Proposal of Switched-mode Matching Circuit inPower Supply for Wireless Power Transfer
Using Magnetic Resonance Coupling
Keisuke Kusaka

Jun-ichi Itoh

Dept. of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka Niigata, Japan
kusaka@stn.nagoakaut.ac.jp

Dept. of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka Niigata, Japan
itoh@vos.nagaokaut.ac.jp

Abstract— This paper discusses on the matching circuit in the
power supply for wireless power transfer using a magnetic
resonance coupling (MRC). The MRC is desired to operate athigh frequency in the Industry Science Medical (ISM) bands
such as 13.56 MHz. The resonance with high quality factor
between the transmitting side and receiving side enables highefficiency for wireless power transfer. Therefore, the output
frequency of the inverter must be aligned identically to theresonance frequency of the resonance coils in purpose of
keeping the high transmission efficiency. In addition, theoutput impedance of the power supply has to be matched to thecharacteristic impedance of the transmission line that is
despites to the output frequency. In this paper, the Switchedmode Matching Circuit (SMC) which operates to stabilize theoutput impedance of the inverter is proposed by the authors.
The results confirmed in experimental and simulation
demonstrates that, the SMC able to provide the variation of
the output impedance.

I.

INTRODUCTION

In recent years, the wireless power transfer systems are
increasingly studied [1-2]. Especially, the wireless powertransfer using a magnetic resonant coupling (MRC) which isreported in 2007 has been attracted in community [3-5]. The
MRC shows advantages compared to other wireless powertransfer methods such as an electromagnetic induction andmicrowave power transfer. First, the MRC enables a wirelesspower transfer at middle range distance such as 1 m at highefficiency over 90%. Second, the declination in transmission
efficiency caused by position gap is relatively small. The
MRC is found suitable to apply in the battery chargers forelectric vehicle (EV). The transmitting device and thereceiving device are placed on the ground of parking areas,
and underneath of the EV respectively. The batteries arecharged automatically when the EV is parked at the parking
areas. The wireless power transfer system enables to improvethe conveniences of the users.

The studies about the resonance coils and a rectifier inthe receiving side have been discussed actively [6-8].
However, a research about high frequency power supply andmatching circuit are not discussed. In the MRC system, thewire length of the resonance coil decreases commensurately
with increasing transmission frequency. The resonance coils
must be mounted on the EV. Furthermore, the resonancecoils are required being small size and light weight. The
wireless power transfer using a MRC satisfies to the standardof Industry Science Medical (ISM) band of around 13.56
MHz. Therefore, a high frequency inverter achieves highefficiency is needed.
In addition, a reflected power occurs at the boundary
point of the impedance in high frequency region. In order tosuppress the reflected power between the power supply andtransmission line, a matching circuit which consists of theinductor and capacitor is placed at the output terminal of theinverter. Generally, the high frequency inverters, which areused in the high frequency applications such as a plasma
generation, often operated in a constant output frequency.
Thus, the matching circuit needs unique parameters toconsistent the output impedance with the characteristic
impedance of the transmission line. However, the resonancefrequency of the resonance coils is fluctuated according to
the transmission distance in the wireless power transfer
systems. Therefore, the output frequency of the inverter mustbe aligned identically to the resonance frequency of theresonance coils in order to keep the high transmission
efficiency. In a conventional matching circuit, the matchingcircuit has a meter movement because the matching circuit
consists of the inductor, variable capacitors and stepping
motors. Therefore, the meter movements decrease a lifetimeand response speed of the matching circuit.
Firstly, the characteristics of the wireless power transfer
system with MRC and fundamental characteristics of thereflected power are described. The reflected power occurs
due to the impedance mismatch. Secondary, the output
impedance of the inverter is discussed in this paper. A
proposed circuit is designed base on the matching circuitwith Low-frequency Pass Filter (LPF) type. Finally, theSwitched-mode Matching Circuit (SMC), which enable toadjust the output impedance of the inverter using the
MOSFETs. The SMC can improve the lifetime and response
speed of the matching circuit. The experimental verificationof the SMC is demonstrated.
II.

