15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad,
SerbiaPower Loss Reduction of a AC-DC Converter
Features 10-V and 10,000-A Sintering Power
SupplyKoji Orikawa1, Jun-ichi Itoh2
1

Nagaoka University of Technology, Nagaoka, Niigata, orikawa@stn.nagaokaut.ac.jp
2
Nagaoka University of Technology, Nagaoka, Niigata, itoh@vos.nagaokaut.ac.jp

Abstract — This paper discusses a high-efficiency AC-DC
converter developed for low-voltage and high-current
conditions for sintering power applications. First, the circuit
configuration and the control principle for the proposed
low-voltage high-current AC-DC converter are described.
The proposed system consists of four 2,500-A units of the
AC-DC converter connected in parallel. The input current
harmonics are suppressed by multiple transformers on the
input side. Also, imbalance issues on the transformer
parameters and the output wiring are discussed. The
proposed system demonstrates that each individual circuit
yields a balanced 10,000-A(10-kA) output. In addition, loss
analysis shows that the power loss on the secondary rectifieris 49% dominated by semiconductor loss. Furthermore, it isshown that by implementing a MOSFET synchronousrectifier instead of a Schottky barrier diode, the loss will be
reduced by 35%. Finally, the input current harmonics are
reduced by using multiple transformers and the validity ofthis result is demonstrated.
Keywords — Sintering,
synchronous rectifier

low-voltage

high-current,

I. INTRODUCTION
Sintering is a technique that creates contacts and bonds
between particles by heating molded powder material
below its melting point. One of the sintering methods
used for powder materials is known as the “pulse
method”. In this method, a pulse voltage is directly
applied to the molded powder material and the surface ofthe powder is excited. Then, the heating and sintering isrepeated. In this process, the pulse voltage requires a lowvoltage and high-current DC power supply. However, aconventional circuit composed of a thyristor rectifier has
low efficiency and input power factor of approximately
60% and 40%, respectively [1]. Therefore, the power
capacity and the weight of the system are increased.
On the other hand, AC-DC power converters using
high-speed power semiconductors, such as IGBT and
MOSFET, have been proposed for application insintering power systems in order to improve theefficiency and also reduce the size [2-5]. In Ref [5], aprototype model with an output of 5,000 A with low
power has been verified. The prototype model consists of
two unit outputs of 2,500 A connected in parallel. The
operation characteristics, the input power factor, theefficiency, and the loss distribution have been evaluated.
However, the circuit was controlled using full analog
control circuits. In analog control, it is difficult to extend
the existing parallel connection in order to obtain higher

current because the circuit parameters in one unit do notagree with the circuit parameters in the other unit. That is,
an imbalance occurs in each unit. Also, the operation
sequence and protection management in analog control
become complicated in parallel systems. In addition, in
past work, there has been no discussion on the imbalanceof transformer parameters and inductance wiring on the
output side. The input current harmonic reduction
methods are not indicated.
This paper proposes a system topology wherein a
10,000-A output current power converter, consisting offour unit outputs of 2,500 A, is connected in parallel.
Each of the converters is controlled by a full digital
controller using a general purpose microcomputer. In the
proposed system, the input current harmonics aresuppressed by multiple transformers with a dioderectifier. A passive rectifier using multiple transformers
has high stability and low EMI compared to an active
rectifier such as a PWM rectifier. In addition, the effectof the transformer parameter imbalance and output wiring
will be discussed. As a result, it is easy to increase theoutput current by increasing the number of parallel units.
First, the circuit configuration of the proposed systemand the fundamental operation for the low-voltage highcurrent AC-DC converter are described in this paper.
Second, the response of the feedback output current
control with different output-side wiring inductances isinvestigated. Next, the balance effect of the current in theparallel output transformer is investigated. Then, theoperation characteristics are confirmed thoughexperiments. In addition, in order to increase theefficiency, the reduction of the power loss on thesecondary side rectifier by implementing a MOSFET
synchronous rectifier is investigated. Finally, the effect ofmultiple transformers is discussed using simulation basedon experimental results.
II. CIRCUIT CONFIGURATION OF THE PROPOSED SYSSTEM
A. Features
Figure 1 shows the circuit configuration of the
proposed system. This circuit can output 10,000 A due tothe four 2,500 A units connected in parallel. The grid
three-phase voltage of 200 V is converted into the input
voltage of the inverter by using a diode rectifier, a DC
reactor, and smoothing capacitors. In addition, multiple
transformers are connected to the input of the dioderectifier in order to reduce the harmonic components
from the input grid current and also to improve the power
factor of the grid. The connection of the secondary side ofsin 15 °sin 120 °sin 45°y=sin120°x=

