Ventec 2021
5th International Electric Vehicle Technology Conference 2021

Flying-capacitor Linear Amplifier with N-channel MOSFETs
for Radiation Noise Reduction of Wireless Power Transfer System

Rintaro Kusui 1) Keisuke Kusaka 1) Jun-ichi Itoh 1)
1) Nagaoka University of Technology, Nagaoka, Niigata, Japan
E-mail: kusui@stn.nagaokaut.ac.jp
ABSTRACT: This paper proposed a flying-capacitor linear amplifier (FCLA) for wireless power transfer (WPT) systems. The proposed
FCLA consists of only n-channel MOSFETs and an unfolder in the output stage. The FCLA with the unfolder output a sinusoidal voltage
and current. Due to the sinusoidal output, the radiation noise harmonics from transmission coils reduces. First, the proposed FCLA
configuration and control method is explained. Then, the operation of the proposed FCLA connected to the WPT system is demonstrated
by simulation. In addition, harmonic components of current on a primary coil are analyzed. As a result, it is confirmed that the third-orderharmonic component is reduced by 49.1 dB in comparison with a conventional two-level inverter. Finally, it is confirmed that the flying
capacitor voltage is automatically balanced by a prototype with two-series MOSFETs in the upper arm. Furthermore, the third-orderharmonic output voltage is reduced by 19.8 dB compared to the square wave.

KEYWORDS: wireless power transfer, radiation noise, flying-capacitor linear amplifier, linear amplifier, flying-capacitor

1. INTRODUCTION

In recent years, a wireless power transfer (WPT) systemfor electric vehicles (EVs) is actively studied(1-3). Especially,
an ultra-fast charging of the WPT system is required tocharge an onboard large-capacity battery in a short time.
However, high-power WPT emits large radiation noise. The
radiation noise may cause malfunctions of other electronicequipment or interferes with wireless communication. The
WPT system must comply with the regulation establishedby CISPR. In particular, the regulation of radiation noise
harmonic for the high-power WPT systems will betightened by approximately 30dB. Thus, a reduction
method of radiation noise in both low-order and high-orderharmonics is required.
Most of the WPT systems previously reported have an
inverter, which outputs a square wave voltage(4). The
harmonic component of the square wave voltage causes the
harmonic current on the transmission coil. The harmonics
components of the current on the coil are the critical reason
for the harmonic components of the leakage magnetic flux.
For this reason, satisfying the regulation is difficult in thehigh-power WPT system.
Besides, a flying-capacitor linear amplifier (FCLA) has
been proposed for suppressing high-frequency leakage
current from a switching power converter and removing LC
filter(5-7), as substitutes for AC-DC or DC-AC converters.
The FCLA efficiently outputs a continuous voltage by
operating one of the MOSFETs in a saturation region.
However, the conventional FCLA needs not only n-channel
MOSFETs (n-MOSFETs) but also p-channel MOSFETs (pMOSFETs), which have inferior characteristics. The p-

MOSFETs in FCLA cause a decrease in efficiency anddistortion of the output waveform.
This paper proposed the FCLA with only n-MOSFETs
for the WPT system in order to reduce the harmonics of theradiation noise. The current on the transmission coils has noharmonics components in the proposed topology. Thus, theradiation noise harmonics from the coils will be reduced.
In the rest of the paper, first, the configuration of the
proposed system is explained. Then, the operation and theself-balancing capability of the flying capacitor (FC)voltage are explained. Finally, the operation of the proposed
FCLA and the FC voltage balancing are confirmed bysimulation and experimental. The new contribution of thispaper is that FCLA with only n-MOSFETs is proposed andthe FC voltage balancing is confirmed by experiments.
2. FCLA WITH AN UNFOLDER FOR WPT
2.1. Conventional FCLA

Figure 1 shows the operating region of a MOSFET. The
operating region of the MOSFET is divided into three
regions, a linear region, a saturation region, and a cutoff
region, depending on the gate-source voltage and drainsource voltage. Traditional switching converters use only
linear and cutoff regions. Hence, the switching circuits
output a discontinuous voltage that causes electromagnetic
interference.
One of the techniques to reduce the harmonics
components, linear amplifiers with MOSFETs operated in
the saturation region are used. However, the efficiency ofthe linear amplifiers is theoretically low because a
conduction loss of the MOSFET is large due to the

Copyright © 2021 Society of Automotive Engineers of Japan, Inc.