WIRELESS POWER TRANSFER SYSTEM

Fig. 1 illustrates the system configuration of a wirelesspower transfer system using the MRC. The system consistsof the function generator (FG), the radio frequency (RF)power supply matched to 50 Ω, two resonance coils and theload. Signal from the FG are amplified by RF power supply.
The RF power supply which can control the output travelling
power is composed by an A-class linear amplifier in the test
bench. The amplified power is supplied to the resonancecoils. The resonance coils are designed according to thespecification shown in Table I. The resonance coil whichplaced in the transmitting side is called as the transmitting
coil. Also the resonance coil, which placed in the receivingside, is known as the receiving coil. Besides the resonancecoils have a same structure of the helical antenna. Thus, theresonance coils have a feeding point at the center of theresonance coil. In consequence, the resonance coils have aself-resonance frequency f0 due to distributed capacitance Cof winding pitch and winding inductance L. The selfresonance frequency is obtained by f0=1/{2π(LC)0.5}.
Fig. 2 presents the equivalent circuit of the wirelesspower transfer using the MRC [9]. The equivalent circuit of
the one-sided resonance coil is presented as a seriesconnected RLC circuit. Thus, the MRC has a sameequivalent circuit to the magnetic induction which has series
resonance capacitors in both sides; transmitting andreceiving, to have a resonance. Equation (1) presents thetransmitting efficiency, where S21(ω) is the transmission
coefficient which is obtained by (2) [10], Lm is the mutual
inductance, R is the simulated resistance of the radiation loss,
copper loss of the resonance coils and dielectric loss which
occurs in the braces for the resonance coils, Z0 is thecharacteristic impedance of the transmission line, and ω isthe transmission angular frequency.
η (ω ) = S 21 (ω ) × 100
2

(1)

2
⎡
⎧
1 ⎞⎫
⎛
S 21 (ω ) = 2 jLm Z 0ω ⎢ L2mω 2 − ⎨R + ⎜ ωL −
⎟⎬ +
ωC ⎠⎭
⎝
⎢⎣
⎩

⎤
⎧
1 ⎞⎫
⎛
2
2 jZ 0 ⎨R + ⎜ ωL −⎟⎬ + Z 0 ⎥
C
ω
⎝
⎠⎭
⎩
⎦

(2)

The transmission coefficient is a proportion of thetransmission power to the travelling power. By substituting
the resonance angular frequencies ωm and ωe into theequation, (3) is obtained
S 21 (ω m ) =

2
1
2− j
kQ

, S 21 (ω e ) =

2
2+ j

1
kQ

(3)

When the transmission frequency equals to the resonancefrequencies of ωm and ωe, the transmission coefficient S21(ω)
has local maximum value. Note that the ωe is larger than theωm. An electromagnetic field distribution between thetransmitting coil and the receiving coil for the wirelesspower transfer is difference in terms of the resonancefrequencies. Furthermore, equation (3) indicates that the
product of inductive coupling coefficient k and quality factor
Q will affect the transmission efficiency. The inductive
coupling decreases in inverse proportion to cubetransmission distance. However, the k·Q still remains highbecause high quality factor Q is in a middle-range distance.
Generally, the magnetic induction is operated with low
quality factor such as several dozens. On the other hand, the
MRC is operated in a few hundred of quality factor.
High quality factor enables high efficiency wirelesspower transfer. However, the resonance frequency depends
on the transmitting distances because of the variation of
coupling coefficient k. Therefore, the transmission frequency
needs to track to the resonance frequency of the transmitting
coils in order to maintain the transmission efficiency.

Figure 1. System configuration of wireles power transfer using MRC.

TABLE I.

SPECIFICATIONS OF RESONANCE COILS.

Number of turnMaterial
RadiusVertical Height

6 [turn]
Magnet wire φ2.3[mm]20 [cm]9.9 [cm]

(a)The reflection coefficient Γ is decided by using thecharacteristic impedance of the transmission line Ż0 and
impedance of the load ŻLoad. The reflection coefficient Γ
indicates the proportion of the reflection voltage to thetravelling voltage. Moreover the reflection coefficient Γ
follows the proportion of the reflection current to thetravelling current. Hence, the ratio of the travelling power toreflected power is a squared reflection coefficient Γ2.
Furthermore, the transmitted power is obtained bysubtracting the reflected power from the travelling power.
When the characteristic impedance of the transmission line
equals to the impedance of the load, reflection coefficient iszero. So, the reflected power does not occur.

