Flying-capacitor Linear Amplifier for Wireless Power Transfer Systems
with Flying-capacitor Voltage Balancing
Rintaro Kusui, Keisuke Kusaka, Jun-ichi Itoh
Nagaoka University of Technology
1603-1, Kamitomioka Nagaoka
Niigata, Japan
Tel.: +81 / (258) – 46.9622
Fax: +81 / (258) – 46.9622
E-Mail: kusui@stn.nagaokaut.ac.jp, kusaka@vos.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/en/index.html

Keywords
Amplifiers, Capacitor voltage balancing, Flying Capacitor Converter, Wireless power transmission

Abstract
In this paper, a flying-capacitor linear amplifier (FCLA) for wireless power transfer systems is
proposed. The proposed circuit has an n-series FCLA with only N-ch MOSFETs and an unfolder. The
flying capacitor (FC) voltages are balanced by selecting the operation state of each MOSFET withphase-shifted carriers. FCLA outputs a continuous voltage that does not contain the harmonics that cause
current harmonics. Due to this, the radiation noise from the transmission coils is reduced. The operationof the WPT system with the proposed 16-series FCLA is demonstrated in a simulation. The proposed
FCLA output the sinusoidal voltage to the resonance circuit. In addition, the harmonics of the primarycoil current are analyzed. From this result, the FCLA significantly reduces the current harmonics thanthe conventional two-level inverter. Then, The FC voltage balance is verified using the prototype witha 2-series FCLA. From the experimental results with a small-scale prototype, the proposed circuit
outputs full-wave rectified sinusoidal output voltage with balanced FC. Furthermore, the harmonics of
the unfolder output voltage are analyzed. From the analyzed result, the third-order harmonics are
reduced by 19.8dB due to FCLA with MOSFET in the active-state in comparison with the theoreticalvalue of harmonics of square wave voltage.

Introduction
In recent years, wireless power transfer (WPT) systems are actively studied for electric vehicles(EVs)[1-5]. The WPT system may improve user convenience due to power transmission without
connecting cables. However, the WPT system generates radiation noise from transmission coils because
the WPT system transmits power through weak magnetic coupling between two coils. The radiationnoise may cause malfunction of electric devices and interference of wireless communication. For thisreason, the International special committee on radio interference (CISPR: Comité International Spécial
des Perturbations Radioélectriques) has published reference levels of radiation noise[6]. Moreover, theregulation of CISPR for electromagnetic field emission from WPT systems, especially for harmoniccomponents of electromagnetic fields (EMF), is planning to be tightened significantly[7]. Accordingly,
the WPT system must reduce the radiation noise.
In conventional WPT systems, the inverter that outputs square wave voltage is used for the primaryside power supply[8]. The current contains low-order harmonics flowing on transmission coils due toapplying the square wave voltage with low-order harmonics to the resonance circuit and transmission
coils. Thus, the radiation noise is generated around the transmission coil not only at the fundamental
component but also at the low-order harmonics.

In [9-11], metal plates, magnetic materials, and additional windings shield the radiation noise fromthe WPT system. The shield reduces the radiation noise by flowing the current on the shield. Due tothis, the eddy current loss occurs by the current through the shield. Improvement of the shieldperformance and cooling cause increasing in the volume of the shield. Ref. [12-14] propose the threephase WPT system with 12-coils. The pair of coils on each phase connected in series in a differential
connection canceled out the radiation noise. A three-phase WPT system with 12 coils complies with thecurrent guidelines; however, it is not enough to comply with generation guidelines.
In this paper, a flying-capacitor linear amplifier (FCLA) for WPT systems is proposed. The proposed
FCLA outputs sinusoidal voltage without PWM. The sinusoidal voltage without PWM reduces thecurrent harmonics on the coils. In other words, the radiation noise from the WPT system will be reducedby the proposed FCLA. However, output voltage distortion occurs by P-ch MOSFETs used in theconventional FCLA [15-16]. In the proposed FCLA, P-ch MOSFETs are removed using an unfolder. In
addition, flying capacitor (FC) voltages are automatically balanced by selecting the operation states ofthe MOSFETs by comparing asynchronous phase-shifted carriers. The originality of this paper is
proposing an FCLA without p-ch MOSFET, which has the self-balancing capability of the FC voltage.
The proposed FCLA for WPT is demonstrated in this paper. It is confirmed that the FC voltage balanceby the prototype.