Etic 2021
5th International Electric Vehicle Technology Conference 2021

V =Vgs−VthLinear region ds

Saturation region
large

Drain current Id

operation in a saturation region. In order to overcome theabove problem, an FCLA has been proposed[5-7]. The FCLA
outputs a sinusoidal voltage by operating one of the
MOSFETs connected in series in a saturation region. The
efficiency of the FCLA is high because the drain-source
voltage of the MOSFET in the saturation region is low[5].
The FCLA operates as a power amplifier that outputs a
voltage equal to the input voltage to the gate of each
MOSFET by the source follower function of MOSFET. A
common reference signal is input to the gate of all of the
MOSFETs. Due to a common gate input, the operation
region of each MOSFET is uniquely determined to be any
linear, saturation, or cutoff region by the output voltage andcurrent. One of the n-MOSFETs is in the saturation region
when the FCLA output the positive current. On the other
hand, the p-MOSFET is in the saturation region when the
FCLA output the negative current.

Vgs

small
Vgs=VthDrain-source voltage Vds

Cut off region

Fig. 1. Operating region of n-MOSFETs
vg1
ifc1
vg2
ifc2

S1
S2

2.2. Configuration of the proposed FCLA

Figure 2 shows the configuration of the FCLA with an
unfolder for WPT. The proposed FCLA consists of only nMOSFETs. The proposed FCLA with unfolder is connectedto the WPT system, which is operated in a unity power
factor due to the resonance characteristic of the WPTsystem. Thus, the FCLA output only a positive current byusing the unfolder. For this reason, it is possible to replace
the p-MOSFETs with diodes.
In addition, gate drive circuits are connected between thegate and source of each MOSFET, which independently
controls the operation region of MOSFET, such as
saturation region, linear region, and cutoff region. Note that
the FCLA has various patterns that output the same voltage.
The flying capacitor (FC) voltages are balanced using thedegree of freedom of the patterns.
2.2. FC voltages balancing using phase-shifted carriers

When a common reference signal inputs to the gates, theFC voltages do not balance. In order to balance the FC
voltages, the operating region of each MOSFET must be
individually controlled. For this purpose, an isolated gate
drive unit (GDUs) is needed. The independent GDUs
connected to each MOSFET change the current path on the
FCLA for balancing the FC voltages. The capable voltage
range for the FC balance control is determined by the
number of n-MOSFETs in the cutoff region. When k
MOSFETs are in the cutoff region in n-series FCLA with n
MOSFETs are connected in series, the controllable voltage
range is expressed asn − k −1
n−k
VDC < vout ≤VDC ·························· (1),nnwhere k is the number of MOSFETs operating in cutoff
region. The output voltage is controlled by the active
operation of one of the MOSFETs, which is not in the cutoff
region. Furthermore, it is possible to control the charge anddischarge of FC by selecting the MOSFETs to be in the
cutoff region according to the output voltage.
However, it is complicated to select the region of each
MOSFET to keep the FC voltages balance because thedegree of freedom of the current path of FCLA is enormous.
In the proposed system, the region of each MOSFET isvg(n-1)
ifcn

Sn

vgn

VDC
C1 C2

Cn

S(n-1)

vgsn

Cr2 iload

Cr1
vac1

Vout

iL1
Lr1

Lr2

R
vac2

Fig. 2. FCLA with the unfolder for WPT.

