A Fundamental Verification of a Single-phase toThree-phase Matrix Converter with a PDM
Control based on Space Vector Modulation
Yuki Nakata and Jun-ichi Itoh
Department of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
nakata@nagaokaut.ac.jp, itoh@stn.nagokaut.ac.jp
Abstract—This paper discusses pulse density modulation(PDM) control methods for a single-phase to three-phasematrix converter for high-frequency applications such as
the grid interface converter for a wireless power transfer
system and high-frequency transformer link system. The
input frequency for this converter is assumed as several
hundred kHz, and at the same time outputting a commercial
frequency, i.e. 50 Hz or 60 Hz. The proposed circuitachieves high efficiency by zero voltage switching from a
PDM control method. In the PDM control using delta-sigma
conversion, the output waveform has inverse voltage pulse
and clamp phenomena on the output voltage waveform.
Hence, an improvement method of the output waveform
based on SVM is proposed. In this paper, the experimental
results using the prototype circuit of indirect matrix
converter (IMC) and conventional matrix converter (CMC)
with the two PDM control methods are compared. As aresult, the THD of the output voltage with delta-sigma
conversion and PDM pattern method based on SVM are
5.96% and 2.15% respectively in the experiment using IMC.
Furthermore, the maximum efficiency has been improved
from 93.4% to 97.3% by applying the proposed PDM
method. From the results, the validity of PDM control basedon SVM has been confirmed. In addition, a prototype of
direct type circuit (CMC) has been built and tested. From
the results, the switching at zero voltage and clear sinusoidal
output waveform has been confirmed too. As a result, theoutput voltage THD, which is controlled by the proposed
PDM based on SVM are 3.25%.
Keywords— delta-sigma conversion, PDM control, space
vector modulation, wireless power transfer

I.

INTRODUCTION

In recent years, wireless power transfer systems havebeen actively researched [1-4]. In the wireless powertransfer system, the frequency of the generated voltage at
the receiving coil is from tens of kHz to several MHz,
which is identical to the power source frequency.
Accordingly, in order to connect this system to a load, aninterface converter which converts the received power
into a controlled output power is required. The
characteristic of this interface converter must have a highinput frequency (several hundred kHz) and a low output
frequency (50 Hz or 60 Hz) which is suitable forcommercial power grid. That is, an AC-to-AC converter

is generally clarified as the interface converter for thissystem. In general, back-to-back (BTB) system, which isconstructed by a PWM rectifier, a smoothing capacitor
and a PWM inverter, is used as this AC-to-AC converter.
However, it is difficult to use the PWM rectifier in the
input side due to high-frequency input.
On the other hand, matrix converters (MC) have been
attracted attentions as the AC interface converter for thewireless system, because it delivers advantages in termsof a size reduction and an energy saving owning to highefficiency [5-7]. However, the implementation of the MCin the high-frequency power source has not been reported.
There are two type topologies for the matrix converter,so called indirect matrix converter (IMC) andconventional matrix converter (CMC). The IMC consistsof a diode rectifier and three-phase inverter, and theconfiguration and the control of the circuit are simpler
than the CMC circuit. However, the IMC has low
efficiency because of the twice power conversion.
Furthermore, the IMC circuit is a unidirectional power
flow converter because the diode rectifier is used in the
input side. On the other hand, the CMC consists ofbidirectional switches. The CMC has high efficiency
because of the only once power conversion. Additionally,
this circuit is a bidirectional power flow converter
because the bidirectional switches are used. However,control of this circuit is more complicated in comparison
than that of the IMC because the input voltage polarity of
the circuit alternates.
The authors have previously proposed a Pulse density
modulation (PDM) [8-11] control method for the highfrequency power source [12-13]. The proposed PDM
control method is applied to the proposed circuit by using
the half cycle of the input voltage as a pulse for PDM
control. Therefore the proposed circuit achieves the
reduction of the switching loss by the switching at zero
input voltage. The PDM signals can be obtained fromdelta-sigma conversion. However, in the delta-sigma
conversion, the inverse voltage pulses and clamp
phenomena occur in the output voltage waveform of the
IMC. When the phase angle between the output voltage