3

Fig. 1. Circuit configuration of the low-voltage, high-current circuit for sintering.

the multiple transformers is different in each unit. In unit
1 and unit 3, each phase winding in the secondary side iscomposed of two windings x and y in series. The phase ofwinding y has a lead or a lag of 120 degrees with respect
to the x winding. In unit 2, the secondary side has a starconnection. In unit 4, the secondary side is a deltaconnection. By designing the turn ratios of thetransformers x and y using (1) and (2), the phase of thesecondary voltage in the multiple transformers is shiftedby 15 degrees among each of the multiple transformers.
As a result, the grid current becomes a closed sinusoidal
waveform.
sin 15 °(1)x=
sin 120 °sin 45 °(2)y=sin 120 °It should be noted that it is more effective to reduce theinput current harmonics when the number of parallel
units is increased for the multiple transformer. However,
if too many units are connected to one multiple
transformer, then fabricating the multiple transformer
becomes difficult because many windings are required.
That is, the multiple transformer becomes large in sizeand expensive. Between 3 to 6 parallel units arerecommended for one multiple transformer.
For the inverter, 600 V/150 A IGBTs are used. The
inverter is operated by phase shift control. The highfrequency transformer is connected to the output of theinverter.
The switching frequency of the inverter was set to 15
kHz in order to reduce the size of the transformer. Notethat a long overlapping period will occur in the switching

Fig. 2. Control diagram.

commutation when a large leakage inductance is applied.
In the prototype circuit, two transformers with 1250 A
rated current are connected in parallel to reduce thecopper loss of the transformers. The output current is
controlled by operating the output voltage of the inverter.
The secondary side of the transformer is a rectifier with
Schottky barrier diodes where the reverse recovery isvery small. Two diode modules that consist of 32 diodes
are connected in parallel because the output current ishigh. In addition, an RCD snubber circuit is applied to thediodes in order to suppress a voltage surge in the diodes
due to the leakage inductance of the transformer and theoutput wiring inductance.

B. Control Strategy
Figure 2 shows a control diagram of the circuit. The
carrier is a 15-kHz sawtooth waveform. The gate signalsof the U-phase are always operated with a 50% duty
cycle. The gate signals of the V-phase are operated byphase shift control and duty control. Command of thephase shift Dps is operated by the difference between the
output current command and the detected output current.
When DC magnetizing occurs in the transformer due tothe variability of the dead-time and the saturation voltageof the switch of the inverter, the duty cycle of the gate
signals of the V-phase is controlled in order to suppress
the dc component of the transformer current. The dc
component of the transformer current is detected by the
low-pass filter and compared to zero, which is thecommand of the DC component of the transformer
current. Then, command of the DC magnetizing
compensation Dmc is decided by the PI controller. The
control method is calculated using a general purpose
microcomputer.
C. Implementation of Phase Shift Control by aGeneral Purpose Microcomputer
The conventional circuit with IGBT has been
controlled by using analog circuits, as described in Ref[5]. In this paper, full digital control is implemented byusing a general purpose microcomputer, due to simplicityof the structure and high reliability. By introducing full
digital control, detection of the imbalance of the output
current and the failure in each unit can be easily achieved.
The model of the general purpose microcomputer used is
SH7216 from Renesas, usually commence in PWM.
Figure 3 shows the relationship between the commands
and the carrier. In the general purpose microcomputer,
one up-counter is used as the carrier. It is difficult toimplement two counters with different phase in the
microcomputer. Therefore, instead of using two counters,
the rise and fall of the gate signal are individually bycomparing the command of the duty cycle and thecommand of the dead-times Dd, Dps, and Dmc to thecounter. The maximum value of the carrier is 1. The gate
signal of the U-phase is decided by 50% of the commandof the duty cycle and Dd. On the other hand, the gate
signal of the V-phase is decided also using Dps and Dmc.
D. Design Method of Parameters in PI Controller
Figure 4 shows the control diagram of output current
control. Feedback of output current control can berequired for each prototype circuit, if the parameters arevaried for each of the prototype circuits. The low-passfilter is used to design the parameters of the PI control,
such as proportional gain and an integral time constant.
The transfer function of the output current is described by(3). By inserting the low-pass filter, it becomes a secondorder element.