Equivalent circuit.

The experimental results confirmed that the reflected
power which is not consumed at the load has to be
suppressed.
PF
(b)

PLoad

PR

Equivalent circuit of type-T.

Figure 2. Equivalent circuit of the wireless power transfer using a MRC.

III.

FUNDAMENTAL CHARACTERISTICS OF THE
REFLECTED POWER

Fig. 3 shows the experimental circuit which clarifies therelationship between the travelling power and the reflected
power. In Fig. 3, PF is the travelling power, PR is thereflected power and PLoad is the transmitted power whichequals to the consumed power at the load resistancerespectively. The resistance load is connected to the RF
power supply through the coaxial cable which has
characteristic impedance of 50 Ω. In the high frequency
region, the reflected power occurs at a certain boundary pointof the impedance when the impedance is mismatched.
Fig. 4 shows the characteristics of the reflected power
and transmitted power when the travelling power is 100 W in
the circuit drawn in Fig. 3. The reflected and transmitted
powers depend on the load resistance when the characteristic
impedance has a constant value. The consumed power isdecreased with increasing the reflected power due toimpedance mismatch. The theoretical formulas of thereflected power and transmitted power are obtained by (4)and (5) respectively.
*
Load

P

(

= PF 1 − Γ

PR* = PF Γ2
by

2

)

(4)
(5)

where Γ is the reflection coefficient which is expressedΓ=Z 0 − Z LoadZ 0 + Z Load

(6).

Figure 3. Experimental circuit which clarifies the relationshipamong a travelling, a reflected and transmitted power.

120
100

*
PLoad

80
60
40

PR*

20
0

20

40

60

80

100

120

Figure 4. Characteristics of the reflected and transmitted power.

IV.

DERIVATION OF OUTPUT IMPEDANCE OF INVERTER

Fig. 5 provides an example of the high frequency power
supply configuration for a wireless power transmission,
where the MRC is used to considerate the output impedanceof the inverter. The output impedance of the inverter which
is operated in a constant frequency at high frequency withsquare wave operation is discussed. Note that the inverter
does not have a voltage controller. Besides, the matchingcircuit, which has same circuit configuration to the LPF, isconnected to the output terminal of the inverter. Since the
LPF circuit consists of an inductor Lm and a capacitor Cm as amatching circuit at one frequency which is used in the designof LPF, the impedance mismatch occurs when the output

frequency is not equals to design frequency. Therefore, thetransmission frequency which equals to the output frequencyof the inverter has to tracks to the resonance frequency.

Where the cut-off frequency is expressed by

Fig. 6 shows the block diagram of the power supply
including the matching circuit where Ed is the DC voltage ofthe inverter, Vcmd is the output voltage command for inverter
and rd is the simulated resistance of the voltage drop due todead time of the inverter. Thus rd is connected to thematching circuit in series to the inductor in Fig. 5. In thisscheme, the output current from the matching circuit isconsidered as a disturbance. The block diagram clarifies thatthe output voltage Vout is obtained byωc = ω

Vout = Gcmd (s )Vcmd + Gd (s )I out(7)where Gcmd(s) is the transfer function in term of output
voltage command Vcmd and Gd is the disturbance transfer
function in term of output current Iout. Note that the output
impedance is defined as Zout=ΔVout/Iout. Therefore, the output
impedance of the inverter without an automatic voltage
regulator (AVR) is obtained from Żo=Gd(s)|s=jω [11]. The
output impedance is decided by the disturbance transfer
function where Gd(s) is presented by
Gd ( s ) =ω c2 (Ls + rd )(8).

r
s 2 + d s + ω c2
L

By substituting (8) into the equation, the output
impedance of the inverter is expressed by (9) where ωc is the
cut-off frequency of the LPF.