and current becomes larger instantaneously, the DC linkcurrent flow backward to the power source and DC link
voltage is clamp to snubber capacitor voltage because theDC link current cannot flow toward the power source.
Therefore the clamp phenomenon of the output voltage
occurs. Additionally, in CMC circuit, the clamphenomenon does not occur because the power
regeneration is allowed in the CMC.
In this paper, the PDM control based on space vector
modulation (SVM) is proposed in order to solve these
problems and improve the quality of output waveform.
The proposed method generates switching patterns basedon SVM in order to minimize the phase angle between
output voltage and current. Therefore, there are no clamp
phenomena on the output voltage waveform of the IMC.
This paper compares and investigates the two PDM
control methods, which are based on the delta-sigma
conversion and SVM are compared and investigated fromthe experimental results using the prototype circuit of
IMC and CMC. Firstly, the configurations of the
proposed circuit are introduced. Secondly, the PDM
control strategy using the delta-sigma conversion and the
proposed PDM method based on the SVM are discussed.
Next, the validity of the proposed method is confirmed in
the experimental results using the prototype circuit of
IMC. Finally, the proposed PDM control method isapplied to a prototype circuit of CMC, and the basic
operation of the proposed PDM control in direct typecircuit is confirmed.
II.

CIRCUIT CONFIGURATION

A. System Configuration
Fig. 1 shows a configuration of the wireless powertransfer system. The receiving coil voltage is a highfrequency AC, which has same as the frequency of thesource. In order to connect to the commercial grid, a
single phase AC to three phase AC converter is required
as an interface converter.
The interface converter inputs several-hundred-kHz
sinusoidal waveform, and outputs the low-frequency
waveform such as 50 Hz and 60 Hz. Hence, PDM control
which uses a half cycle of the input voltage as a pulse canbe applied to the interface converter.
Therefore, the use of the matrix converter as aninterface converter for wireless power transfer system is
proposed. The matrix converter has high frequency byapplying proposed PDM control. The detail of PDM
control is explained in next section.
B. Indirect Single-phase to Three-phase Matrix
Converter
Fig. 2 shows circuit configuration of the proposed
single-phase to three-phase IMC. This circuit isconstructed from a diode rectifier as an input interface
and a three-phase inverter for the rear side. Since thisconverter does not required electrolytic capacitors in theDC link, the lifetime is longer and the size is morecompact than the conventional system, which isFig. 1. Configuration of the wireless power transfer system.

Fig. 2. Single-phase to three-phase indirect matrix converter.

r

Lf

iin
Sru

Srv

Srw
u

vin

v

Cf

w

Ssu
s
Input filter

Lload Rload

Ssv

Ssw
BidirectionalswitchFig. 3. Single-phase to three-phase conventional matrix converter.

constructed by a PWM rectifier, electrolytic capacitors
and a three-phase PWM inverter.
The IMC has low efficiency because the power
conversion number of the IMC is twice. Furthermore, theIMC circuit is a unidirectional power flow converter
because the diode rectifier is used in the input side.
However, the control of the circuit are simpler than the
CMC circuit because the inverter is controlled only.
Note that, in the experimental circuit, a snubber circuit
is connected to the DC link as a protection circuit. It isconstructed by a diode, a small capacitor and a resistor.
The prototype of this circuit configuration is used in
the first experiment, in order to compare two PDM
methods, which is explained in chapter III and confirm
the validity of the proposed method explained in section
III-C.
C. Single-phase to Three-phase Matrix Converter
Fig. 3 shows the circuit configuration of the proposed
single-phase to three-phase CMC. This circuit isconstructed by six bidirectional switches. Since thisconverter does not require electrolytic capacitors in theDC link, the lifetime is longer and the size is morecompact than that of the conventional system, which isconstructed by a PWM rectifier, electrolytic capacitors
and a three-phase PWM inverter. Further, the efficiency
of a CMC is higher than a conventional system because
the conversion number is reduced in comparison with theconventional system. However, control of this circuit ismore complicated in comparison than that of the IMC
because the input voltage polarity of the circuit alternates.
Note that, in the experimental circuit, a snubber circuit
is connected to the output side of the converter as aprotection circuit. It is constructed by a diode, a small
capacitor and a resistor.
The prototype of this circuit configuration is used in
the second experiment, in order to confirm the basic
operation and validity of proposed PDM method
explained in section III-C in CMC.
D. Design of the Input Filter
The impedance matching is important on the circuit
for the high-frequency application. In this system, theinput filter is connected to the input side as an impedance
matching circuit, which can match the impedance of thevoltage source and the circuit. The design method, whichmatches the impedance Zin to 50 Ω is explained in thissection because the general high-frequency powersources have 50 Ω of matching impedance.
Fig. 4 shows the configuration of input filter. It isconstructed from a reactor Lf and a capacitor Cf. The
impedance of the load connected to the filter is expressedby resister Rload as shown in Fig. 4. The value of Lf and Cf
are decided in order that the real part of the synthetic
impedance equals to 50 Ω and the imaginary part equals
to 0 Ω to achieve the 50 Ω of matching impedance. Lf
and Cf are calculated by (1) and (2), where, ω=2πf is the
input voltage angular frequency. Lf and Cf are 80 μH and
16 nF respectively, when the frequency of f is 100 kHz,and Rload is 100 Ω. These values are used in theexperiment.