Kp
I out
I out

=
*
s2 +

Lout Ti
K p + Rout

2

s+

Kp

=

ωn
(3)
2
2
s + 2ζω n s + ω n

Lout
Lout Ti
where Kp is the proportional gain, Ti is the integral time
constant, Rout is a load resistance, Lout is an output sidewiring inductance, ξ is a damping factor, and ωn is anatural angular frequency for output current control. Then,
Kp and Ti are given by (4) and (5)Fig. 3. Relation between commands and carrier.

⎛ 1 + sTi ⎞⎟K p ⎜⎜⎟⎝ sTi ⎠

1
1 + sTi

1sLout + RoutFig. 4. Control diagrams of the output current control.

1
1 + sTi⎛ 1 + sTi ⎞⎟K p ⎜⎜⎟⎝ sTi ⎠

1sLsmall+ 2Rout

1
1 + sTi⎛ 1 + sTi ⎞⎟K p ⎜⎜⎟⎝ sTi ⎠

1
skLsmall+2Rout

Fig. 5. Control diagrams of the parallel operation.

K p = 2ζω n Lout − Rout

Ti =
III.

Kp
2

ω n Lout(4)(5)

IMBALANCE OF TRANSFORMER PARAMETERS AND
WIRING INDUCTANCE OUTPUT SIDE

A. Variability of the wiring inductance of output side
When the units are connected in parallel, the output
current response for each of the units is different due tothe variability of the output-side wiring inductance. In
this section, using Fig. 4, the output current response isinvestigated when the circuit is operated with two units inparallel.
Figure 5 shows the control diagram when two units areoperated in parallel. In this control diagram, Lsmall
represents the small inductance and kLsmall represents thelarge inductance. The constant k is greater than 1. It iscomplicated to design the damping factor of the PI
controller by measuring each of the output-side wiring
inductances. However, it is easier to design using just oneof the output-side wiring inductances than measuring all
the wiring inductances one by one. In this section, thedesign method of the damping factor is clarified.

Figure 6(a) shows the simulation results using theparameters designed using (4) and (5) where the output
inductance Lout is Lsmall. In this section, the naturalangular frequency ωn used is 4,000 rad/s. Note that thenatural angular frequency is set based on thespecifications of the powder material. In addition, thedamping factor is set to 0.7 in order to suppress
overshoot of the current response. In Fig. 6(a), thedesigned value of the overshoot, which is normalizedwith the output current, indicates the overshoot value ofthe response. The smallest inductance Lsmall in each unit
is used to calculate the designed value. From Fig. 6(a), it
is confirmed that the overshoot of the output current of
the unit with a larger inductance become larger than one
using a smaller inductance. Then, the damping factor andthe overshoot normalized to the output current can be
expressed by (6) and (7).
K + 2 RoutTi
1(6)
ζ L = kL = p
=
ζ
out
small
2
K p kLsmall
k Lout = Lsmall⎞⎛
π ζ L =L
⎟
⎜
out
small
(7)
= exp⎜ −
⎟
2
I out
⎟
⎜
k − ζ L =L
out
small
⎠
⎝
From Eq. (6), the damping factor of the output current
response with a larger inductance becomes k to thepower of minus one half of that with a smaller
inductance. In the case wherein the damping factor ξ ofthe unit that uses Lsmall is 0.7, the damping factorξ of theunit that uses kLsmall becomes 0.495. Therefore, theovershoot of the output current of the unit that uses kLsmall
is increased. The parameters of the PI control should
consequently be designed based on the largest
inductance.
Figure 6(b) shows the simulation results obtained using
the parameters that were designed by a larger inductancekLsmall. Here, k is 2. Therefore, the damping factor ξ ofthe unit that uses Lsmall is 0.99, and the damping factor
ξ of the unit that uses kLsmall becomes 0.7. From thesimulation results, it is confirmed that both the output
current responses with the smaller inductance and withthe larger inductance are within the designed value.
Therefore, the design method of the PI control parameters
should use the largest inductance because the output sidewiring inductance could be imbalanced depending on thelayout of the prototype.
B. Exciting inductance and the transformer current
In the prototype circuit, two transformers are connectedin parallel in order to increase the output power andreduce the volume of the transformers. If the parameters,such as the winding resistance and the exciting
inductance, are different between each transformer, thecurrent of the transformer can be imbalanced. The current
imbalance causes magnetic saturation and overheating of
the transformer. Therefore, in this section, the relation
between the exciting inductance and the current in thetransformer is clarified.