Flying-capacitor linear amplifier for wireless power transfer
System configuration
Figure 1 shows the static characteristics of an N-ch MOSFET. The operation states are divided into
ON, OFF, and active states depending on the drain-source and gate-source voltages. Traditionalswitching power converters use only the ON and OFF states. The high-frequency leakage current
generates high-order components of the radiation noise. Besides, FCLA outputs a continuous voltage
using one of the series-connected MOSFETs in the active state. The conventional FCLA needs
complementary MOSFETs [4-7]. One of the N-ch MOSFETs is in the active state when the FCLA
output the positive current. On the other hand, the P-ch MOSFET is in the active state when the FCLA
output the negative current. In the conventional FCLA, the P-ch MOSFETs decrease efficiency due totheir higher conduction loss and switching loss than the N-ch MOSFETs.
ON state

Vds =Vgs−Vth

Active state

Drain current Id

large

Vgs

small
Vgs =VthDrain-source voltage Vds

OFF state

Fig. 1. Operation state of N-ch MOSFET.

Figure 2 shows the system configuration of the WPT system with the proposed FCLA. The
proposed circuit has an n-series FCLA with n N-ch MOSFETs and n diodes connected in series
and an unfolder. The proposed FCLA outputs a full-wave rectified voltage. The unfolder
outputs a sinusoidal voltage by switching the polarity of the FCLA output voltage. Meanwhile,
the WPT is operated in a unity power factor, i.e., the voltage and the current are in phase. For
these reasons, in the proposed FCLA, only N-ch MOSFETs are used in the active state for
output voltage control. Therefore, the P-ch MOSFETs can be replaced by diodes.
An isolated gate drive unit (GDU) is connected to each MOSFET. The GDU adds the DC bias
to gate-source voltage to control the state of MOSFET. The current path of FCLA depends on

vg1

Q1

vg2

Q2

vg(n−1)

Qn−1

ifc1
ifc2

ifcn

vgn
VDC C1 C2

Cn

Qn
vgsn
iL1

Cr1

Vout

vac1

Lr1

Cr2

Lr2

vac2

iload
R

Fig. 2. FCLA with the unfolder for WPT.

the combination of MOSFET states. The charge or discharge of FCs is switched by the current
path. Accordingly, the flying capacitor (FC) voltages are balanced by the appropriate selectionof each MOSFET state.
State selection for MOSFET
Figure 3 shows a method for selecting the operation state of each MOSFET in a 4-series FCLA using
phase-shifted carrier comparison. The state selection to FC voltage balancing is complicated because ofenormous flexibility in the current paths of FCLA. The state is selected by the phase-shifted carriers
comparison using conventional flying capacitor converter in the proposed system. The phase-shifted
carriers are compared with the stepped thresholds value to select the state of MOSFET from ON, OFF,and active states. The thresholds depend on the output voltage command. The output voltage range of
FCLA is change by the number of the MOSFET in the OFF state. Assuming balanced FC voltages, theoutput voltage range of the n-series FCLA when k N-ch MOSFETs are operating in the OFF state isexpressed asn − k −1
n−k
VDC < vout ≤
VDC
n
n

(1).

Accordingly, the threshold to select off state is stepped value changed by 1/n depended on output
command. The threshold to select ON state is 1/n smaller than the threshold to select OFF state. The
ON state is selected when the carrier is smaller than the threshold for the ON state, and the OFF state is
selected when the carrier is larger than the threshold for the OFF state. Furthermore, the MOSFET,
which is not selected ON or OFF state, is an active state. The carrier frequency is set close to the output
frequency to avoid changing the state redundancy. When the carrier frequency is synchronized with theoutput frequency, the same current path is selected for each cycle. Due to this, the FC voltage isimbalanced because the integral of the FC current does not equal zero. On the other hand, the integral
Threshold for OFF stateOutput voltage ref.
Threshold for ON state1

OFF state
0.75
Active state

0.5
0.25

ON state

Q1 Q2 Q3 Q4
Fig. 3. State selection by comparing with phase-shifted carrier for 4-series FCLA.