Lf =

Cf =

C f Rload2

1 + (ωC f Rload ) 2
1
ωRload

III.

Rload
−1
50

(1)
(2)

CONTROL STRATEGYS

A. Concept of PDM Control
A PDM control method is applied to the proposedsystem in order to reduce the switching loss of theconverter. PDM controls the density and the plus/minusof the constant-width pulse, and then these pulse signals
are used as the output unit.

Fig. 4. Configuration of the input filter.

Fig. 5. PDM control waveform of proposed circuit.

(a) Control block diagram using delta-sigma conversion (overall).

(b) Block diagram of the delta-sigma conversion.
Fig. 6. PDM control block diagram using delta-sigma conversion.

Fig. 5 shows a frame format of PDM control
waveform for the single-phase to three-phase CMC.
Assuming that the single-phase to three-phase CMC isconnecting to a wireless power transfer system, it isreceiving high frequency sinusoidal voltage as an input.
Therefore the PDM control can be applied to the
proposed circuit by using the half cycle of the input
voltage as a pulse for PDM control as shown in Fig. 5.
B. PDM Control using Delta-sigma Conversion
Fig. 6 shows the PDM control block diagram using
delta-sigma conversion. The PDM signals used for theswitching can be obtained by applying the delta-sigma
conversion to each phase command values (vu*, vv*, vw*).
In general, delta-sigma conversion is used for analogdigital conversion. These PDM signals are used to turnon/off the inverter arm of IMC shown in Fig. 2.
Additionally, the zero cross points exist with respects
to the frequency since the input voltage is a sinusoidal
waveform. The turn-on and off of the each switching
devices are implemented at every zero cross points of the
input voltage in order to achieve the switching at zerovoltage. The loss from the switching devices at theconverter can reduce drastically because the switchingloss can be decreased nearly to zero by the
implementation of the switching at zero voltage.
However, there are problems in this method, due tothe inverse voltage pulses and clamp phenomena that are
constant voltage areas occur shown as Fig. 8. Deltasigma conversion generates the inverse voltage pulses inorder to cancel the quantization error shown in Fig. 5(b).
In the clamped parts, switching loss increases because theswitching at zero voltage cannot be achieved. The clamp
phenomenon occurs because when the phase angle
between the output voltage and current becomes larger
than 30 degrees, the DC link current flows backward to
the power source in the inverter side. As a result, the DC
link voltage is equaled to the snubber capacitor voltage.
In order to resolve this problem, the PDM based on
SVM is proposed to apply for the generator of PDM
patterns. The detail of this method is explained in thenext section.
C. PDM Control based on Space Vector Modulation
Fig. 7(a) shows the PDM signal generation blockbased on the SVM. The selected vector signals generated
from the SVM is the input to the D flip flop (D-FF). The
plus/minus detection signal from the input voltage is used
to detect the zero cross points of input voltage, and thissignal is an input to the CLK of the D-FF. The output of
the D-FF, “Q” is synchronized at the edge of plus/minus
signal, which is the zero cross point of the input voltage.
After that, the switching signals which correspond to thevectors in Fig. 7(b), are generated from output signals of
the D-FF using pattern table in Fig. 7(c). These signals
are Switching signals for IMC shown in Fig. 2.
Furthermore, in order to apply this method to CMC
shown in Fig. 3, the switching signals are exclusive
NORed with the polarity of the input voltage, because itis necessary to exchange the switching signals of theupper arm and the lower arm depending on the polarity of
the input voltage.
Therefore, the switching patterns generated by SVM
are quantized by the pulse whose width is half cycle ofthe input voltage and the switching timing is
synchronized with the zero cross point of the input
voltage. As a result, this proposed method based on SVM
can achieve switching at zero voltage.
IV. EXPERIMENTAL RESULTS USING INDIRECT MATRIXCONVERTER AND CONVENTIONAL MATRIX CONVERTERIn this chapter, a prototype circuit of IMC and CMC
are built and tested in order to demonstrate the validity ofthe proposed PDM methods.
First, the single-phase to three-phase IMC was tested
in the experiment with the two PDM control methods in
section IV-A and IV-B. A high-frequency power source,
where the matching impedance is 50 Ω is used as the
input of the circuit in order to confirm the basic principleof the two PDM control methods. Table I shows the(a) PDM signals generation block diagram based on SVM.