Threshold for cut off region
Output voltage ref.
Threshold for linear region
1
Cut off region

0.75

Saturation region

0.5

0.25

Linear region

S1 S2 S3 S4Fig. 3. Region selection based on phase-shifted PWM.

selected by the phase-shifted carrier-based PWM, which isused in the conventional flying capacitor converter.
Figure 3 shows the selection method of the MOSFET'sregion of a 4-series FCLA using carrier comparison with thephase-shifted asynchronous carrier. The region of each
MOSFET is selected from linear, cutoff, or saturation
region. In this method, the region is selected by comparing
two thresholds with the carrier. One is the threshold value
for selecting the cutoff region, which changes stepwise
according to the output voltage. When the carrier is larger
than the threshold for the cutoff region, the MOSFET is in

Copyright © 2021 Society of Automotive Engineers of Japan, Inc.

Etic 2021
5th International Electric Vehicle Technology Conference 2021

the cutoff region. The other is the threshold for selecting thelinear region, which is 1/n smaller than the threshold forselecting the cutoff region. When the carrier is less than thethreshold for the linear region, the MOSFET is in the linear
region. Moreover, one MOSFET, which does not in thelinear region nor cutoff region, is in the saturation region.
The carrier frequency must be asynchronous with the output
frequency in order to select a region that balances the FC
voltage. In FCLA, the carrier frequency is set to a value
close to the output frequency to avoid redundant changes.
When the carrier frequency is close to the output frequency,
the FC voltages balance do not keep because the summationof the product of current and conduction time of each FC is
not zero. When the carrier frequency is out ofsynchronization with the output frequency, the MOSFET
region changes every cycle. As a result, the FC voltage
balances in a longer period than the output period because
the FC charge/discharge current path also changes every
cycle.

Vth
vin

+

+ va

+

K

A1

vout

++

1
1
0

vgsk

2

Sk_off

+
−

1

A3

+
Von Voff

Sk_on

+
−

0

MUX

A2

+

−

0

Sk_on
1
1
0

MUX
Sk_off
1
0
1

vgsk
A1
A2
A3

Fig.4. Voltage control diagram.

Q1

Q1

Q1

Q1

Q2

Q2

Q2

Q2

2.3. The output voltage control

Figure 4 shows a block diagram of the FCLA voltage
control. The FCLA operates as a current amplifier withunity voltage gain with respect to the gate-to-groundvoltage vgn by the function of the source follower of the
MOSFET. Hence, the independent GDUs must output agate-source voltage vgsn , whose gate-ground voltages vgn are
equal to the output voltage Vout. The gate-source voltages
vgsn are controlled by the feedback of the output voltage Voutand adding the offset Von, Voff according to the selection of
the region of each MOSFET. Furthermore, the feedback
control suppresses disturbances caused by nonlinearity of
MOSFET and a region transition.
The output voltage of the FCLA is expressed asnn −1VVout = DC  Sk +  ∆V fck ( Sk +1 − Sk ) ················· (2),n k =1k =1where Sk is the state of the k-th MOSFET, and represents
the cutoff region as “0”, the linear region as “1”, and thesaturation region as 0 < Sk < 1. The second term in (2) showsthe effect of FC voltage error on the output voltage range.
From (2), when the FC voltage is unbalanced, the output
voltage changes. Due to this, the output voltage does notfollow the command voltage in the pattern selected bycomparing with the carriers.
Figure 5 shows the current path in a two-series FCLA.
The FCLA has several patterns of the operation region that
output the same voltage range. However, the current paths
are different among the pattern which output the same
voltage range. In other words, the charge or discharge of
FCs is controllable by variation of the patterns.
Figure 6 shows the output voltage ranges for each patternof the two-series FCLA. Fig. 6(a) shows the range when the
FC voltage is balanced, and Fig. 6(b) and (c) show the range
when the FC voltage is unbalanced. The controllable rangeof the FC voltage varies with the FC voltage error. However,
the operating range is selected based on the assumption ofbalance. Thus, the FCLA with unbalancing FC does not
output the voltage following the command value. When the
output voltage command is in the unable voltage range

FC: Discharging

FC: Charging

In linear region(a) Q1: Cutoff

In saturation region

In cut-off region(b) Q1: Saturation (c) Q1: Saturation (d) Q1: Linear(a) Q2: Saturation (a) Q2: Linear(a) Q2: Cutoff(a Q2: Saturation

Fig.5. Current path of 2-series FCLA.