of the FC current becomes zero in a few cycles because the different current path is selected in eachperiod when the asynchronous carrier is used. In other words, the FC voltages keep balancing by using
asynchronous carriers to select the operation state.
Output voltage control
Figure 4 shows a block diagram of the FCLA voltage controller. In the proposed system, the output
voltage is controlled by proportional control. The operation state of each MOSFET is controlled byadding a DC bias depending on the selected state. Moreover, the controller changes the states to balance
the FC voltages when the FC voltages are imbalanced. The output voltage Vout of the FCLA is expressedasVout =

n −1
VDC n
S
+
∆V fci ( Si +1 − Si ) i 
n i =1k =1(2),where Si is the state of the i-th MOSFET, and represents the OFF state as “0”, the ON state as “1”, andthe active state as 0 < Si < 1. The second term of (2) shows the effect of the error ∆Vfci of the FC voltage
on the output voltage. From (2), the FC voltages imbalance changes the output voltage range. Due tothis, it is impossible to output the voltage in the reduced range by FC voltage imbalance. Then, thevoltage controller increases or decreases the gate-source voltage vgsk to transition the operation point of
MOSFET.
Vth
vin

+

+ va

+

K

A1

vout

++

1
+

0

Sk_on

A3

0

2

Sk_off

+
−

1

vgsk

+
Von Voff

−

1

MUX

A2

+

−

Sk_on
0
1
0

MUX
Sk_off
0
0
1

vgsk
A1
A2
A3

0

Fig. 4. Voltage control diagram.

Figure 5 shows the current paths in each pattern of the operation state of the two-series FCLA. A twoseries FCLA has four patterns because one of the MOSFETs connected in series operates in the active
state. The FCs in n-series FCLA are charged or discharged in the current paths which one or more
MOSFETs are in OFF state. In two-series FCLA, the FC is charged or discharged in the current path (a)and (c). The FC voltage is balanced when the integral of the FC current in the current path (a) is equal
to it in the current path (c). Similarly, the FC voltages in the n-series FCLA are balanced when the
integral of FC current is zero. However, when the FC voltage is imbalanced, the current path must bechanged to compensate for the error from the nominal FC voltage.

Q1

Q1

Q1

Q1

Q2

Q2

Q2

Q2

FC: Discharging

FC: Charging

ON state(a) Q1: OFF(a) Q2: Active b

OFF state(b) Q1: Active(c) Q1: Active) Q2: ON (c) Q2: OFF
Fig. 5. Current path of 2-series FCLA.

Active state(d) Q1: ON
Q2: Active

0,0
S2_off = 0

S1_off = 0
S2_off = 1
S2_off = 1

S1,0

0,S2

chargeDischarge

S1_off = 1

S1_off = 1
S2_on = 1

S1_on = 1

S1_off = 1

orVout*>VDC/2+∆Vfc

or
Vo ut*>VDC/2−∆Vfc

or
Vout*<VDC/2+∆Vfc

S2_off = 1

orVout*<VDC/2−∆Vfc

S1_on = 1
S1_on = 1

1,S2

S1,1

S2_on = 1

S2_on = 1(a) State machine diagram of 2-series FCLA

VDC
S1

∆Vfc

VDC
2

∆Vfc

Controllable range

S2

Uncontrollable range
Minimum output level0(0,S2)(S1,1)(S1,0)(1,S2)

without FC voltage error∆Vfc = 0(0,S2)(S1,1)(S1,0)(1,S2)

FC voltage excess∆Vfc > 0(0,S2)(S1,1)(S1,0)(1,S2)

FC voltage shortage∆Vfc < 0(b) Controllable range of output voltage of 2-series FCLA.
Fig. 6. Automatically self-balancing capability for FC voltage in two-series FCLA

Fig. 6 (a) shows the state-machine diagram and (b) shows the controllable voltage range for each of
the selected states in a two-series FCLA. The state of two MOSFETs is represented as (S1, S2), where
OFF state is represented as “0”, the ON state is represented as “1”, and the active state is represented as
S1 or S2. In Fig. 6 (b), the red arrows are the range of controllable voltages, and the black line is theminimum output voltage for each pattern. The sum of the red arrow and the black line is the maximum
voltage. When the FC voltages are balanced, the transition of the state is caused by carrier comparisonand not by the voltage controller. The voltage controller changes the state when the output voltage range
is reduced by the FC voltage imbalance. The controllable range of output voltage with imbalance FCs
is expressed asn − k −1n−k
VDC + ∆V fci ( Si +1 − Si ) < Vout ≤VDC + ∆V fci ( Si +1 − Si )
n
n

