電気学会論文誌●（●●●●●●●部門誌）
IEEJ Transactions on ●●●●●●●●●●●●●●●
Vol.●● No.● pp.●-●
DOI: ●.●●/ieejeiss.●●.●

Paper
Reduction of Reflected Power Loss in an AC-DC Converter
for Wireless Power Transfer Systems
Keisuke Kusaka＊, Student Member,

Jun-ichi Itoh＊a), Member(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)
This paper discusses a method to reduce reflected power in an AC-DC converter in high-frequency wireless power transfer
systems. First, conventional capacitor input-type rectifiers with silicon carbide (SiC) and gallium nitride (GaN) diodes areexperimentally tested. From an analysis of the results, it is confirmed that the reflected power occurs at the input stage of therectifiers owing to impedance mismatching. The reflected power should be suppressed because it will decrease the transmission
efficiency.
In order to solve the above-mentioned problem, an AC-DC converter that implements input impedance matching is proposed in
the last half of the paper. This paper presents the basic characteristics of the AC-DC converter and the experimental results, whichshow that the input impedance of the AC-DC converter enables a conversion from 13.56 MHz AC to DC with an input
impedance of 29.6 + j0.51 Ω. Thus, the reflected power is suppressed by 37.8% compared with the conventional capacitor
input-type diode bridge rectifier with a load resistance of 25 Ω. From the experimental results, it is confirmed that the AC-DC
converter is a valid circuit configuration for wireless power transfer systems.
Keywords : wireless power transfer, AC-DC converter, high-frequency, input impedance matchingsmall because the transmitting efficiency is proportional to the
product of a quality factor and a coupling coefficient(16). Note thata coupling coefficient decreases inversely with a cube of distance.
Considering to apply the wireless power transfer with MRC in thebattery chargers for electrical vehicles (EV), the coil for thetransmitting side and also for receiving side are planted on the
ground of parking areas, and underneath of EVs, respectively. This
technology can improve the convenience for users because users
are not required to charge the battery with electrical cables(17).
In the wireless power transfer system with the MRC, the size ofthe transmitting coils depends on the transmitting frequency(12).
The wireless power transfer systems are expected to operate inhigh-frequency in order to achieve high power density.
Additionally, MRC should be operated in the industrial, scientificand medical (ISM) band because noise from the wireless powertransfer system is prohibited to influence the operation of neither
the electronic devices nor the radio communication equipment.
For this reason, 13.56 MHz is used as the transmitting frequency
in this paper.
For this reason, an AC-DC converter, which can convert from13.56 MHz-AC to DC, is required in the receiving side of thewireless power transfer system. In addition, an impedance
matching is necessary in such high-frequency region in order tosuppress the occurrences of reflected power(18). A reflected poweroccurs at boundary points of the impedance when impedances aredifferent from the input impedance of an AC-DC converter withthe characteristic impedance of the transmission line(19). In orderto suppress reflected power, an input impedance of an AC-DC
converter should be matched to the characteristic impedance of thetransmission line. However, the input impedance matching
methods for the AC-DC converter has not been reported in such as
the high input frequency operation on the AC-DC converter are
not reported. It is difficult to make an input impedance matching

1. Introduction
Wireless power transfer methods such as the electromagnetic
induction method, the micro-wave power transfer and the lasertransfer have been attracted in community(1-5). However, thesewireless power transfer methods have issues about the efficiency
and transmission distance. In the electromagnetic induction
method, the transmission distance of the wireless power transfer
which can maintain the transmission efficiency at high is limited
up to only a few centimeters due to the effect of leakage
inductances. On the other hand, the micro-wave and the lasertransfer methods can transfer power wirelessly in a longtransmission distances, however these methods have insufficientof power conversion efficiency between an electric energy and aradioactive energy of electromagnetic waves(3-6).
Recently, the wireless power transfer using magnetic resonant
coupling (MRC), which is reported by A. Karalis et al. in 2007,
has been intensively in recent years (7-14). The MRC shows betterfeatures compared with the conventional wireless power transfer
methods such as the electromagnetic induction and the microwave
power transfer methods. First, the MRC allows a wireless powertransfer in a middle-range transmission distance such as a few
dozen of centi-meters at high efficiency of over 90%(15). Second,the declination of the transmission efficiency caused by a position
gap of the transmitting coils is relatively small. These advantages
are reason of the characteristic constructions from the transmission
coils. The transmitting coils have high quality factor Q owing to
the low parasitic resistance of the coils. The high quality factor
allows an efficient wireless power transfer in a middle-range
transmission distance even when the coupling coefficient k isa) Correspondence to: Jun-ichi Itoh. E-mail: itoh@vos.nagaokaut.ac.jp＊
Nagaoka University of Technology
1603-1, Kamitomioka-machi, Nagaoka, Niigata, Japan 940-2188© 200● The Institute of Electrical Engineers of Japan.

1Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)because the high input frequency constrains the latitude of thecircuit configurations.
This paper proposes and validates the AC-DC converter which
achieves the power conversion from 13.56-MHz AC to DC
without high-frequency switching. Additionally, the unity power
factor is achieved by simple circuit configuration using a LC
resonance.
The first section in this paper describes the principle of the
MRC and the experimental setup with MRC. Secondly, theconventional capacitor input type diode bridge rectifiers(CI-DBRs) with wide-band gap semiconductor devices are tested
as an AC-DC converter in the receiving side. The analysis of theexperimental results confirmed the effect of the input impedance
matching. Then, the required conditions for input impedance
matching of AC-DC converters are clarified. Thirdly, the AC-DC
converter which can achieve the input impedance matching is
proposed in order to suppress reflected power. The proposed
circuit is validated based on the simulation and experimental
results.

to the transmitting coil and the Pout is the power which is pickedup from the receiving coil. Thereby transmitting efficiency isdefined by
ηT =

Pout
× 100 [%] ............................................................ (1)
Pin

Table 1 shows the specifications of the open-end resonancecoils, which is used for the experiments, where the Rohm is acalculation value of an ohmic loss with considering skin effect.
Also, the inductance L and the capacitance C are measured by a
LCR meter (HIOKI, 3535). Additionally, mutual inductance Lm isderived by the frequency characteristics when the transmitting
distance is 150 mm. The coupling coefficient k of 0.09 is
calculated from the inductance L and the mutual inductance Lmusing k = Lm/L. The transmitting coil and the receiving coil have asame structure. In order to stabilize the figures of the windings,
the windings are implemented to the grooves on the fixture which
made from the acrylic. The resonance coils have a same structure
to the helical antenna. Thus, the resonance coils have a feeding
point at the center of the resonance coil such as a dipole antenna.
It means that both of the coil-ends are open. In consequence, theresonance coils have a self-resonant frequency f0 owing to the
distributed capacitance C of the winding pitch and the winding
inductance L. The self-resonance frequency is obtained by

2. Wireless Power Transfer System
2.1 Peripheral Circuits
Fig. 1 illustrates theconfiguration example of the wireless power transfer system with
MRC. The system consists of a PWM rectifier, a high-frequency
inverter, a transmission part, an AC-DC converter and a battery.
Generally, the high-frequency inverter is placed on the output
stage of the PWM rectifier for actual uses. However, PWM
rectifiers do not affect the wireless power transfer system because
a role of the PWM rectifier is conversion from commercial
frequency AC to DC. Additionally, this paper aims to evaluate theeffect of the reflected power which occurs at input stages of the
AC-DC converters. Hence, the PWM rectifier and thehigh-frequency inverter are not discussed in this paper.
The AC-DC converter, which has the battery as a load is placeon the EV. In this paper, the AC-DC converters in the receivingside are discussed. A reflected power occurs at the boundary
points of impedances owing to impedance mismatching whencircuits are operated in a high-frequency. For this reason, atransmitting coil is connected from an output stage of an inverter
via a coaxial cable with the characteristic impedance of 50 Ω.
Similarly, a coaxial cable is used between the receiving coil andthe AC-DC converter.
In the wireless power transfer systems with MRC, the size oftransmission coils depends on the transmission frequency. Thus, ahigh-frequency transmission is desired from the standpoint of apower density of the wireless power transfer system. In this paper,
the transmission frequency of 13.56 MHz that meets the ISM bandis used.
2.2 Configuration of Experimental System
Fig. 2shows the system configuration of the experimental setup of thewireless power transfer system with MRC. The system consists ofa function generator (FG), a radio frequency (RF) power supply
which has the output impedance of 50 Ω, two resonance coils anda load. Signal from the FG is amplified by RF amplifier. The RF
amplifier which can control the output travelling power iscomposed by an A-class linear amplifier in the test bench. The RF
amplifier can output an arbitrary travelling power up to 500 W.
Note that the output impedance of the RF amplifier is 50 Ω. The
outputted power is delivered to the load in the receiving side usinga magnetic resonant where the Pin is the power which is supplied

Fig. 1. The configuration example of the wireless powertransfer system.