⎧
r2 ⎫rd ωc4 + jωωc2 ⎨ L ωc2 − ω 2 − d ⎬L⎭⎩Z o = Gd (s ) |s= jω =(9)2
⎛ rd ⎞22 2
ωc − ω + ⎜ ω ⎟
⎝L ⎠

(

(

)

)

o

Cm =

rd2ω 2 Re[Z o ](rd ω − ω − ω
4
c

2
c

Re[Z O ] − rd
ω 2 Lm Re[ZO ])2 2Re[Z 0 ]

d

1

(12).

Lm Cm

Therefore, to match the output impedance of the inverterto the characteristic impedance of the transmission line, boththe inductance and capacitance should be adjusted. Note thatthe output voltage of the inverter including the LPF is asinusoidal waveform due to the resonance when the output
impedance is matched.
Fig. 7 presents the frequency characteristic of the output
impedance of the inverter which is designed to match the
impedance to 50+j0 Ω at 13.56 MHz where the inductance
Lm is 115 nH and the capacitance Cm is 1.15 nF. Fig. 7 shows
the design of the output impedance is correct, although bothof the output impedance; real part and imaginary parts havevariation when the frequency does not equal to the design
frequency of the LPF. The reflected power occurs due to thefluctuation of the output impedance between the power
supply and transmission line according to (5). Assuming thatthe frequency fluctuation of the MRC is plus or minus 1
MHz, the output impedance has maximum variation of 30 Ω.
Fig. 8 shows the proportion of the reflected power to thetravelling power Γ2 when the output frequency of theinverter has fluctuation where the inductance Lm is 115 nH
and the capacitance Cm is 1.15 nF. Note that the LPF isdesigned in respects to the output impedance of 50+j0 Ω at
13.56 MHz. Assuming the frequency fluctuation of theinverter is ±1 MHz, the proportion of the reflected power totravelling power reaches up to 11.9%. It means that 11.0 %power loss occurs due to impedance mismatch. As a result, astanding wave occurs in the transmission line due to thereflected power. Therefore, the output impedance of theinverter has to be matched to the characteristic impedance of
the inverter.

The output frequency of the inverter should be matchedto the characteristic impedance of Ż0=Re[Ż0]+j0 Ω. It should
be noted that the characteristic impedance does not composeof the imaginary part because the standard of thetransmission line does not have characteristic impedancewith imaginary part. By solving the simultaneous equation interms of L and ωc, the inductance and capacitance of the LPF
is obtained by (10) and (11) [12].

Lm =Re[ Z o ]=Re[ Z ] − r

I inv

I out

Vinv

Vout

Figure 5. Basical matching circuit design
without of consideration of the output frequency fluctuation.

I out

(10)
Vcmd

Ed

Vinv

I inv
1
rd + sLm

1
sCm

(11)
Figure 6. Block diagram of the power supply
including the matching circuit.

Vout

100

40

80

20

60

0

40

-20

20
0
12

Fig. 10 shows the control brock diagram of the SMC. The
two control methods are proposed in this paper. In bothproposed control diagram, the switches of the matchingcircuit are synchronized with the output voltage of theinverter which is operated in square wave operation. The
SMC is operated according to the frequency command fcmd,
duty Dm and phase command θ for S1-4. The frequency
command is decided based upon to the high transmission
efficiency of the MRC. Note that, frequency tracking method
is not discussed in this paper.

12.5

13

13.5

14

14.5

-40
15

Figure 7. Frequency characteristic of output impedance.

25
20
15
10
5
0
12

12.5

13

13.5

14

14.5

15

Figure 8. Frequency characteristic of reflected power.

V.

The gate signal is generated using a carrier comparison
method. The carrier signal is provided to the comparator
through the phase shifters which are controlled according to
the phase command. The Dm controls the conduction time ineach output period of the SMC which is equaled to theswitching period because the domain of the Dm is from 0.5 to
1. Besides, two control block diagrams are considered. In thecontrol diagram which shown in (a), the phase command
which is used in the carrier comparison for S1-4 is controlled.
On the other hand, the phase command which is used for S5
and S6 is manipulated in control block diagram which shownin (b). The control periods of the Dm and θ are allowed tolonger than the switching period of the inverter and SMC.
The variation of the resonance frequency occurs as a result of
the position gap between the transmitting coil and thereceiving coil, is not changing rapidly.