(a) ξ is designed with smaller inductance Lsmall.

I out _ max(b) ξ is designed with larger inductance k*Lsmall.
Fig. 6. The output current response waveforms.

The effective values of the exciting current and thecurrent of the transformer are expressed by (8) and (9),respectively. In this section, the leakage inductance andthe winding resistance of the transformers are neglected.
In addition, it is assumed that the output current is DC
current that does not have a ripple current.
⎛⎞⎜⎟
1 V dc1 Vdc ⎜ I out Rout T ⎟(8)
I m _ rms =t on =2 Lm
2 Lm ⎜ Vdc 2 ⎟
⎜
⎟
⎝ n
⎠
I out
I trans _ rms =(9)nwhere Vdc is the input voltage of the inverter, Lm is theexciting inductance, ton is the time of applying Vdc to thetransformer, Iout is the output current of the unit, Rout isthe load resistance, n is the turn ratio of the transformer,
and T is the period of the switching frequency. Therefore,
from (8) and (9), the ratio of the exciting current withrespect to the transformer current is expressed by (10).
I m _ rms
n 2 Rout(10)=
T
I trans _ rms
4 Lm

Eq. (10) becomes 0.4% and 0.08% in the cases where
Lm is 1 mH and 5 mH, respectively, under the conditions
shown in Table 1. The reason for this is high output
current occurs due to the small resistance connected in
the load. As a result, the ratio of the exciting current withrespect to the transformer current is very small.
Therefore, the variability of the exciting inductance does
not cause an imbalance in the transformer current.

TABLE I
EXPERIMENTAL CONDITIONS
10 (kA)
Output current Iout
DC reactor L1
0.5 (mH)
Smooth capacitor C1, C25800 (μF)
Switching frequency fsw
15 (kHz)
Dead time Td
4 (μs)
Turn ratio nn=N1/N2=17
Exciting inductance Lm
1-5 (mH)
Output side wiring inductance Lout
0.1 (μH)
Load resistance Rout
0.21 (mΩ)(a) Waveform of the inverter output voltage and the Schottky
barrier diode voltage.

Fig. 7. Experimental waveform of the transformer current andoutput current.

IV.

EXPERIMENTAL VERIFICATIONS

A. Operation waveforms
Table 1 shows the experimental conditions used. The
exciting inductance of the prototype transformers have a
specific value. The rated output voltage of the prototype
circuit is 10 V. Note that metal wires are used as the test
load for the prototype. The metal wire can accept 10,000
A, but the resistance is smaller than that of the actual
material in sintering. Therefore, the tested output power
and voltage are smaller than the rated power and voltage.
Figure 7 shows the operation waveforms of two units
that output 2,500 A. From Fig. 7, it is confirmed that thecurrent in each transformer connected in parallel isbalanced even when each of the exciting inductances isdifferent in this experiment. Note that the output current
was measured by the current sensor.
Figure 8(a) shows the voltage waveforms of theinverter and Schottky barrier diode, respectively. A shortpulse is confirmed from Fig. 8(a). This short pulse isgenerated by the leakage inductance of the transformer.
The width of the short pulse is decided by the discharge
time of the leakage inductance.
Figure 8(b) shows the operation waveforms when thecircuit outputs 10,000 A. Fig. 8(b) confirms that each unit
outputs 2,500 A equally.
Figure 9 shows the response waveforms of each output
current by a step input of the phase shift command. It is
confirmed that the imbalance of the response does notoccur because the output side wiring inductance and theresistance of the load are almost same between two units.

3000(A)

Iout(Unit1)0(Unit1 Iout)

3000(A)

Iout(Unit2)0(Unit2 Iout)

3000(A)

Iout(Unit3)0(Unit3 Iout)

3000(A)Iout
fsw: 15(kHz)(Unit4) Td: 4( s)
10( s)

0(Unit4 Iout)(b) Waveform of the output current of each unit.
Fig. 8. Experimental voltage and current waveform.

