This study presents a singlephase power factor correction AC–DC converter that operates in discontinuous conduction mode. This converter uses the pulsewidth modulation technique to achieve almost unity power factor and low total harmonic distortion of input current for universal input voltage (90 V
_{rms}
to 264 V
_{rms}
) applications. The converter has a simple structure and electrical isolation. The magnetizinginductor energy of the transformer can be recycled to the output without an additional third winding. The steadystate analysis of voltage gain and boundary operating conditions are discussed in detail. Finally, experimental results are shown to verify the performance of the proposed converter.
I. INTRODUCTION
DC power sources are widely used in industrial products and consumer electronics, such as battery chargers, DC power supplies, uninterruptible power supplies, inverters, and instruments. Thus, AC–DC power conversion is an important consideration. Diodebridge or thyristor rectifiers can realize AC–DC power conversion, but such rectifiers will result in power pollution, including pulsating input current, low power factor, and high total harmonic distortion of input current(THD
_{i}
). Several power factor correction (PFC) AC–DC converters have been investigated to address these issues. These converters possess nonisolated and isolated topologies. Nonisolated topologies include the boost
[1]

[4]
, buck
[5]

[7]
, buckboost
[8]

[10]
, Cuk
[11]
, SEPIC
[12]
,
[13]
, and ZETA types
[14]
. These converters are operated in continuous conduction mode and discontinuous conduction mode (DCM) for different outputpower applications. Isolated topologies include forward
[15]

[17]
and flyback types
[18]