(b) Space vector diagram.
(c) Switching pattern table.
Fig. 7. Control block diagram of the PDM control based on SVM
Table I. Experimental Parameters for IMC.
Parameter
Value
Input voltage
200 V
Input frequency
100 kHz
Output line-to-line voltage
100 V
Output frequency
50 Hz
Carrier frequency(in proposed PDM control
5 kHz
based on SVM)
Rload
100 Ω
Load
Lload
10 mH
Table II. Experimental Conditions for CMC.
Parameter
Value
Input voltage
70.7 V
Input frequency
100 kHz
Output line-to-line voltage
40 V
Output frequency
50 Hz
Carrier frequency
5 kHz
Rload
16 Ω
Load
Lload
10 mH

experimental conditions.
Secondly, the single-phase to three-phase CMC wastested in the experiment with the proposed PDM control
methods, which is based on SVM. A high-frequency
power source, where the matching impedance is 0 Ω isused as the input of the circuit in this experiment. Table
II shows the experimental conditions in order todemonstrate the validity of the proposed PDM methods
in CMC in section IV-C.
A. Experimental Results using IMC with PDM Control
using Delta-sigma Conversion
Fig. 8(a) shows the operation waveforms of the
proposed circuit with delta-sigma conversion. From theresult, the output voltage and current are 50-Hz
sinusoidal waveforms. The PDM control operation using
delta-sigma conversion can be verified and confirmed at
the experimental results. Similarly to the simulation

results, certain voltage pulses are inversed due to thefailure on the pattern conversion.
Fig. 8(b) shows the extended view of the interval “A”
in Fig. 8(a). The results confirm that the switching at zerovoltage is approximately performed at the zero crosspoint of the input voltage waveform. However, theswitching has a 1 μs delay due to the following reasons;(i) detection of the zero cross points is slow and (ii) thedead time of the inverter. The delay of the zero crosspoint detection is approximately 0.5 μs, and dead time of
the inverter is set to 0.5 μs. The delay can be improvedby modifying the zero cross point detection circuit. Thus,
the dead time period can be improved by studying andevaluating the device parameters. Additionally, although
the switching has a short delay, the surge voltage is lower
than that of the hard switching method. However, due tothe clamp phenomena, as covered in the section III-B,
switching loss increases because switching at zerovoltage cannot be achieved. Therefore, the circuit has low
efficiency in this experiment.
In addition, Fig. 9 shows the harmonics analysis on
the output voltage and input current. From (a), output
voltage does not include low-order harmoniccomponents, and the integral-multiple harmonic nearlyclosed to 200 kHz. The frequency is DC link voltage
fluctuating frequency is included in the high-orderharmonic components. The output voltage THD of 5.96%
is obtained. Moreover, (b) shows that the input current
has the integral-multiple harmonic nearly closed to 100
kHz, and therefore input current THD is 79.7%.
B. Experimental Results using IMC with PDM Control
based on Space Vector Modulation
Fig. 10(a) shows the operation waveforms of the
proposed circuit in the experiment with the PDM control
based on SVM. The result confirms that 50 Hz sinusoidal
waveforms are obtained on the output voltage andcurrent. The PDM control operation based on SVM canbe verified and confirmed from the experimental results.
Notice there are no inverse voltage pulses in this case.
Fig. 10(b) shows the extended view of the interval “B”
in Fig. 10(a). As a result, the output line-line voltage vuv
confirms that the switching of the inverter is happened at
approximately each zero cross point of the 100 kHz
sinusoidal input waveform. However, the switching has a
1 μs delay due to the same reasons as mentioned in the
explanation of Fig. 8.
Fig. 11 shows the harmonics analysis on the output
voltage from experimental result with the PDM control
based on SVM. From the result, the low-order harmoniccomponents closely to 50 Hz are not included in the
output voltage, and the output voltage THD of 2.15% can
be obtained. Therefore, the improvement of the output
voltage waveform is confirmed. In this case, output
voltage includes of the integral-multiple harmonic nearly
to the carrier frequency of 5 kHz, which is the switchingfrequency. Additionally, the integral-multiple harmonicnearly to the 200 kHz is included in the output voltage