Fig. 2. System configuration of the experimental setup.
Table 1. The specifications of the resonance coils.
Number of turn
6 [turn]2

Material

Magnet wire φ2.3[mm]Radius20[cm]

Length9.9[cm]

Ohmic resistance Rohm

151

[mΩ]

Inductance L

66.0

[µH]

Capacitance C

3.0

[pF]

Mutual inductance Lm

6.3

[µH]

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)

f0 =

1
2π

LC ................................................................. (2)Fig. 3 presents the equivalent circuit of the wireless powertransfer with MRC using open-end helical coils. The equivalentcircuit of the one-sided open-end helical coil is obtained as aseries RLC circuit because a winding capacitance in helical coils
is represented as series capacitor(20). Thus, MRC has a sameequivalent circuit to the electromagnetic induction, which hasseries resonance capacitors in the both sides; transmitting andreceiving sides. It should be noted that the equivalent circuits of
the MRC are different between the short-end transmission coil andthe open-end transmission coil. The equivalent circuit of theshort-end transmission coil is obtained as a parallel resonancecircuit. On the other hand, the equivalent circuit of the open-end
transmission coil is presented as a series resonance circuit.
Equation (3) provides the transmitting efficiency, where S21(ω)
is the transmission coefficient obtained by (4)(20), R is the sum of
the simulated resistance of a radiation loss, an ohmic loss of theresonance coils and a dielectric loss which occurs in the braces of
the resonance coils, Z0 is the load impedance and the output
impedance of the power supply, and ω is the transmission angularfrequency.

(a) Equivalent circuit.

(b) Equivalent circuit of type-T.

Fig. 3. Equivalent circuits of the wireless power transfer
with MRC.

Fig. 4. Experimental setup with conventional diodebridge rectifier.

η (ω ) = S 21 (ω ) × 100 ..................................................... (3)
2

2


1 

S 21 (ω ) = 2 jLm Z 0ω  L2m ω 2 −  R +  ωL −
 +
ωC 




Table 2. Ratings of the diodes for CI-DBR
shown in Fig. 4.

....... (4)



1 

2 jZ 0 R +  ωL − + Z 02 
ωC 




Diode

2
1
2− j
kQ

, S 21 (ω e ) =

2
2+ j

1
kQ

Rated current

Forward voltage drop

VR [V]IF [A]VF [V]

4

1.8

6

1.9

3

3

SiC-SBD

The transmission coefficient is proportional to the transmitted
power to the travelling power. By substituting the resonanceangular frequency ωm and ωe into (4), (5) is obtained(21) when theterm of simulated resistance R is assumed zero.
S 21 (ω m ) =Rated voltage

GaN-diode
Si-FRD

600

transmission loss, a reflection loss and a conversion loss of the
CI-DBR.
3.1 Experimental Setup
Fig. 4 presents theexperimental setup with conventional CI-DBR where vtr is thetransmitting coil voltage, itr is the transmitting coil current, vin is
the receiving coil voltage, iin is the receiving coil current and voutis the rectifier output voltage. The SiC or GaN diodes are used as
power devices in order to achieve a high-frequency operation of
the rectifiers because the switching devices with wide-band gap
semiconductors such as SiC and GaN are suitable for ahigh-frequency operation(22-25). The ratings of the power devices
which have voltage rating of 600 V and the current rating ofseveral amperes are shown in Table 2. Note that the schottky
barrier diode (SBD) is chosen for SiC. Additionally, the fast
recovery diode (FRD) is used for Si device in order to compare thecharacteristics of the rectifiers. The forward voltage drops of thediodes at the rated currents and a junction temperature of 25 deg
are described in the each datasheets.
The rectifiers are mounted on the each printed circuit boards(PCB) for a high frequency operation. The rectifiers have an input
terminal of a coaxial connector. Accordingly, the rectifier isconnected using a coaxial cable which has characteristics
impedance of 50 Ω to operate in a high-frequency. In addition, thelaminated ceramic capacitor of 0.47 µF (Murata,
GRM43DR72E474KW01L) is used as a smoothing capacitor in......................... (5)When the transmission frequency is equal to the resonancefrequency of ωm and ωe, the transmission coefficient has local
maximum value. Beside, (5) indicates that the product of inductive
coupling coefficient k between the primary and the secondary sideand quality factor Q of the transmission coils affects thetransmission efficiency. It should be noted that the (5) is valid only
when an output impedance of the power supply is equal to the load
impedance. Generally, the transmission efficiency using theelectromagnetic induction method is not so high in a middle-range
transmission distance because a coupling coefficient k decreases
inversely with a cube of transmission distance. In contrast, thehigh quality factor Q allows high efficiency wireless powertransfer in the MRC even when a coupling coefficient has a smallvalue.