VDC
S1

∆Vfc

V DC
2

∆Vfc
S2
0

(0,S2)(S1,1)(S1,0)(1,S2)(0,S2)(S1,1)(S1,0)(1,S2)(0,S2)(S1,1)(S1,0)(1,S2)

Cont rollable range

Un cont rollable range

Minimum output l evel(a) FC voltage balance (b) FC voltage excess (c) FC voltage shortage
Fig. 6. Controllable range of output voltage of 2-series FCLA.

Parameters

Table 1. Simulation conditions
SymbolValue

Primary voltage
Secondary voltage
Output power
Transmission freawuency
Coupling Coefficient
Primary inductance
Secondary inductancePrimary capacitance
Secondary capacitance
Number of series
Flying capacitance
MOSFETs in FCLAMOSFETs in unfolder

Copyright © 2021 Society of Automotive Engineers of Japan, Inc.

VDC1
283 V
vout
200 V
P
1 kW
f
85 kHzk
0.3
L1
250 µHL2
250 µHCr1
14.0 nF
Cr2
14.0 nF
n
16
Ck
1 µF
TK5R1E06PL (Toshiba)
SCT3017AL(Rohm)

Etic 2021
5th International Electric Vehicle Technology Conference 2021

shown in blue arrows in Fig. 6, the voltage controllertransitions the operating region of the MOSFET to follow
the command value. A pattern with an unable range is apattern that has a current path increasing the error of the FC
voltage. The voltage controller transitions this pattern to thepattern that does not increase or decrease the voltage error.
This capability automatically keeps balancing the FC
voltage.
3. SIMULATION OF PROPOSED SYSTEM
3.1. Operation waveform

Figure 7 shows the simulation waveform of the proposed
FCLA with the unfolder connecting to the WPT system, andTable 1 shows the simulation conditions. The simulation isdemonstrated with SPICE simulator using the MOSFET
models, which are provided by the MOSFET manufacturer.
Fig. 7 (a) shows the FCLA output voltage command, output
voltage, and the voltage and current waveforms on the
primary and secondary sides of the transmission coil. Figure.
7 (b) shows the FC voltages waveform. From Fig. 7 (a), it
is confirmed that the output voltage of FCLA follows thecommand. In addition, it is confirmed that the proposed
FCLA inputs a sinusoidal voltage to the transmission coiland operates the WPT in resonant conditions. From Fig. 7(b), it is confirmed that the FC voltages are balanced by
selecting the operation region of the MOSFETs using thephase-shifted carriers.
Figure 8 shows the operating waveform when the voltage
of Cfc15 is 20% of the balanced condition. From Fig. 6,
FCLA with the unfolder output a sine wave when the FC
voltages are unbalanced. After the 100 ms from the start ofthe simulation, the FC voltages are balanced by the FC
voltages self-balancing capability.

Output voltage reference vo ut * [V]

300
200
100
0
300

FCLA output voltage vo ut [V]

200
100
0
300
150
0
-150
-300
8
4
0
-4
-8

Unfolder output and load voltage va c1, va c2 [V]

va c1
va c2
Prim ary coil and load current iL1, ilo a d [A]iL1
ilo a d5 µs/div(a) FCLA output voltage reference, output voltage, primary and secondarytransmission coils voltage and current
DC and flying capacitor volt age VDC, Vfc k [V]

300

VDC
Vfc1
Vfc2
Vfc 3
Vfc 4
Vfc5
Vfc6
Vfc7
Vfc9
Vfc1 0
Vfc1 1
Vfc1 2
Vfc1 3
Vfc1 4
Vfc1 5

250
200
150
100
50
0
5 µs/di v(b) Flying capacitor voltages
Fig. 7. Simulation waveform
Unfol der output and load voltage vac1, vac2 [V]