Input voltage vin 0[500 V/div]
Input current iin 0[10 A/div]0

Output voltage vuv[500 V/div]0

Output current iu[2 A/div]A

2 ms/div(a) Input and output operation waveforms.

(b) Extended view of each operation waveform.
Fig. 8. Operation waveforms of the proposed circuit in the experimentwith PDM using delta-sigma conversion in IMC.

(a) Harmonics analysis of output voltage.

(b) Harmonics analysis of input current.
Fig. 9. Harmonics analysis of output voltage and input current with
PDM control using delta-sigma conversion in IMC.

because of the same reason as case of Fig. 9.
Furthermore, input current includes the integral-multiple
harmonic nearly closed to 100 kHz and input current
THD is 55.5%.
From these results, the validity of the proposed PDM
control for waveform improvement is confirmed.
Therefore, in next chapter, the proposed PDM control
method is applied to CMC (direct type circuit) in order tocheck the basic operation of the PDM control in a direct

type circuit.
C. Experimental Results using CMC with PDM Control
based on Space Vector Modulation at low voltage
condition
Fig. 12(a) shows the operation waveforms of the
proposed circuit in the experiment with PDM control
based on SVM. The result confirms that 50 Hz sinusoidal
waveforms are obtained on the output voltage andcurrent. The PDM control operation based on SVM canbe verified and confirmed at the experimental results.
However, the output waveform has a surge voltage
because of the switching delay due to the zero cross point
detection circuit.
Fig. 12(b) shows the extended view of the interval “C”
in Fig. 12(a). As a result, the output line-to-line voltage
vuv confirms that the switching of the CMC is happened
at approximately each zero cross point of the 100 kHz
sinusoidal input waveform. Therefore, basic operation of
the proposed PDM control based on SVM is confirmed.
Fig. 13(a) shows the harmonics analysis on the output
voltage from experimental result with PDM control basedon SVM. From the result, the low-order harmoniccomponents of 50 Hz are not included in the output
voltage, and the output voltage THD of 3.25% can beobtained. In addition, the output voltage includes theintegral-multiple harmonic nearly to the carrier frequencyof 5 kHz, which is the control cycle. Additionally, theintegral-multiple harmonic nearly to the 200 kHz is
included in the output voltage in the high-order harmoniccomponents because the output voltage has thefluctuation, which is twice of the input frequency.
Furthermore, Fig. 13(b) shows the harmonics analysis
on the input current. From the result, the input current
includes the integral-multiple harmonic nearly closed to
100 kHz and the input current THD is 48.5%, which islarge value. However, the harmonics can be eliminatedby using small input filter with small capacitor because
the cutoff frequency can be very high frequency.
Therefore, the basic operation of the proposed PDM
control method in direct type circuit is confirmed fromthese results.
V.

(a) Input and output operation waveforms.

(b) Extended view of each operation waveform.
Fig. 10. Operation waveforms of the proposed circuit in the experimentbased on SVM in IMC.

(a) Harmonics analysis of output voltage.

EFFICIENCY CHARACTERRISTICS AND LOSSANALYSIS

Fig. 14 shows the efficiency characteristics of theindirect type circuit (IMC) with PDM control using deltasigma conversion and PDM control based on SVM. The
input and output voltage conditions are same as shown intable 1, and the output power is controlled by changing
the load value. From the result, the efficiency of thecircuit is improved as output power increases in both the
PDM control methods. Furthermore, the efficiency for
the PDM control based on SVM is higher than that for
the PDM control using delta-sigma conversion at allmeasurement regions. This is because the switching loss
decreases due to resolution of the clamp phenomenon andreduction of the switching frequency applying the PDM(b) Harmonics analysis of input current.
Fig. 11. Harmonics analysis of output voltage and input current with
PDM control based on SVM in IMC.