[20]
. The forward types achieve low output voltage ripple and high THD
_{i}
. Nevertheless, this converter requires the third winding to recycle the magnetizinginductor energy of the transformer. The flyback types are shown in
Fig. 1
(a). This converter achieves high power factor and low THD
_{i}
. Moreover, flyback types have a simple structure and low cost but have low efficiency because of the transformer leakage inductor. The clamping method is presented in
[21]
,
[22]
to recycle leakage inductor energy. However, this method makes the power circuit complicated.
(a) Conventional singlephase AC–DC flyback converter and (b) proposed singlephase AC–DC converter.
We propose a singlephase PFC AC–DC converter, as shown in
Fig. 1
(b). The proposed converter circuit configuration is very simple. The configuration includes only a set of input filter
L_{f}
–
C_{f}
, a diodebridge rectifier, a transformer
T_{r}
, an inductor
L
_{1}
, an output diode
D_{o}
, and an output capacitor
C_{o}
. The proposed converter does not have the transformer leakage inductor issue associated with the flyback converter. Moreover, transformer magnetizinginductor energy can be recycled to the output without an additional third winding. This converter is operated in DCM by using the pulse–width modulation technique to achieve high power factor and low THD
_{i}
for universal inputvoltage applications.
II. OPERATING PRINCIPLES
The equivalent circuit of the proposed converter is shown in
Fig. 2
. The transformer is modeled as a magnetizing inductor
L_{m}
and an ideal transformer. Some key waveforms in a half linesource period are shown in
Fig. 3
. The operating principle is analyzed as 0 <
ωt
< π, where
ω
is the line angular frequency, because of the symmetrical characteristics of the singlephase system.
Equivalent circuit of proposed converter.
Key waveforms of the proposed converter for 0<ωt<π.
Mode 1, [kT_{s}, t_{k1}]: S
_{1}
is switched on. The current flow path is shown in
Fig. 4
(a). The line source energy is transferred to the magnetizing inductor
L_{m}
of the transformer and the inductor
L
_{1}
. Thus, the currents
i_{Lm}
and
i
_{L}
_{1}
are increased linearly. Given that magnetizing inductor
L_{m}
is significantly larger than inductor
L
_{1}
, the magnetizinginductor current
i_{Lm}
becomes lower than inductor current
i
_{L}
_{1}
. The energy stored in magnetizing inductor
L_{m}
is the residual magnetism of the transformer. The energy stored in output capacitor
C_{o}
is discharged to load
R
. This mode ends when
S
_{1}
is switched off.
Current flow path of the proposed converter for 0<ωt<π.
Mode 2, [t_{k1}, t_{k2}]: S
_{1}
is switched off. The currentflow path is shown in
Fig. 4
(b). The energies stored in magnetizing inductor
L_{m}
and inductor
L
_{1}
are released to output capacitor
C_{o}
and load
R
. The currents
i_{Lm}
and
i
_{L}
_{1}
are decreased linearly. This mode ends when the currents
i_{Lm}
and
i
_{L}
_{1}
are equal to zero. Therefore, the transformer residual magnetism can be released to empty during each switching period.
Mode 3, [t_{k2}, (k+1)T_{s}]: S
_{1}
remains switched off. The currentflow path is shown in
Fig. 4
(c). The energies stored in magnetizing inductor
L_{m}
and inductor
L
_{1}
are empty at
t
=
t_{k2}
. The energy stored in output capacitor
C_{o}
is discharged to load
R
. This mode ends when
S
_{1}
is switched on at the beginning of the next switching period.
III. STEADYSTATE ANALYSIS
Given that the singlephase system is symmetrical, the following analysis is discussed for 0 <
ωt
< π. For simplicity, the effect of the input filter is neglected. The line voltage is given by
where
V_{rms}
and
V_{m}
are the rootmeansquare value and line voltage amplitude, respectively. The line voltage is considered a piecewise constant during each switching period because switching frequency
f_{s}
is larger than line frequency
f
_{1}
. If
m
is the switching number within [0, π/
ω
], then
m
is equal to
f_{s}
/2
f
_{1}
. The following analysis is considered during switching period [
kT_{s}
, (
k
+1)
T_{s}
], where
k
= 0, 1, …..,
m
1. The magnetizing inductor
L_{m}
is ignored in the following analysis because it is significantly larger than inductor