3. Conventional Rectifiers with Wide-band Gap
Semiconductor Devices
Considering the application to EV chargers requires an AC-DC
converter which converts power from high-frequency AC to DC in
the receiving side. In this chapter, the experimental results with aconventional CI-DBR as AC-DC converters in the receiving side
are shown. In addition, the power losses are separated to a
3

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)ideal voltage source, it is known that CI-DBRs have an input
current with large harmonics components. However, only
fundamental component is efficiently delivered from thetransmitting side to the receiving side in this experimental setup
because the wireless power transfer systems with MRC have large
quality factor Q. It means that any frequency components
excepting the resonance frequency cannot be transmitted bywireless power transfer with MRC. Thus, the input voltage ofrectifier has large distortion.
Focusing on the output voltage vout, the DC voltages with low
voltage ripples are obtained when the SiC and GaN diodes areused as shown in Fig. 5 (a) and (b). On the other hand, the DC
voltage has large voltage ripples when the Si diode is used asshown in (c). The voltage ripples are 34.1% with SiC-SBDs,
38.5% with GaN-diodes and 78.6% with Si-FRDs respectively.
When the Si-FRD is used as a switching device, a limitation of
the switching speed narrows the conduction time of the diodes.
The shortening of the conduction time is verified by the increaseof output voltage ripple. The shortening of the conduction timemeans the increase of input impedance of the CI-DBR. Thus,
much reflected power occurs rather than the others CI-DBR.
The transmitting coil voltage includes a large component of
second harmonics from the transmission frequency due to thestanding wave. Generally, the standing wave which is synthetic
wave of the travelling power and reflected power becomes the loss
in transmission line. Furthermore, the standing wave causes aradiation of electromagnetic wave from transmission lines. So, thereflected power which causes a standing wave should be
suppressed.
The total efficiency which includes the transmission loss,
reflection loss and conversion loss, that is obtained from thewireless power transfer system with SiC, GaN and Si diodes, canreach to 75.2%, 69.2% and 5.2% respectively. The experimental
results verified that the wide-band gap semiconductor devices are
more suitable for the wireless power transfer system than Si
device.
3.3 Power Loss Separation
Fig. 6 shows a bar chartthat indicates the loss of the wireless power transfer system
including the diode rectifiers using the SiC and GaN diodes. Eachloss is separated according to loss separation method shown in Ref.
(19).
The SiC and GaN follow the similar characteristics. The
conversion loss of the rectifier using the SiC or GaN decreases
with an increase in load resistance. This can determine that a
conduction loss of the diodes dominates a conversion loss. The
difference of the forward voltage drops widely affects theconversion losses. In this experiment, the conversion efficiency
with SiC-SBD is higher than the GaN-diodes.
Moreover, the conduction loss of the diodes decreases with theincrease in load resistance because the input travelling power has
configured constantly. Beside the sum of the reflection loss of theresonance coils dominates an over half of the total loss. It should
be noted that the sum of the reflection loss become minimum atthe load resistance of 50 Ω. The reflection loss of the transmitting
coils can be reduced because the reflection loss depends on the
impedance of the resonance coils, which depends on the shape andmaterials of the resonance coils.
On the other hand, the reflected power depends on the input
impedance of a CI-DBR. The input impedance of the CI-DBR
fails to match to the characteristic impedance due to the input

purpose of smoothing the high-frequency voltage ripples.
3.2 Experimental Verifications with CI-DBR
Fig. 5presents the operation waveforms of the rectifiers, which uses the
SiC, GaN and Si diodes when the transmission frequency is 11.18
MHz, the load resistance of the rectifiers is 100 Ω, the travelling
power is 100 W and the transmission distance is 150 mm. Note
that, the resonance frequency does not agree with a 13.56 MHz inthese experiments because the resonance frequency depends on
the transmission distance.
From Fig. 5 (a) (b), the rectifier input voltage vin includes large
harmonics components. Generally, when CI-DBRs are operated by(a) With SiC-SBDs.

(b) With GaN-diodes.

Transmitting coil voltage vtr [250V/div]

0
Transmitting coil current itr [2A/div]0
Rectifier input voltage vin [50V/div]0
Output voltage vout [25V/div]

040[ns/div](c) With Si-FRDs.