300
150
0
-150
-300

vac1 vac2

8

Figure 10 shows the circuit configuration of a prototype
to verify the balancing flying capacitor voltages in FCLA.
The prototype has two-series connected MOSFETs. As thepower supply for the WPT system, the FCLA should havemore than 16-series connected MOSFETs considering theefficiency and the breakdown voltage of MOSFET.
However, the purpose of the prototype is to verify the FC
voltage balance. Thus, the prototype has only two-seriesconnected MOSFETs. In addition, the DC voltage of the

iL1

-8

iloa d300

DC and fl ying capacitor volt age VDC, Vfc k [V]

VDC
Vfc 1

250
200
150

Vfc 9
100

..

4. EVALUATION OF FC VOLTAGE BALANCE

0-4...........

Figure 9 shows the harmonics analysis results of thecurrent on the primary coil when 16-series FCLA with theunfolder and 17-level FCC are used as the power supply of
the WPT systems, respectively. In addition, the analysis
results when an inverter that outputs a square wave voltage,
which is typically used in a conventional WPT system, iscompared. From Fig. 9, the current harmonics are reduced
by using the FCLA, in which the MOSFET operates in thesaturated region. Focusing on the third harmoniccomponent, the harmonic of current using FCLA is reducedby 13.2dB in comparison with using the FCC, and 49.1dB
in comparison with using the inverter. Moreover, thecurrent harmonics are reduced by 10 dB or more for the
odd-numbered components over the 5th.

Prim ary coi l and load current iL1, iloa d [A]450

17.7 V
3.5V

050 µs/div

Fig. 8. Simulation waveform when the FC voltage unbalanced
40
primary coils current iL1 [dB]3.2. Analysis of current harmonics

2-level inverter049.1 dB
13.2 dB-40

17-level FCC
16-seri es FCLA

-80

-120
-160
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Number of harmonics

Fig. 9. Harmonic analysis for primary coil current

Copyright © 2021 Society of Automotive Engineers of Japan, Inc.

Etic 2021
5th International Electric Vehicle Technology Conference 2021

prototype is 80 V to make the voltage applied to each
MOSFET equal to the high-power WPT system with 16series FCLA. The command value of the output voltage is afull-wave rectified voltage waveform with an amplitude of
80 V and a frequency of 50 Hz. In addition, a 100 Ω resistor
is connected to the unfolder as a load.
Figure 11 shows the output voltage command value,
FCLA output voltage, FC voltage, and unfolded output
voltage of the prototype. From Fig. 11 (a), it is confirmedthat the FC voltage is balanced at 40V, which is half of theDC voltage, due to the operation region selection by the
carrier comparison and the output voltage controller. From
Fig. 11 (b), it is seen that the FCLA outputs a full-wave
rectified voltage following the output voltage command. In
addition, the unfolder outputs a continuous sinusoidal
voltage to the load. The distortion of the FCLA output
voltage is caused by the voltage controller losing control of
the MOSFET due to its nonlinearity and the time delay of
the isolation amplifiers used in the GDUs.
Figure 12 shows the results of harmonic analysis of theunfolder output voltage. It also shows the theoretical valueof the harmonic components of the square wave, which is
output by inverter used in conventional WPT system as theprimary power supply. From Fig. 12, it is seen that the
FCLA reduces odd-order harmonic components by morethan 15 dB compared to the square wave. In particular, thethird-order harmonic component of the output voltage isreduced by 19.8 dB. However, even-order components canalso be observed in the prototype. This is due to the
distortion of the FCLA output voltage and the phasedifference between the output voltage and unfolded
switching.

Q1

Q2

Vfc
VDC

C1

Vout

R

vac

Fig.10. Circuit configuration of prototype.