(a) Unit1.

(b) Unit2.
Fig. 9. Response waveforms of each output current by a step
input of the phase shift command.

In addition, it is confirmed that the time constant of theload is 692μs. This result is used to design the PI
parameters which are shown by (4) and (5).
Figure 10 shows the step response of output current
waveform with current feedback control. The stepcommand of the output current is set from 0.0p.u to
0.4p.u. In this case, ωn=2,000 rad/s and ξ is varied from =2, 0.9 and 0.7. From Fig. 10, it is confirmed that the step
response waveform of output current corresponds to thestep response waveform of the second order system eventhe ωn is changed. The natural angular frequency
calculated from the time for reaching the peak ofovershoot which are obtained from Fig. 10. As a result, it
is confirmed that the ωn of Fig. 10(b) and (c) are 2110
rad/s and 1815 rad/s, respectively. The error rate ofnatural angular frequency is less than 9%. This error iscaused by a dead-time and voltage drops in the prototype
circuit.
Figure 11 shows the step response of the output current
waveform when two units are operated in parallel. The
command of the output current is varied from 0.0p.u to
0.4p.u. In this case, ωn=2,000 rad/s and ξ = 0.7. From Fig.
11, it is confirmed that the responses of the output
current are almost same between two units because theoutput side wiring inductance and the resistance of theload are almost same. In the prototype, the same circuit
parameters are achieved due to the symmetrical layout of
prototype. As a result, the proposed design method for
the PI parameters is not needed in this prototype. If theimbalance of the circuit parameters occurs due to thesymmetrical layout of prototype, the proposed design
method for the PI parameters should be adopted.

(a) ωn=2000rad/s, ζ=2.

(b) ωn=2000rad/s, ζ=0.9.

(c) ωn=2000rad/s, ζ=0.7.
Fig. 10. Step response waveforms of the output current.

B. Power Loss Evaluation
Figure 12 shows the experimental results for theefficiency. The efficiency is measured from the input
power of the diode rectifier to the power of the load.
Note that the power consumption of the control circuit is
not included. A maximum efficiency of 69.0% (Output
current = 10,000 A) was obtained in the experiment. The
reason for this low efficiency in the experiment is thatthe load uses a very small resistance. When a small
resistance is used, the output voltage becomes small
because the output current is controlled to be constant.
On the other hand, the power loss of the secondary side
rectifier, which mainly dominates the total power loss, is
proportional to the output current. Therefore, it isexpected that the efficiency will be increased when theactual material is used because the output voltage
becomes higher than that of the experimental condition.
Figure 13 shows the loss analysis using the circuit
simulator Piece-wise Linear Electrical Circuit Simulation(PLECS, Plexim GmbH). In particular, the power loss iscalculated from the instantaneous voltage and theinstantaneous current in the simulation circuit, based on
the table of switching devices data in the appropriate
datasheet. The validity of this simulation method is
described in Ref. [8]. The simulation results agree wellwith the experimental results. In the prototype, the power
loss in each main circuit cannot be measured because
wiring between the converters is short and close in orderto reduce the volume. Therefore, the power loss is
discussed based on the simulation results. In this section,
the power losses include that of the diode rectifier,inverter, and Schottky barrier diodes only. The power
losses of the transformer are not considered. From theloss analysis, it is confirmed that the power loss of theFig. 11. Step response waveforms of the output current when two units
are operated in parallel.

100
90
80
70
60
50
40
30
20
0

fsw: 15(kHz)
Td: 4( s)Rout: 0.21(m )2000 4000 6000 8000 10000
Output current (A)Fig. 12. Experimental results for the efficiency as a function of
output current.