Fig. 5. Experimental waveforms when the conventional
CI-DBR is connected to the wireless power transfer
using MRC as a load.
4

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)converter, Iin is the fundamental input current and θ is the phaseangle between the input voltage and the input current. In a
low-frequency region, power factor correction (PFC) circuits witha PWM control are used widely(26-30). The PFC circuits can satisfy
the above-mentioned conditions due to the input current control
with the PWM. However, the PWM needs high-frequency
switching compared with an input frequency. Thus, it is difficult to
operate the conventional PFC circuits when the input frequency isconstrained to high-frequency such as 13.56 MHz in the wirelesspower transfer system. As a result, an AC-DC converter without ahigh-frequency switching is required in the receiving side of thewireless power transfer system.
4.2 Circuit Configuration
Fig. 7 shows the circuit
configuration of the proposed AC-DC converter. The proposed
converter consists of a resonant-type rectifier which is reported by
K. Matsui et al.(31-32) and a bidirectional boost chopper. The
resonant-type rectifier achieves the PFC operation using theresonance between the inductor which is connected in series to the
input terminal and the capacitors in parallel to the upper arm. The
resonant-type rectifier has been demonstrated in a commercial
frequency in Ref. (31). However, this converter becomes a low
power density in the low-frequency operation because a huge
inductor and capacitors as resonance components are required.
Additionally, the possibility of the input impedance matching is
not discussed. In this paper, the resonant-type rectifier is operated
at a high-frequency and the function of the input impedance
matching is evaluated. The high-frequency operation improves thepower density owing to the downsizing of the passive
components.
In addition, Ref. (32) pointed that the amplitude of the input
current and the input power factor are changed by load conditions
when a resistance load is connected directly to the resonant-type
rectifier. It means that the input impedance of the stand-alone
resonant-type rectifier depends on the load conditions widely. In

current with large distortion. Moreover, the input current has
fluctuation due to the load of the CI-DBR. In order to increase theefficiency, the input impedance should be matched to thecharacteristic impedance of the transmission line regardless ofload conditions. In the next chapter, the conditions of the
impedance matching are described.

4. AC-DC Converter with Input ImpedanceMatching
4.1 Required Input Impedance Matching
Generally,
high-frequency circuits are constructed with an impedance
matching. Namely, a characteristic impedance of the power supply
and the input impedance have same impedances to thecharacteristic impedance of the transmission line. In particular, thecharacteristic impedance of 50 Ω is used widely. Thus the 50 Ω isused in this paper. Besides, the input impedance of AC-DC
converters with a battery is required to implement an impedance
matching regardless of load conditions.
Generally, a characteristic impedance of transmission lines
which is a reference value for the input impedance of the AC-DC
converter, do not include an imaginary part. It means that the 50 Ωof the characteristic impedance implies the 50 + j0 Ω. Therefore,
input voltage and current of the AC-DC converter are required tofulfill the following conditions.
(a) Vin/Iin = 50 Ω(b) Input power factor is 1 (cos θ = 1)
where Vin is the fundamental input voltage of the AC-DC
50
40
30
20
10
0

(a) With SiC-SBD.

50
40
30

Fig. 7. The proposed AC-DC converter with input impedance
matching for a high-frequency wireless power transfer system.

20
10

1
1 + sTiv

01
1 + sTic

1
sL2

1
sC4

(b) With GaN-diodes.

Fig. 6. Loss separation results of the wireless powertransmission system with CI-DBR.