SWITCHED-MODE MATCHING CIRCUIT TOPLOGY

Fig. 9 presents the proposed Switched-mode Matching
Circuit (SMC). The SMC, which consists of six MOSFETs,
two capacitors and two inductors, are connected to the output
terminal of the inverter in series. As a result, the SMC shows
the similar characteristics to the LPF. The switchingfrequency of the SMC is constrained by the output frequencyof the inverter.
The specifications of the SMC are obtained by Table II.
The switches of the S1-4 are operated to make a variation of
the output impedance of the inverter. The additional
capacitance C2 is connected to the L1 in series when both theS2 and S3 or both the S1 and S4 are turn-on. On the other hand,the additional inductance L2 is connected to the C1 in parallel
when both the S3 and S5 or both the S4 and S6 are turn-on.
The SMC controls the timing of the switches. Therefore, theimpedance of parallel connected L2 and C1 have same
impedance to the Cm in Fig. 5. Additionally, the relationshipbetween the L1 and C2 should respects to (13) when the
output frequency has a fluctuation to f’ [13]. Also, the output
impedance should be matched to ŻO when the S1-4 are turnon. So, the inductor is designed to L1=Lm and matches theoutput impedance.
2πf ′L1 >1
2πf ′C 2(13)

Figure 9. Switched-mode Matching Circuit (SMC).

TABLE II.
Items
MOSFET
Capacitor
Inductor

SPECIFICATION OF SMC.

Manufacturers
Sinv1-4
S1-6
L1
L2
C1
C2

Microsemi
TDK
TDK
TDK
TDK

Value
1 MHz
13.56 MHzARF463BP1G(500V, 9A)
114nH
1.5μH
100nH
0.80μH
47nF
2.5nF
22nF
1.4nF

(a) Control method I.
Carrierfcmd

Carrier
generator

1
0

0.5

+

Dm

(Dm>0.5)

Sinv1, Sinv4
Sinv2, Sinv3

Phase shifter+

S2, S3Phase shifter+

S1, S4Phase shifter

+

≤ ≤
+
+

0.5

S5
S6

(b) Control method II.
Figure 10. Control block diagram of the SMC.

VI.

EXPERIMENTAL RESULTS

A. Experimental Methodology
In this chapter, the experimental results of the SMC arepresented. Then experimental setup of the SMC including asquare wave operated inverter and the carrier signal isprovided from the FG. Note that, the output frequency andswitching frequency are 1 MHz due the setup limitation.
Then the parameters of the SMC are changed to L1=1.5μH,
L2=0.75μH, C1=47nF, C2=22nF according to Table II.
i.

On-off method for detection of output impedance
The on-off method is implemented to detect the output
impedance of the inverter for experiments which is describedlater. The on-off method detects the output impedance of theinverter using the difference between the no-load output
voltage and loaded output voltage. The output impedance isobtained byVZ o = o − R Load
I

(14)

where İ is the load current, RLoad is the load resistance and
Vo is the source voltage which equals to no-loaded output
voltage. When the load resistance does not include theimaginary part of the impedance, the load current is obtainedby output voltage of the SMC and a phase difference
between the output voltage of the inverter and output voltageof the SMC in terms of the fundamental components.

ii.
Current injection method for detection of output
impedance
The accuracy of the output impedance with the on-off
method is lower than the current injection method. Therefore,
the current injection method is used in generally as adetection method of the output impedance. The current
injection method measures the voltage of the output terminaland current which is injected into output terminal. The
injected current is a sinusoidal wave consists of the same
frequency to the output frequency of the inverter. The output
impedance is calculated by the amplitude and the phasebetween the generated voltage and injected current. Note that,when the output terminal voltage has distortion and DC bias,
the detection of the phase returns an error. Thus, in such a
way as to reject the DC bias and distortion, a Bandfrequency Pass Filter (BPF) is added to the detector of thevoltage and currents.
The on-off method as described previously is used in theexperimental described in next chapter because the output
impedance can be calculated simply compared to the current
injection method. On the other hand, the current injection
method is used in the simulation results to considerate theoperation of the SMC in detail.