control based on SVM. As a result, the validity of PDM
control based on SVM is confirmed about efficiency
improvement.
In addition, the maximum efficiency with PDM
control using delta-sigma conversion and with PDM
control based on SVM are 93.4% and 97.3% respectively.
Fig. 15 shows the efficiency characteristics of thedirect type circuit (CMC) with PDM control based on
SVM. The input and output voltage conditions are sameas shown in table II, and the output power is controlled
by changing the load value as the case of IMC. From theresult, the maximum efficiency is 91.5% at load of 35 W.
This value is lower than that of IMC. The cause of low
efficiency in the CMC circuit is investigated from theresult of the loss analysis.
Fig. 16 shows the result of the loss analysis. From theresults, it is confirmed that the cause of low efficiency in
the CMC circuit is the conduction loss of the switching
device is larger than that of IMC. In this experiment, thecurrent value, which flows through switching devices islarger than case of IMC to output same power because
the input and output voltage of the circuit is lower thanthe case of IMC. It is a limitation of the voltage source,which is used in this experiment. In addition, thebidirectional switches have high on-resistance because
the bidirectional switches used in CMC construct of two
unidirectional switching devices connected in anti-series.
Therefore, the efficiency of IMC improves by making
an experiment at high voltage condition and choosing theswitching devices, which have lower on-resistance.
It is noted that the recovery losses of the freewheeling
diodes (FWD) and diode rectifier are not included in thissimulation. Thus the value of the total loss is lower thanactual value.
VI.

(a) Input and output operation waveforms.

(b) Extended each operation waveform.
Fig. 12. Operation waveforms of the proposed circuit in the experimentbased on SVM in CMC.

CONCLUSIONSIn this paper, the implementation of PDM control
methods in a single-phase to three-phase matrix converter
for high frequency application is discussed and evaluatedby the experiments. In the PDM control using deltasigma conversion, the output waveform has inverse
voltage pulse and clamp phenomena on the output
voltage waveform. Hence, an improvement method of theoutput waveform based on SVM is proposed. In SVM,
the phase error between the voltage and current aredramatically reduced.
At first a prototype of indirect type circuit has been
built and tested. From the results, the switching at zerovoltage and clear sinusoidal output waveform have been
confirmed. On the other hand, it is confirmed that thePDM control based on SVM can resolve the problems
with clamp phenomenon. As a result, the THD of theoutput voltage with delta-sigma conversion and PDM
pattern method based on SVM are 5.96% and 2.15%
respectively. Furthermore, the maximum efficiency has
been improved from 93.4% to 97.3% by applying the
proposed PDM method. From the results, the validity of
PDM control based on SVM has been confirmed.
Secondly, a prototype of direct type circuit was built
and tested. From the results, the switching at zero voltage
and clear sinusoidal output waveform have been
confirmed too. As a result, the output voltage THD and
input current THD, which is controlled by the proposed
PDM based on SVM are 3.25% and 48.5%, respectively.
In addition, the AC-to-AC converter for the highfrequency application such as the proposed circuit isnecessary in other case. For example, the MC for high-(a) Harmonics analysis of output voltage.

(b) Harmonics analysis of input current.
Fig. 13. Harmonics analysis of output voltage and input current with
PDM control based on SVM in CMC.

frequency application can be applied to trans-linked
converter, whose secondary side is connected tocommercial grid. For downsizing the converter, thetransformer for high-frequency link size is a majorbottleneck [14]. Therefore, the size of the transformer canbe small by higher frequency converter using high-speed
switching devices such as SiC and GaN.
In future work, efficiency characteristics of the
proposed circuit will be measured, and the zero crosspoint detection circuit will be improved to reduce theswitching loss and the switching surge.
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Fig. 14. Characteristics of the proposed circuit’s efficiency in theexperiment using IMC.

Fig. 15. Characteristics of the proposed circuit’s efficiency in theexperiment using CMC.

6
Switching lossof the FETs

5

Conduction lossof the FWDs

4
3

Conduction lossof the rectifier
Conduction
loss of the
FETs

2
1
0

Snubberloss

IMC with
Delta-sigma
conversion

IMC with
proposedmethodCMC with
proposedmethodFig. 16. Loss analysis of the IMC and the CMC with 100-W load.