0

Output reference Vout* [10 V/div]

0

FCLA output voltage Vout[25 V/div]
Flying capacitor Vfc [25 V/div]0(b)Unfolder output voltage vac [50 V/div]

40 ms/div(a) Operation waveforms in long-period

In this paper, the FCLA for WPT systems with theunfolder is proposed in order to reduce the harmonics of theradiation noise. The proposed topology needs no p-channel
MOSFET. The FCLA with unfolder does not output theharmonics of current to the transmission coils because the
FCLA outputs a continuous voltage. Due to the sinusoidal
output, the harmonics components of radiation noise will
not be emitted from coils. In addition, the FCs
charging/discharging are also controlled by the individual
GDU connected to each MOSFET. The operation of the
proposed FCLA connected to WPT is verified by simulation,and it is confirmed that power transmission is possible. It isalso confirmed that the operation when the FC voltage isunbalanced, and the self-balancing capability of the FC
voltages. Moreover, the harmonics of the primary coilcurrent are compared when 16-series FCLA or 17-level
FCC is used as a power supply for the WPT system. As aresult, using the FCLA reduced the 3rd current harmonics
by 13.2 dB compared to using the FCC. Finally, it isconfirmed by the prototype that the FC voltage is balancedby the selection of the operation region by carriercomparison and the output voltage controller. In addition,
the proposed FCLA reduces the odd-order harmonics of theoutput voltage by more than 15 dB compared to the square
wave.

0

Output reference Vout* [10 V/div]

0

FCLA output voltage Vout[25 V/div]
Flying capacitor Vfc [25 V/div]0
4 ms/div

Unfolder output voltage vac [50 V/div](b) Enlarged operation waveforms
Fig. 11. Operation waveforms of 2-series FCLA.
40

Output voltage vac [dB]

5.CONCLUSION

30
20−19.8 dB @ 3rd order harmonic

Square voltage(theoleticcal)
Prototype output

10
0
-10
-20
-30
-40
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Number of harmonic

Fig. 12. Harmonic analysis of unfolder output voltage.

Copyright © 2021 Society of Automotive Engineers of Japan, Inc.

Etic 2021
5th International Electric Vehicle Technology Conference 2021

REFERENCES(1) S. Li, C. C. Mi, "Wireless Power Transfer for Electric
Vehicle Applications," IEEE Journal of Emerging and
Selected Topics in Power Electronics, Vol. 3, No. 1, pp.
4-17 (2015)(2) R. Ota, N. Hoshi, J. Haruna, "Design of Compensation
Capacitor in S/P Topology of Inductive Power Transfer
System with Buck or Boost Converter on SecondarySide," IEEJ Trans. on Industry Applications, Vol. 4, No.
4, pp. 476-485 (2015)(3) K. Kusaka, R. Kusui, J. Itoh, D. Sato, S. Obayashi, M.
Ishida: "A 22 kW-85 kHz Three-phase Wireless Power
Transfer System with 12 coils", Energy Conversion
Congress Exposition 2019, pp. 3340-3347 (2019)(4) K. Kusaka, J. Itoh: "Development Trends of Inductive
Power Transfer Systems Utilizing Electromagnetic
Induction with Focus on Transmission Frequency andTransmission Power", IEEJ Journal of Industry
Applications, Vol. 6, No. 5, pp. 328-339 (2017)(5) T. Ohno, M. Katayama, H. Obara, and A. Kawamura,"Flying Capacitor Linear Amplifier to Realize Both
High-efficiency and Low Distortion for Power
Conversion Applications Requiring High quality
Waveforms", IEEE International Conference on PowerElectronics and Drive Systems (PEDS) 2017, 338,
pp.907-912, (2017)(6) H. Obara, T. Ohno, and A. Kawamura, "Multi-level
topology based linear amplifier family for realization ofnoise-less inverters", International Power Electronics
Conference (IPEC) -ECCE Asia 2018, pp.1649-1654,(2018)(7) T. Ohno, M. Katayama, H. Obara, and A. Kawamura,"Flying-Capacitor Linear Amplifier with Capacitor
Voltage Balancing Control for Efficient and Low
Harmonic Power Conversion", IEEE Applied PowerElectronics Conference (APEC) 2019, pp. 412-418,(2019)

Copyright © 2021 Society of Automotive Engineers of Japan, Inc.