Fig. 8. Control block diagram for S1 and S2 in the proposed
AC-DC converter.
5

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)5. Simulation Results of the Proposed AC-DC
Converterorder to overcome this problem, the bidirectional boost chopper isconnected at the rear side of the resonant-type rectifier in Fig. 1.
The bidirectional boost chopper is operated in purpose to fix theoperating point which is decided by the rectifier output voltage vchof the resonant-type rectifier. The MOSFET S1 is used for an
initial charge of the C4 instead of a diode because the input power
factor closes to zero when the rectifier output voltage vch is aroundzero.
The input impedance is determined by the input voltage andinput current. Therefore, the bidirectional boost chopper controls
the ratio between the input voltage and input current in the
proposed circuit. On the other hand, the phase angle is fixed at aresonance point in the rectifier in order to achieve the imaginary
part of zero. In detail, the input impedance of the proposed circuit
is determined by the three parameters; the resonance inductance L1,
the resonance capacitance C1, C2 and a voltage ratio αV where thevoltage ratio is the ratio of the rectifier output voltage vch to the
input maximum voltage Vm. The voltage ratio should be constantin order to achieve the intended input impedance. Note that, thevoltage ratio, which achieves the intended input impedance,
depends on the combination of the resonance capacitance andresonance inductance. The control method of the rectifier output
voltage is shown in the next subsection.
The control for the chopper circuit does not need a highdynamic response. Thus, the chopper circuit does not need neither
high-speed nor high-frequency switching. Thus, the chopper may
be operated in a low switching frequency such as 20 kHz.
However, a switching frequency of 100 kHz is selected in thispaper with the objective of the downsizing of the inductor L2 in
Fig. 1. Note that, the SiC schottky barrier diodes (SiC-SBDs) areused in the rectifier because rectifying diodes are required to havea performance to rectify the 13.56-MHz AC.
4.3
Control Method of Bidirectional Boost Chopper
Fig. 8 shows a control block diagram of the bidirectional boost
chopper where Tic is the integral action time of an automaticcurrent regulator (ACR) and Tiv is the integral action time of an
automatic voltage regulator (AVR). The bidirectional boost
chopper is operated in order to stabilize the voltage ratio αV. Thus,
the reference value of the rectifier output voltage is provided as

Fig. 9 presents the simulation results of the AC-DC converter
where the input voltage is 223 V, rated input power is 1 kVA. The
chopper current ich and the chopper voltage vch track thereferenced chopper current ich* and the referenced rectifier output
voltage vch* respectively. It looks like the chopper current does nottrack to the reference value. On the contrary, the input current
tracks to its reference value completely. It is caused by the low
switching frequency of the chopper circuit.
The rectifier output voltage includes second harmoniccomponents from the input frequency because the capacitor C3 ischarged by the rectifier current irec. The difference of the
impedance between the capacitor C3 and L2 allows the rectifier
current to flow into only the capacitor C3.
Focusing on the Fig. 9, the input current with a sinusoidal
waveform of the AC-DC converter is obtained because the voltage
control over the rectifier output. Additionally, the input power
factor of the AC-DC converter is closed to 1 approximately. Thus,an absolute value of the input impedance |Żin| is calculated as 49.6
Ω from the simulation results; the fundamental input voltage is223.4 V, and the fundamental input current is 4.50 A. The input
impedance is focused based on the fundamental component
because the wireless power transfer with high quality factor Q
enable a power transmission without harmonics components. The
input impedance is calculated from the fundamental component of
the input voltage and input current as a 49.6 + j0 Ω. It means thatthe proposed converter is capable of the input impedance
matching to the 50 + j0 Ω at the reflection coefficient which isdefined by (6) of 0.4%.
Γ=Z& 0 − Z& in=
Z& 0 + Z& in

PR...................................................... (6)PFwhere Ż0 is the characteristic impedance which is 50 + j0 Ω inthis paper, PF is the travelling power, PR is the reflected power
which are measured in the high-frequency power meter in the RF
amplifier. The squared reflection coefficient means the ratio ofreflected power to travelling power.

vch* = Vm×αV*.
Note that, the capacitance C3 can be negligible because thecapacitance C3 dominant in the combined capacitance of thecapacitors C3 and C4. The resonant-type rectifier achieves a PFC
operation regardless of the battery voltage VB. This is attributed toan ACR in chopper current ic and an AVR in the rectifier output
voltage vch of the bidirectional boost chopper. Namely it isassumed that the voltage source is connected to the rear end of theresonant-type rectifier.
In the proposed circuit, a fast dynamic response of thebidirectional boost chopper is not necessary. So, the AVR control
is constructed by a PI control with a natural angular frequency of
400 rad/s. Also the ACR is constructed by a PI control with 4000
rad/s as an inner loop in the AVR. The input current from therectifier irec is deal as a disturbance. The input impedance of the
proposed AC-DC converter is determined by the resonantcapacitors and the inductor. The design method of theseparameters is omitted in this paper because of space limitations.

Fig. 9. Operation waveforms of the proposed AC-DC
converter in simulation.
6

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)

6. Experimental Results of the Proposed AC-DC
Converter

converter enable the conversion from 13.56 MHz of AC to DC
without a high-frequency switching. Note that, the input voltage
distortion results from noises which are mixed into an input stageof the high-frequency power supply which used as instead of
output coils of wireless power transfer system.
6.3
Harmonics analysis
Fig. 11 indicates the
harmonics analysis results of the input voltage and input current of
the proposed AC-DC converter in the experiments. The harmonic
analysis is performed with an oscilloscope in order to inspect theexperimental waveforms. The input impedance of the proposed
circuit is derived from the harmonics analysis. The input
impedance is expressed by (7).