B. Experimental Waveforms of SMC with Control
Block Diagram I
Fig. 11 shows the experimental results of the SMC andhigh frequency inverter with the control block diagram I
when the duty Dm is 0.5 and phase command θ is 0˚. In theseresults, the switching frequency is approximately 1 MHz andthe output voltage shows a sinusoidal waveform. During the
no-load condition, the output voltage is 18.6 Vrms. On theother hand, output voltage of 14.2 Vrms is obtained when theresistance load 50 Ω is connected. In consequence, theoutput impedance 59.6 Ω is calculated using (14). In these
conditions, the capacitor voltage of C2 has resonance. Notethat the calculated impedance has a margin of error due to a
detection error of the phase angle between the drain-source
voltage and output voltage. Besides, the output voltage of theinverter and output voltage waveform include the distortions
due to the dead time. The distortions affect the accuracy.
Fig. 12 shows the experimental waveforms when thecontrol parameters are changed to θ=-90˚. In these cases, theoutput voltage is 15.4 Vrms at no-load condition and 11.9 Vrms
with resistance load of 50 Ω, respectively. Similarly, theoutput impedance 64.7 Ω is calculated using (14). In thiscase, the output impedance increases compared to conditionof θ=0˚ because the voltage fluctuation of C1 decreases.
Therefore, the validity of the SMC can be confirmed. Also,
to control the phase reference θ and duty Dm of the SMC, theoutput impedance of the inverter can be changed by using
the SMC. It means that, the SMC can reduce the reflected
power which occurs at the boundary point of the impedance
due to the impedance mismatch to adopt the frequency
tracking control.

C. Simulation Results of SMC with Control Block
Diagram II
Fig. 13 shows the simulation results, where the output
impedance is varied when the operating frequency is aconstant value. The SMC is modeled using a circuit
simulator to clarify the fluctuation of the output impedance.
Note that the control block diagram II is used in thisconsideration. The matching circuit is designed to match theoutput impedance to 50+j0 Ω at Dm=1 and fcmd=13.56 MHz.
The simulation results yields that real part of the output
impedance increase shown in (a) with changing the phaseangle of carrier θ. The simulation results present that thephase command θ enables to control the real part of theoutput impedance. The phase command is controlled in thedomain of between -90˚ and 45˚. Also both the real part andimaginary parts have fluctuations with increasing Dm. The
detail of the operation will be considered.

(a) No-load.

(b) 50 Ω load.
Figure 12. Experimental result of the SMC when the Dm=0.5, θ=-90˚5048(a) No-load.

46
44
42
40
-90

-45

0

45

90

45

90

.
(a)

Real part.

10(b) 50 Ω load.
Figure 11. Experimental result of the SMC when the Dm=0.5, θ=0.

8
6
4
2
0
-90

-45

0
(b)

Imaginary part.

Figure 13. Output impedance of the inverter including the SMC atconstant frequency.

VII. CONCLUSION
In this paper, the matching circuit in the high frequency
power supply for wireless power transfer with MRC is
discussed. In the MRC system, the resonance frequency uses
to obtain the maximum transmission efficiency has
fluctuation is because of the transmission distance. Thus, theoutput frequency of the inverter needs to track the resonancefrequency. In addition, the reflected power occurs at the highfrequency region due to the impedance mismatch between
the output impedance of the inverter and characteristic
impedance of the transmission line. Therefore the output
impedance of the high frequency power supply is required tomatch with the characteristic impedance of the transmission
line despites of the output frequency. However, thefluctuation of the output frequency at the power supply
affects the output impedance when the matching circuit isconstructed by only inductor and capacitor. In this paper, theSMC which is used to adjust the output impedance of thepower supply is proposed.
The experimental results confirmed that the output
impedance has changed from 59.6 Ω to 64.7 Ω from thechanges of the control parameter θ. In addition, thesimulation results showed the control range of the SMC.
Therefore, the simulation and experimental results also
confirmed that the SMC can adjust the output impedance.
In the future work, the detail of the design method of the
SMC will be optimized.

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