L
_{1}
.
When
S
_{1}
switched turned on, the voltage across inductor
L
_{1}
is obtained as
where es(tk) is the inputvoltage level during switching the period [
kT_{s}
, (
k
+1)
T_{s}
], and the turns ratio of transformer
n
=
N
_{2}
/
N
_{1}
. Then,
The inductor current
i
_{L}
_{1}
is given by
When
t
is equal to
t
_{k}
_{1}
, the peak value of inductor current
i
_{L}
_{1}
is
where
t_{on}
=
t
_{k}
_{1}
–
k_{Ts}
=
d_{Ts}
.
When
S
_{1}
is switched off, the voltage across inductor
L
_{1}
is given by
Then,
By solving (7), we derive the inductor current
i
_{L}
_{1}
as follows:
Given that
i
_{L}
_{1}
(
t
_{k}
_{2}
) = 0, the peak value of inductor current
i
_{L}
_{1}
is
where
t_{r,k}
=
t
_{k}
_{2}
–
t
_{k}
_{1}
.
Using (5) and (9), time duration
t_{r,k}
can be given by
 A. Power Factor Correction
As shown in
Fig. 3
, the average value of unfiltered input current
i
_{N}
_{1}
in one switching period
T_{s}
can be computed as
where
i
_{L}
_{1}
_{p}
is the inductor current peak value for each switching period. Substituting (1) and (5) into (11), we derive the following equation:
The average value of unfiltered input current
i
_{N}
_{1}
is sinusoidal and in phase with the input voltage. Moreover, the harmonic components of current
i
_{N}
_{1}
are distributed over the switching frequency multiples. The harmonic components are easily filtered out by using input filter
L_{f}
–
C_{f}
. The input filter cutoff frequency is significantly lower than the switching frequency.
 B. Voltage Gain
From
Fig. 3
, the average value of the outputcapacitor current
i_{co}
during [
kT_{s}
, (
k
+1)
T_{s}
] can be obtained as
Substituting (1), (5), and (10) into (13) yields
The average value of output–capacitor current
i_{co}
during a half linesource period [0, π/
ω
] is written as follows:
Given that
m
is larger than 1, equation (15) is approximated as:
The output voltage differential equation is given by
The DC model equation is written as
where
V_{o}
and
D
are the DC quantities of
v_{o}
and
d
, respectively.
The normalized inductor time constant is then defined as
Substituting (19) into (18), the voltage gain is derived as
 C. Boundary Condition
The current
i
_{L}
_{1}
must be zero in each switching period to ensure that the proposed converter is operated in DCM. From
Fig. 3
, time duration
t_{s,k}
is obtained as
When the maximum value of
t_{s,k}
is equal to
T_{s}
and 
e_{s}
 is equal to
V_{m}
, the proposed converter is operated in boundary conduction mode. Therefore, substituting
t_{s,k}
=
T_{s}
and 
e_{s}
 =
V_{m}
into (21) can determine the boundary voltage gain as
Using (20) and (22), the curves of voltage gain and boundary voltage gain are shown in
Fig. 5
. When the voltage gain
M
is equal to its boundary voltage gain
M_{bc}
, the boundary normalized inductor time constant τ
_{L}
_{1}
_{B}
is given by
Voltage gain and boundary voltage gain (under n = 0.5).
τ
_{L}
_{1}
_{B}
is plotted in
Fig. 6
. We can observe that the proposed converter is operated in DCM when τ
_{L}
_{1}
< τ
_{L}
_{1}
_{B}
.
Boundary operating condition.
IV. SELECTIONS OF INDUCTOR AND CAPACITOR
 A. Selection of Inductor L1
The appropriate τ
_{L}
_{1}
_{B}
is selected under the required voltage gain to ensure that the proposed converter is operated in DCM. The inductor
L
_{1}
needs to satisfy the following inequality:
 B. Selection of Output Capacitor Co
Using (14), the average value of output–capacitor current
i_{co}
during one switching period is simplified as follows:
Substituting (18) into (25), output–capacitor current
i_{co}
is expressed as
Therefore, the output voltage ripple in one switching period is given by
Then, the output voltage ripple function during time interval [0, π/
ω
] is obtained as
Using (28), the output voltage ripple during time interval [0, π/
ω
] is derived as
Thus,
Output capacitor
C_{o}
must satisfy the following inequality to meet the following output voltage ripple percentage specification:
V. EXPERIMENTAL RESULTS
The prototype circuit is applied in the laboratory to demonstrate the performance of the proposed converter. Electrical specifications and circuit components are set as follows:

 Input voltageVrms= 90 V to 264 V (Vm= 127 V to 373 V)

 Output voltageVo= 100 V

 Line frequencyf1= 60 Hz

 Switching frequencyfs= 50 kHz

 Output powerPo= 20 W to 100 W (R= 100 Ω to 500 Ω)

 TransformerTr:n= 0.5 (60 turns:30 turns), core ETD–49,Lm= 850μH

 Input filterLf= 3.6 mH andCf= 330 nF

 SwitchS1: IXFR34N80

 DiodeDo: DSEC30–04A
The voltage gain
M
is varied from 0.27 to 0.79 according to the electrical specifications. Substituting
M
= 0.79 and
n
= 0.5 into (22), the maximum duty ratio
D_{max}
is derived as 0.61. Substituting
D_{max}
= 0.61 into (23), τ
_{L}
_{1}
_{B}
is obtained as 0.038. Using (24), the inductor
L
_{1}
is given by
The inductor
L
_{1}
is 60
μ
H, and the core is EI40. Thus, τ
_{L}
_{1}
is equal to 0.03 at full load
R
= 100 Ω and is equal to 0.006 at light load
R
= 500 Ω. Substituting the two values of τ
_{L}
_{1}
and
n
= 0.5 into (20), the operating area of the experimental prototype is shown in
Fig. 7
. The proposed converter is operating in DCM.
Operating range of the prototype circuit.
Under the operating conditions
V_{rms}
= 90 V and
R
= 100 Ω,
M
and τ
_{L}
_{1}
are derived as 0.79 and 0.03, respectively. Substituting
M
= 0.79,
n
= 0.5, and τ
_{L}
_{1}
= 0.03 into (20), duty ratio
D
is obtained as 0.55. The ripple percentage of
V_{o}
is selected as 5%. From (31), the output capacitor inequality is given by
Thus, output capacitor
C_{o}
is selected as 600
μ
F.
The control circuit is shown in
Fig. 8
.
Figs. 9
and
10
show the experimental waveforms under
V_{rms}
= 115 V,
V_{o}
= 100 V,
P_{o}
= 100 W and
V_{rms}
= 230 V,
V_{o}
= 100 V,
P_{o}
= 100 W, respectively. In
Figs. 9
(a) and
10
(a), we observe that input current is sinusoidal and is in phase with input voltage. The current waveforms of the transformer primary and secondary sides
i
_{N}
_{1}
and
i
_{N}
_{2}
are shown in
Figs. 9
(b) and
10
(b), respectively. The waveforms are taken at the peak value of input voltage. The current
i
_{N}
_{2}
drops to zero during each switching period, which indicates that the transformer residual magnetism is released to empty during each switching period. The currents
i
_{L}
_{1}
and
i_{Do}
are shown in
Fig. 9
(c) and
10
(c), respectively. We observe that the proposed converter is operated in DCM. The waveform
v
_{S}
_{1}
across the switch drain source is shown in
Figs. 9
(d) and
10
(d). The measured efficiencies of the proposed converter and flyback converter are compared in
Fig. 11
. We observe that efficiency is improved in the proposed converter. The measured power factor and THD
_{i}
are shown in
Fig. 12
. The measured power factor is higher than 0.96, whereas the measured THD
_{i}
is lower than 5.8%.
Control circuit of the proposed converter.
Experimental waveforms at 115–V_{rms} line voltage: (a) e_{s} and i_{s}, (b) i_{N}_{1} and i_{N}_{2}, (c) i_{L}_{1} and i_{Do}, (d) v_{S}_{1}.
Experimental waveforms at 230–V_{rms} line voltage: (a) e_{s} and i_{s}, (b) i_{N}_{1} and i_{N}_{2}, (c) i_{L}_{1} and i_{Do}, (d) v_{S}_{1}
Measured efficiency for the proposed converter and conventional flyback converter.
Measured results: (a) power factor and (b) THD_{i}.
VI. CONCLUSIONS
The forward and flyback PFC AC–DC converters are efficient choices for electrical isolation because of their simple structure. However, the forward AC–DC converter cannot achieve high power factor and low THD
_{i}
. Additionally, this converter requires a third winding to recycle transformer magnetizing inductor energy. The flyback AC–DC converter can achieve high power factor and low THD
_{i}
. Nevertheless, the transformer leakage inductor results in low efficiency. Therefore, we present a singlephase AC–DC converter that has a simple structure and is operated in DCM to achieve high power factor and low THD
_{i}
. A steadystate analysis is conducted. We implement a hardware circuit with simple control logic in the laboratory. The experimental results reveal the performance of the converters. The measured efficiencies reveal that the proposed converter exhibited higher efficiency than the conventional flyback converter.
Acknowledgements
The authors gratefully acknowledge the financial support from the National Science Council of Taiwan under project NSC 1022221E269010.
BIO
ChiaChing Lin was born in Taiwan, R.O.C., in 1959. He graduated from the Department of Electrical Engineering , Far East University, in 1980. He received his M.S. degree in Electrical Engineering from National ChengKung University in 2006. He is currently with the Department of Electrical Engineering, Far East University, Tainan, where he is an Assistant Professor. His research interests are power factor correction and dcdc converters..