(3),

where ∆Vfci is the voltage error of i-th FC voltage from nominal value and k is the number of MOSFETs
in OFF state. From (3), the voltage range of the two-series FCLA in the state of S1 in the active state is
reduced when the FC voltage excess half of the DC voltage, i.e., the voltage error is positive. Due tothis, the state of FC not discharging changes the state of FC discharging, and the state of FC charging
changes one of FC charging. Besides, the voltage range is reduced when the state of S2 is active and the
FC voltage error is negative. Because of this, the voltage controller reduces the discharging period andincreases the charging period. For these results, the voltage controller automatically compensates theimbalance of FC voltage. Similarly, the FC voltages in n-series FCLA are automatically balanced bycarrier comparison and voltage controller.

Parameters

Table 1. Simulation condition
SymbolPrimary voltage
Secondary voltage
Output power
Transmission freawuency
Coupling Coefficient
Primary inductance
Secondary inductancePrimary capacitance
Secondary capacitance
Number of series
Flying capacitance
800
600
400
200
0
800
600
400
200
0
800
400
0
−400
−800
120
60
0
−60
−120

VDC1
vout
P
f
k
L1
L2
Cr1
Cr2
n
Ck

Output reference Vout*

Value
650 V
460 V
30 kW
85 kHz0.3
43.9 µH
27.0 µH
79.8 nF
130 nF16
10 µF
Flying capacitor Vfc1 -Vfc15
Vfc 1

600

Vfc 2
Vfc 3

FCLA output voltage Vout

500

Vfc 4
Vfc 5
Vfc 6

400

Vfc 7
Vfc 8

WPT input and output voltage vac1,vac2
vac1
v

300

Vfc 9
Vfc 1 0ac2

Vfc 1 1
200
Vfc 1 2WPT input and output current iac1,iac2
iac1
iac2

Vfc 1 3100

Vfc 1 4
Vfc 1 502µs/div(a) FCLA output voltage reference, output voltage,(b) Flying capacitor votages
primary and secondary transmission coils voltage and current
Fig. 7. Simulataion waveforms of 16-series FCLA and WPT system

100µs/div

Simulation of the WPT system with proposed FCLA
Operation waveform
Figure 7 shows simulation waveforms of the WPT system with 16-series proposed FCLA and table 1
shows the simulation conditions. The simulations are used the MOSFET model for the SPICE simulator
provided by the MOSFET manufacturers. 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 waveforms. From Fig. 7 (a), it is confirmed that the output
voltage of FCLA follows the command. In addition, it is confirmed that the proposed FCLA applies asinusoidal voltage to the transmission coil and operates the WPT in resonant conditions. From Fig. 7(b), it is confirmed that the FC voltages are balanced by selecting the operation state of the MOSFETs
using the phase-shifted carriers.
Figure 8 shows the simulation waveforms at the start-up of 4-series FCLA with zero-voltage FCs. In
this simulation, the DC voltage is 160V. From Fig. 8, it is seen that the FC voltages converge at nominal
value in the steady-state. From this result, it is confirmed that the voltage controller has the capabilityof automatically balancing for the FC voltages.

Analysis of coil current harmonics
Figure 9 shows the harmonics analysis results of the current on the primary coil in the WPT systembecause the radiation noise from the WPT system is proportional to coil current. The current harmonics
are analyzed with 16-series FCLA, 17-level flying capacitor converter (FCC), and two-level inverter as

120

Vfc 1

100
80

Vfc 2

60
40
Vfc 3

20

Normalize primary coil current [dB]Flying capacitor Vfc1 -Vfc3

0
16-seri es FCLA
17-level FCC-50

2-level inverter

-100
-150
-200
-250
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Number of harmonic
Fig. 9. Harmonic analysis for primary coil current

0200µs/div
Fig. 8. FC voltage balancing capability in 4-series FCLA

Q1

Q2

Vfc
VDC

C1

Vout

vac

R

Fig.10. Circuit configuration of prototype.

the power supply in the WPT system, respectively. In addition, each analysis result is normalized basedon the fundamental frequency component. From Fig. 9, the current harmonics are significantly reduced
by using the FCC or FCLA. Focusing on the third harmonics components, the 17-level FCC reduces thecurrent harmonics by 50dB, and the 16-series FCLA reduced it by more than 100dB in comparison withusing the inverter.