diodes in the secondary side is 49% dominated bysemiconductor loss.
In order to reduce the power losses, a synchronous
MOSFET rectifier was implemented. MOSFETs with low
on-resistance were selected and connected in parallel toreduce the conduction loss of the secondary side rectifier.
Figure 14 shows the circuit configuration of thesynchronous rectifier with the MOSFET and a simplifieddiagram of the gate signal. The gate signals of switches
S5 and S7 are synchronized with the gate signal Gate1 of
the inverter. On the other hand, the gate signals ofswitches S6 and S8 are synchronized with the gate signal
Gate3 of the inverter.
Figure 15 shows the calculation results of the loss
reduction by adopting the synchronous rectifiercomposed of the MOSFET (IXTZ550N055T2, 55V,
550A IXYS). The number of MOSFETs was 12 in one
device, while the number of Schottky barrier diodes was
32 in one device. From Fig. 15, it is confirmed that thepower losses of the secondary side rectifier can be
reduced by 35% compared to the ones with the Schottky
barrier diodes when the output current per unit is 2,500
A. As a result, the maximum efficiency is improved to70%. In the case of a larger resistance in the load, themaximum efficiency will be greatly improved.
C. INPUT CURRENT EVALUATION AND POWER FACTORCORRECTION
The proposed system uses multiple transformers to
reduce the input current harmonics. Unfortunately, it wasdifficult to prepare multiple transformers for experiments
in laboratory tests. Instead, the effect of multiple
transformers was evaluated in simulations based on the
input current waveform obtained from experimental
results.
Figure 16 shows the voltage and current waveforms ofthe grid and the input of the diode bridge rectifier without
connecting multiple transformers in the experiment.
From Fig. 16, it is confirmed that the input current of thediode rectifier has a large distortion. Therefore, in orderto suppress this large distortion of the input current, apower factor correction circuit, such as multiple
transformers, is required in the prototype circuit.
Figure 17 shows the simulation results with improved
input power factor. From the simulation results, it isconfirmed that the input current distortion of each unit islarge. On the other hand, the input current for themultiple transformers has low distortion. Therefore, thesimulation results confirm that multiple transformers arevalid to reduce the harmonic components in the input
current. As a result, the current in the grid has almost asinusoidal waveform.
Figure 18 shows the measurement and simulation
results of the total harmonic distortion (THD) in the input
current. From Fig. 18, it is confirmed that the THD
without connecting multiple transformers is over 60%.
On the other hand, the THD after connecting multiple
transformers is improved by 90% compared to the casewithout connecting multiple transformers.
Figure 19 shows the measurement and simulation
results of the input power factor. From Fig. 19, it isconfirmed that the power factor is 0.85 when the output
current of each unit is 2,300 A in the experiment without
connecting multiple transformers. On the other hand, inthe region of low output current, the power factor
becomes less than 0.7 in the experiment. This is because
the ratio of the reactive output power with respect to theFig. 13. Loss distribution as a function of the output current.

(a) Circuit configuration of the synchronous rectifier with the
MOSFET.

Gate1(Inverter)
Gate3(Inverter)

Gate drive unit
Isolation
Isolation
Isolation
Isolation

S5
S6(MOSFET)
S7
S8(b) Simplified diagram of the gate signal of the MOSFET.
Fig. 14. Circuit configuration of the synchronous rectifier andsimplified diagram of the gate signal of the MOSFET.

Fig. 15. Loss reduction with the synchronous rectifier of
MOSFET.

active output power is low. In the case of the simulation,
the characteristic of the power factor is similar to themeasurement result. On the other hand, the input powerFig. 16. Voltage and current waveforms of the prototype circuit without
multiple transformers.

Fig. 18. Input current THD as a function of output current.

Fig. 19. Input power factor as a function of output current.

current.
REFERENCES[1]
Fig. 17. Simulation waveforms of the prototype circuit withmultiple transformers.

[2]

factor with multiple transformers exceeds 0.98 in thesimulation. Therefore, the simulation results confirm thatmultiple transformers are valid and effective to obtain ahigh input power factor.

[3]

VI. CONCLUSION
In this study, a prototype model was developed with
output of 10,000 A in order to apply middle-large power
for application in sintering. The prototype model consistsof four units with output of 2,500 A in parallel. The
response of the feedback output current control withdifferent output side wiring inductances is investigated. It
was confirmed that the damping factor should bedesigned with the largest inductance in order to suppress
the overshoot current within the designed value. The
experimental results confirmed that the circuit outputs
10,000 A. The loss analysis by simulation confirmed thatthe power losses of the secondary side rectifier with a
MOSFET synchronous rectifier can be reduced by 35%
compared to those with Schottky barrier diodes. In
addition, the simulation results confirmed that multiple
transformers are valid to obtain low-distortion input

[4]

[5]

[6]

[7]

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