6.1 Experimental Setup
Experimental verifications areshown in this chapter. Table 3 provides the circuit parameters forthe experimental setup. The circuit parameters, which affect the
input impedance, are designed by cut and try because a
relationship between the input impedance and these parameters is
not linear. The design method of the resonance parameters will beshown in other paper.
The resonant capacitors are modified from 140 pF to 150 pF by
reason of a convenience of procurement. Moreover, the inductor
L2 is made by authors from an electrical steel sheet core. Note thatthe bidirectional boost chopper in the proposed AC-DC converter
is operated in open-loop control for simplicity. Also, a RF
amplifier which has 50 Ω of output impedance is used instead of
the receiving coil of the wireless power transfer system.
Furthermore, the battery is simulated by the stabilized DC power
supply, which cannot operate in a regeneration mode, with diodeand a resistance for blocking a return of the current to the DC
power supply.
The AC-DC converter; especially the part of the resonant-type
rectifier is mounted on the printed circuit board (PCB) in order tocut down the effects of parasitic inductance and parasitic
resistance between the circuit components. In particular, theparasitic inductance of a wire which is used in series to resonant
inductance affects the input impedance. For this reason, theresonant-type rectifier should be mounted with keeping in mind of
the parasitic inductances.
Besides, a laminated ceramic capacitor, which has low parasitic
inductance in the high-frequency, is connected in parallel to theelectrolytic capacitor in order to improve a characteristic of thesmoothing capacitor C4 because the rectifier voltage includes thesecond harmonics of the input frequency of 27.12 MHz. Similarly,
the SiC-SBDs are used for a high-frequency operation of theresonant-type rectifier.
6.2
Experimental Waveforms
Fig. 10 presents theoperational waveforms of the proposed AC-DC converter where
the simulated battery voltage VB is set to 90 V. The experimental
waveforms show that the input current can achieve a sinusoidal
waveform with small distortion. Additionally, the input current has
similar characteristics to the result which is obtained by using thesimulation. Besides, DC voltages of the rectifier output voltage vch
and the output voltage VB are obtained. It means that the AC-DC

Z& in =

Vin _ 1st
I in _ 1stcosθ + j

Vin _ 1st
I in _ 1stsin θ ................................... (7)where Vin_1st is the fundamental component of the input voltage,
Iin_1st is the fundamental component of the input current, θ is thephase difference between the input voltage and the current on thefundamental harmonic.
The analysis results shown in Fig. 11 are scaled on the basis ofFig. 10. Experimental waveforms of the proposed AC-DC
converter.

Table 3. Parameters of the circuit components.
Items

Manufactures

Model number

Value

MOSFET

S1 , S2

VishayIRFB11N50APBF

500 V, 11 A

Diode

D1-D4

Cree

C3D08060A

600 V, 8 A

VLF10040T-1R5N8R9
L1

TDK

L2

-

-

2.3 mHTDK

C3216C0G2J151JT

150 pFC3TDKCKG57NX7R2J474M

C4nichicon

C1

950 nH(Remodeled)

Inductor

C2
470 nF(in parallel)

Capacitor

220 µF
UPW2V221MRD(in parallel)
BHC
C5

ALS30A221DB450

Fig. 11. Harmonics analysis of the input voltage andinput current of the proposed AC-DCconverter.

220 µF

Components

7

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Reduction of Reflected Power in an AC-DC Converter (Keisuke Kusaka et al.)high-frequency wireless power transfer system. Furthermore, adesign considering the parasitic capacitances of diodes in theresonant-type rectifier can further reduce the reflection coefficient.