Evaluation of FC voltage balance with two-series FCLA
Figure 10 shows the configuration of the prototype to verify the FC voltage balance. The prototype
has a two-series FCLA and an unfolder. The MOSFET for the FCLA should be 60-V breakdown voltage
and low on-resistance for efficiency and availability. For this reason, the DC voltage is 80 V so that theapplied voltage of one MOSFET is about 40 V. The load R is 100 Ω, and the output voltage command
Vout* is a full-wave rectified voltage with an amplitude of 80 V and a frequency of 50 Hz for thedemonstration of the voltage balance.
Figure 11 (a) shows the operation waveforms of two-series FCLA, and Fig. 11 (b) shows the enlarged
waveform of fig.11(a). From Fig. 11(a), the average FC voltage is 40 V, which is half of DC voltage. In
other words, the FC voltage is balanced by carrier comparison. From Fig. 11(b), the FCLA outputs thefull-wave rectified voltage following to command value. Furthermore, the unfolder switches the polarity
of FCLA output voltage and outputs sinusoidal voltage. However, the distortion of FCLA output voltage
occurs by the nonlinearity of MOSFET and the time delay on the analog isolation amplifier in the voltage
controller.
Figure 12 shows the operation waveform at the start-up of the 2-series FCLA. The FC voltage is 0 V
in the initial condition, i.e., the FC voltage is imbalanced. From Fig. 12, the FC voltage is converged at
a nominal value. Accordingly, it is confirmed the automatically self-balancing capability of the voltage
controller.

0

0

0

Output reference Vout* [10 V/div]

0

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

Output reference Vout* [10 V/div]

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

0

0
(b)
Unfolder output voltage vac [50 V/div]

40 ms/div

Unfolder output voltage vac [50 V/div]

4 ms/div(a) Operation waveforms in long-period(b) Enlarged operation waveforms
Fig. 11. Operation waveforms of 2-series FCLA.

040

Output reference Vout* [10 V/div]

Output voltage vac [dB]0

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

0

30
20

−19.8 dB @ 3rd order harmonic

Square voltage(theol eticcal )Protot ype output

10
0
-10
-20
-30
-40

Unfolder output voltage vac [50 V/div]
Fig. 12. Start-up of the 2-series FCLA

100 ms/div

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

Fig. 13. Harmonic analysis of unfolder output voltage.

Figure 13 shows the harmonics analysis results of prototype output voltage. The voltage harmonic isevaluated because the load is pure resistance load. In addition, Fig. 13 shows the theoretical value of
harmonics of the square voltage whose fundamental components are equal to the prototype output
voltage. From the analysis results, the odd-order harmonics are reduced by 15dB or more than squarevoltage. Focusing on the third harmonic, the FCLA reduces the voltage harmonic by 19.8dB.

Conclusion
This paper proposed the FCLA with only N-ch MOSFET to reduce the radiation noise harmonics
from the WPT system. The proposed circuit has an n-series FCLA and an unfolder. The FCLA outputs
a sinusoidal voltage without harmonics by operating one of the MOSFETs in the active state. The
operation state of each MOSFET is selected by comparing with phase-shift carriers to keep balancing
the FC voltages. In addition, the output voltage is controlled by output voltage feedback. The selection
by phase-shifted carries and controller balances the FC voltages. From this result, the proposed FCLA
reduces the current harmonics in comparison with using the conventional two-level inverter by applying
the continuous sinusoidal voltage to the resonance circuit. Then, The balancing of the FC voltage by the
carrier comparison and the voltage controller is verified with the 2-series FCLA. From the experimental
results, it is confirmed that the FCLA outputs voltage following the command while the FC voltage isbalanced. In addition, the harmonic of the unfolder output voltage is analyzed. The third-order harmonicis reduced by 19.8dB than the theoretical value of square voltage.

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