LungSheng Yang was born in Taiwan, R.O.C., in 1967. He received his B.S. degree in Electrical Engineering from National Taiwan Institute of Technology, Taiwan, his M.S. degree in Electrical Engineering from National TsingHua University, Taiwan, and his Ph.D degree in Electrical Engineering from National ChengKung University in 1990, 1992, and 2007, respectively. He is currently with the Department of Electrical Engineering, Far East University, Tainan, where he is an Assistant Professor. His research interests are power factor correction, dcdc converters, renewable energy conversion, and electronic ballasts.
RenJun Zheng was born in Taiwan, R.O.C., in 1987. He received his B.S. and M.S. degrees from the , and 2007, respectively. He is currently with the Department of Electrical Engineering, Far East University, in 2011 and 2013, respectively. His research interests include power factor correction converter and electronic ballasts.
Tahami F.
,
Poshtkouhi S.
,
Ahmadian H. M.
2011
“Piecewise affine control design for power factor correction rectifiers,”
Journal of Power Electronics
11
(3)
327 
334
DOI : 10.6113/JPE.2011.11.3.327
Yao K.
,
Ruan X.
,
Mao X.
,
Ye Z.
2012
“Reducing storage capacitor of a DCM boost PFC converter,”
IEEE Trans. Power Electron.
27
(1)
151 
160
DOI : 10.1109/TPEL.2011.2105507
Wang J. M.
,
Wu S. T.
,
Jiang Y.
,
Chiu H. J.
2011
“A dualmode controller for the boost PFC converter,”
IEEE Trans. Ind. Electron.
58
(1)
369 
372
DOI : 10.1109/TIE.2010.2051391
Kimy Y. C.
,
Jin L.
,
Lee J.
,
Choi J.
2010
“Direct digital control of singlephase AC/DC PWM converter system,”
Journal of Power Electronics
10
(5)
518 
527
DOI : 10.6113/JPE.2010.10.5.518
Alonso J. M.
,
Costa M. A. D.
,
Ordiz C.
2008
“Integrated buckflyback converter as a highpowerfactor offline power supply,”
IEEE Trans. Ind. Electron.
55
(3)
1090 
1100
DOI : 10.1109/TIE.2007.908530
Itoh R.
,
Ishizaka K.
,
Oishi H.
,
Okada H.
1999
“Singlephase buck rectifier employing voltagereversal circuit for sinusoidal input current waveshaping,”
IEE Electr. Power Appl.
146
(6)
707 
712
DOI : 10.1049/ipepa:19990469
Cheng H. L.
,
Hsieh Y. C.
,
Lin C. S.
2011
“A novel single stage highpowerfactor AC/DC converter featuring high circuit efficiency,”
IEEE Trans. Ind. Electron.
58
(2)
524 
532
DOI : 10.1109/TIE.2010.2047825
Andersen G. K.
,
Blaabjerg F.
2006
“Current programmed control of a singlephase twoswitch buckboost power factor correction circuit,“
IEEE Trans. Ind. Electron.
53
(1)
263 
271
DOI : 10.1109/TIE.2005.862252
Alonso J. M.
,
Vina J.
,
Vaquero D. G.
,
Martinez G.
,
Osorio R.
2012
“Analysis and design of the integrated double buckboost converter as a highpowerfactor driver for powerLED lamps,“
IEEE Trans. Ind. Electron.
59
(4)
1689 
1697
DOI : 10.1109/TIE.2011.2109342
Fardoun A. A.
,
Ismail E. H.
,
Sabzali A. J.
,
AlSaffar M. A.
2012
“New efficient bridgeless Cuk rectifiers for PFC applications,”
IEEE Trans. Power Electron.
27
(7)
3292 
3301
DOI : 10.1109/TPEL.2011.2182662
Ismail E. H.
2009
“Bridgeless SEPIC rectifier with unity power factor and reduced conduction losses,”
IEEE Trans. Ind. Electron.
56
(4)
1147 
1157
DOI : 10.1109/TIE.2008.2007552
Mahdavi M.
,
Farzanehfard H.
2011
“Bridgeless SEPIC PFC rectifier with reduced components and conduction losses,”
IEEE Trans. Ind. Electron.
58
(9)
4153 
4160
DOI : 10.1109/TIE.2010.2095393
Zhang H.
,
Zhang Y.
,
Ma X.
2012
“Distortion behavior analysis of general pulsewidth modulated zeta PFC converter operating in continuous conduction mode,”
IEEE Trans. Power Electron.
27
(10)
4212 
4223
DOI : 10.1109/TPEL.2012.2191161
Chang L. K.
,
Liu H. F.
2005
“A novel forward AC/DC converter with input current shaping and fast output voltage regulation via reset winding,”
IEEE Trans. Ind. Electron.
52
(1)
125 
131
DOI : 10.1109/TIE.2004.841103
Nagao M.
2000
“A novel onestage forwardtype power factor correction circuit,”
IEEE Trans. Power Electron.
15
(1)
103 
110
DOI : 10.1109/63.817368
Daniele M.
,
Jain P. K.
,
Joos G.
1999
“A singlestage power factor corrected AC/DC converter,”
IEEE Trans. Power Electron.
14
(6)
1046 
1055
DOI : 10.1109/63.803398
Singh B.
,
Chaturvedi G. D.
2007
“Analysis, design and development of a single switch Flyback buckboost ACDC converter for low power battery charging applications,”
Journal of Power Electronics
7
(4)
318 
327
Zhang J.
,
Lu D. D. C.
,
Sun T.
2010
“Flybackbased single stage powerfactorcorrection scheme with timemultiplexing control,”
IEEE Trans. Ind. Electron.
57
(3)
1041 
1049
DOI : 10.1109/TIE.2009.2028336
Lazaro A.
,
Barrado A.
,
Sanz M.
,
Salas V.
,
Olias E.
2007
“New power factor correction ACDC converter with reduced storage capacitor voltage,”
IEEE Trans. Ind. Electron.
54
(1)
384 
397
DOI : 10.1109/TIE.2006.888795
Siu K. W.
,
Lee Y. S.
2000
“A novel highefficiency flyback powerfactorcorrection circuit with regenerative clamping and soft switching,”
IEEE Trans. Circuits Syst. I, Fundam. Theory Appl.
47
(3)
350 
356
DOI : 10.1109/81.841917
Papanikolaou N. P.
,
Tatakis E. C.
2004
“Active voltage clamp in flyback converters operating in CCM mode under wide load variation,”
IEEE Trans. Ind. Electron.
51
(3)
632 
640
DOI : 10.1109/TIE.2004.825342