-20

Vd
Id

-4

5

10
15
20
Time [ µsec]

25

30-30

(a) Input(b) Output
Fig. 6 Voltage/current waveforms of S/SP system
150

4

60

30

40

20

20

10

0

0

-20

-10

3

100

2

(18)

Voltage [V]
0 Vd N 2  I d  .
N 1 

40

100

and (9) can be rewritten as: N1V IN   N 2
 I  =  IN 
 0


30

4

Here, μ0 is the permeability, S is the cross-sectional area of thecoil, and l is the coil length. If these parameters hold:µ 01 = µ 02 , S1 = S 2 , l1 = l2 ,

60

150

Current [A]

N

F. B.
AC/DC
Converter

S/SP or LCC/S
Circuit

50

1

0

0
-1

-50

That is, when coils having the same shape and dimensions on
the primary side and the secondary side are used, the I/O ratioof the WPT circuit can be determined by the turn ratio of thecoils alone, as in a general transformer.
In this experiment, litz wire with 42 turns on the primaryside and 12 turns on the secondary side was wound around aferrite core, as shown in Fig. 4 (b), and coils with a turn ratio of
3.50 were created. The distance from the center of the primarycoil to the center of the secondary coil is 15 mm, and every
parameter for the coils in this setup was as shown in Table I.
Fig. 5 shows the simulation and experimental circuit structures,with the conditions as shown in Table II. The input voltage VIN
was adjusted so that the power PL applied to the load resistancewas 150 W.
The waveforms of the I/O voltage and current are shown in
Fig. 6 and Fig.7. In both S/SP and LCC/S systems, the input
current IIN has a delayed power factor with respect to VIN, and it
can be seen that ZVS can be realized. VIN in both methods, andthe output voltage Vd in the LCC/S method are square waves.
Table III shows the root mean square (RMS) value of eachparameter result. Because VIN in both methods and Vd in the
LCC/S method are square waves, the I/O voltage ratio was

Current [A]

li

2
i

F. B.
DC/AC
Converter

Current [A]Voltage [V]Li =µ0i Si

Regulated
DC
Power
Supply,,,,Current [A]

L1 / L2

Voltage [V]3.50

Voltage [V]N1 / N2

80 mm

230
18.3
31.6
0.240
0.04565 mm

Table I. Transformer parameters42
L1 [μH]12
L2 [μH]0.487
M [μH]
511
r1 [Ω]
213
r2 [Ω]

50 mm

N1 [Turn]
N2 [Turn]
k
Q1
Q2

-2
-100
-150 0

VIN
I IN
5

10
15
20
Time [ µsec]

-3
25

30-4

-40
-60 0

-20

Vd
Id
5

10
15
20
Time [ µsec]

25

30-30

(a) Input(b) Output
Fig. 7 Voltage/current waveforms of LCC/S system
Table III. Experimental/simulation results
Method
SS/P
LCC/S
108
121
VIN [V]
2.11
1.51
IIN [A]
0.728
0.862
pf
27.4
33.8
Vd [V]
8.08
5.18
Id [A]
97.3
96.7
ηTR [%]
3.54
3.60
VIN / Vdcalculated using 0.9 times the RMS value of the square wave,
which is the RMS value of the fundamental wave. In the S/SP
method, the difference between the voltage ratio and the squareroot (SQRT) of the self-inductance ratio is -0.574%, and thedifference between the voltage ratio and the turns ratio is+1.04%. In the LCC/S method, difference between the voltage

In addition, in the S/SP system, the same power supply
experiment was conducted under load fluctuation. Fig. 8 shows
the I/O voltage ratio when the load resistance changes, and also
displays the SQRT of the self-inductance ratio and the turns
ratio. The voltage ratio did not change significantly, even whenload fluctuation occurred, and the results were roughly
consistent with the theory.

3.6

3.55
Ratio

ratio and the SQRT of the self-inductance ratio is +1.41%, andthe difference between the voltage ratio and the turns ratio is+2.86%. Both systems are generally consistent, demonstrating
the validity of the theory.

3.5

3.45

3.4 0

5

10

Voltage Ratio
sqrt of Inductance Ratio
Turn Ratio
15
20
25
30
RL [ Ω ]35

Fig. 8 Lad fluctuation characteristics of ratio

V. CONCLUSION
We focused on ease in designing WPT products, andshowed how to select the compensation capacitor and inductor
so that the I/O ratio could be determined solely by the selfinductances of the coils through an analysis of the S/SP and
LCC/S systems. Results of the power supply experiment andsimulation carried out for S/SP and LCC/S methods indicatedthat the I/O voltage ratio matched the turns ratio of coils having
the same shape and dimensions on the primary side and thesecondary side. The experiment also showed that the voltage
ratio did not change even when the load resistance fluctuated.
Similar experiments must be conducted in the future when gap
changes occur.
In this study, the power feeding experiment and simulation
were performed with solenoid type coils, but in the case of
WPT where mounting in small products and EVs is taken into
account circular coils have been extensively employed. Our
future work investigates whether the I/O ratio can be obtained
based on the turn ratio of the coils in the case of using circularcoils as well.

ACKNOWLEDGMENTS
We would like to thank Editage (www.editage.jp) for
English language editing.

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