amplitude at 13.56 MHz. Additionally, a sampling frequency ofthe oscilloscope is 1.25 GHz. Note that, the probes; a differential
probe (Tektronix, P5205) and a current probe (Tektronix, TCP305),
which are used in these experiments, provide a limitation to thefrequency bandwidth at 100 MHz. For this reason, the harmonics
components over 7th are considered as reference values. The input
current harmonics is suppressed less than -20 dB in the frequency
bandwidth from 2nd to 20th. Thus, the input current distortion(THD) is 11.2% (reference value) in the bandwidth by 20th from a13.56 MHz.
Focusing into the fundamental components of the input voltage
and current, the input voltage of 19.8 V and input current of 0.67
A are obtained from the harmonics analysis. It shows that an
absolute value of the input impedance |Żin| is 29.6 Ω. Also, 4.1 degof phase difference between the input voltage and the input current
is obtained. The phase angle presents the input power factor cos θ
is 0.99. Hence, the input impedance of the proposed AC-DC
converter is 29.6 + j0.51 Ω. The experimental results contain ameasurable error in the real part since the design value is 50 + j0Ω. An additional simulation results confirmed that the error occurs
subject to the parasitic capacitances of the diodes of theresonant-type rectifier. A parameters design taking account of theparasitic capacitors can reduce the error and the reflection
coefficient.
6.4
Comparison of the Reflection CoefficientFig. 12presents a comparison in terms of the reflection coefficient
between the conventional CI-DBR with SiC-SBD shown in Fig. 4
and the proposed AC-DC converter.
It should be noted that all of reflection coefficient is measured
in 13.56 MHz when the AC-DC converters are connected to the
RF amplifier directly. The reflection coefficient should be zero
because the reflected power is not input into a circuit.
The reflection coefficient of the CI-DBRs is measured at eachof four different loads: 25 Ω, 33.3 Ω, 50 Ω and 100 Ω, because theinput impedance of a conventional CI-DBR depends on the loadcondition. The proposed AC-DC converter minimizes thereflection coefficient among the others configuration with theconventional CI-DBR. Especially noteworthy is the fact that thereflection coefficient is suppressed by 37.8% in comparison with
the CI-DBR with a load of 25 Ω. The experimental results showthat the AC-DC converter can suppress the reflection loss which
occurs at input side of the proposed AC-DC converter in7.

Conclusion

In this paper, a reduction method of the reflected power isexperimentally demonstrated using the AC-DC converters for ahigh-frequency wireless power transfer system with magnetic
resonant coupling. A high-frequency AC-DC converter is requiredin the receiving side of the wireless power transfer systems which
is operated at high-frequency such as 13.56 MHz. Additionally,
the input impedance of an AC-DC converter should be matched tothe characteristic impedance of the transmission line in order toreduce the reflection loss.
In order to apply the wireless power transfer into practical use,
the CI-DBRs with SiC-SBDs and GaN diodes are tested. However,the loss separation results clarify that the reflection loss which
occur at the input stage of the CI-DBRs drastically reduces thetransmission efficiency because of the large harmonics and theload dependence of the input current. In order to solve the problem,
the AC-DC converter, which that implements input impedance
matching, is proposed. The experimental verifications confirmedthat the proposed AC-DC converter enables a conversion from13.56 MHz AC to DC without a high-frequency switching. In
addition, the input impedance of 29.6 + j0.51 Ω is obtained fromexperiments. The reflection coefficient is reduced by 37.8%
compared with the conventional CI-DBR with a load of 25 Ω.
Thus, this is clear that the AC-DC converter is a valid circuit
configuration to perform as a receiving side of the high-frequency
wireless power transfer system.
In the future work, the detail of the design method of the
proposed AC-DC converter will be optimized.

References
(1)

(2)

[%]

(3)

Reflection coefficient

(4)

(5)
(6)

(7)

(8)

Fig. 12. Comparison of the reflection coefficients of theconventional CI-DBR and the proposed AC-DC
converter based on the experimental results.

(9)8

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Keisuke Kusaka(Student Member) received his B.S. and M.S.
degrees in electrical, electronics and informationengineering from Nagaoka University ofTechnology, Niigata, Japan in 2011 and 2013,
respectively. Since 2013, he is currently working
towards to a PhD degree in electrical andelectronics engineering. His research interests
include high-frequency converters and wirelesspower transfer systems.

(Member) received his M.S. and PhD degrees inelectrical and electronic systems engineering from
Nagaoka University of Technology, Niigata, Japan
in 1996 and 2000, respectively. From 1996 to 2004,
he was with Fuji Electric Corporate Research andDevelopment Ltd., Tokyo, Japan. Since 2004, He
has been with Nagaoka University of Technology
as an associate professor. He received the IEEJ
Academic Promotion Award (IEEJ TechnicalDevelopment Award) in 2007 and the Isao Takahashi Power Electronics
Award in 2010. His research interests include matrix converters, DC/DC
converters, power factor correction techniques and motor drives. He is amember of the Institute of Electrical Engineers of Japan and the Society ofAutomotive Engineers of Japan.
Jun-ichi Itoh9

IEEJ Trans. ●●, Vol.●●, No.●, ●●●