Design Criteria for Sepic and Cuk Converters
as Power Factor Preregulators in
Discontinuous Conduction Mode
D.S.L. Simonetti, J. Sebastiin, F. S. dos Reis and J. Uceda *
Division de Electronica - E.T.S.I. Industriales
Universidad Politecnica de Madrid
c/ Jose Gutierrez Abascal, 2 - 28006 - Madrid - Spain
Phone: (0341) 4117517
FAX: (0341) 5645966
ABSTRACT
There are two major approaches in implementing control
circuits in PFP: the multiplier approach and the voltage-follower
approach.
The multiplier approach is used when the converter is operating
in continuous conduction mode. In this case, there are two control
loops: one, controls the output voltage; the other, controls the input
current. To provide output voltage regulation, a multiplier circuit
is used to control the amplitude of the sinusoidal current reference
signal in accordance with the output voltage error (Figura 1.a).
Power Factor Preregulators (PFP) have been used to improve
input current waveform of off-line power supplies. There are two
major approaches in implementing control circuits in PFP: the
multiplier approach and the voltage-follower approach. The
simplest one is the voltage-follower approach because the converter
operates in discontinuous conduction mode (DCM), and only one
loop control is required. SEPIC and CUK converters present a
great advantage over boost and fly-back topologies in DCM: an
input current with low harmonic content can be obtained by
correctly choosing inductors L, and L, of the converter with a fixed
operation frequency, as is demonstrated here. Also some discussion
about the intermedium capacitor C, as well some advantages and
disadvantages of the aplication is done. Simulation and
experimental results support the approach. Therefore, SEPIC and
CUK converters in DCM seem to be good choices to use as PFP.
a)
1. INTRODUCTION
Conventional off-line power supply usually include at its input
a full-bridge rectifier and a large input filter capacitor, which
produces a high level of harmonic distortion on the line and
excesive peak input currents, leading to a bad power factor.
Recently, this problem has been overcome by using a Power
Factor Preregulator (PFP), which draws a sinusoidal-current at the
input of converters [l-71. In general, boost, buck-boost (flyback),
SEPIC or CUK converters can be used as PFP. In Table I, the
advantages and disadvantages can be seen of each one. Despite its
problems, the most popular topology used as PFP is the boost
converter. Although, SEPIC and CUK converter present several
important advantages to be used as PFP.
I
I
I
1
Figure 1 . Control Circults in PFP (a) multiplier approach;
(b) Voltage-follower approach
In voltage-follower approach the converter operates in
discontinuous conduction mode, where the on-time of the switched
converter is controlled by the output voltage error signal (Figure
1.b). As the average value of the input inductor current in a
switching period is determined by the input voltage, this current
naturally fol~ows the sinusoidal line voltage waveform. The
voltage-follower approach provides a simple control scheme,
loop'
requiring Only One
Using boost or buck-boost converter as PFP in discontinuous
conduction mode requires an input filter, C,, because a large
Table 1. Characteristics of converters for PFP
- Domingos S . L. Simonetti is a professor at the Departament of Electrical
Engineering, Universidade Federal do Espinto Santo, Brazil. Femando S . dos
Reis is a professor at the Department of Electronics, Pontificia Universidade
Cat6lica do R.G.do Sul, Brazil. Both are perforaling their doctoral course at
Universidad Politknica de Madrid with a scholarship from the Brazilian Agency
CAPES.
283
0-7803-0582-5 /92$3.0001992 IEFE
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v2
.
harmonic content is present. Besides, when using boost converter
in voltage-follower approach its input current is distorted [8].
As shown in [9], SEPIC converter [lo] in discontinuous
conduction mode (DCM) presents an input current with a
"sinusoidal dc level", under constant duty cycle, not requiring input
filter. This is because the discontinuity is present at the output, and
not at input. In this paper, design criteria for applying SEPIC and
CUK converter as PFP-voltage-follower approach will be studied,
demonstrating their advantages.
'm1 =
d2Vg
rvg = K.r
(8)
Where i,, is the average input current in a switching period.
Substituting equations (4), (5) and (7) in (8):
d 2 Vglsino tl
zln1 =
2 Kasin2 t
2. STUDY OF SEPIC AND CUK CONVERTERS IN DCM AS
PFP
.
~
R
2sinzot
2.1. SEPIC Converter
The basic structure of the SEPIC converter with a transformer
is shown in figure 2. Applying volt-second balance to the converter
in DCM we obtain:
Equation (9) shows that the SEPIC converter when operating in
DCM as PFP and with constants switching frequency and duty
cycle presents an averaged input current in a switching period
proportional to the input voltage. Therefore, SEPIC converter is
indicated to operate as PFP in "voltage follower approach". The
duty cycle is obtained by [9]:
Where:
(3)
Where M is the voltage relation in DCM; d is the duty cycle
(transistor on); d' is related to the time diode is on; and T, is the
switching period.
To operate in DCM, K, must verify [l 11:
The input current, in a switching period, can be drawn as in
K
=
(5)
2K, sin'ot
IO
-
i
_
t
The load r "seen" by the converter is:
r = - R
2sinzot
(7)
TS
Considering unity power factor, we have the following power
balance equation in a switching period (switching frequency is
assumed much greater than line frequency):
Pi, = Po,,
.
=)
V*'lml =
Figure 3. Input current (i,,) and iL,, in a switching period.
Normally a PFP contains a rectifier at the input; therefore the
design of a converter which allows I,, < 0 means distortion at the
input current. From figure 3, writing the average current &,,:
-P
r
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To guarantee I, > 0 in the CUK converter:
iml = Io + vsdTs (d + d')
2Ll
d
L, >
- ndlsinotl
-~
L
2
M
nM
From (9), (17) and (19) we can obtain the desired relation
between average current and ripple current in a switching period:
(3), (9) and (14) in (13):
To guarantee I, > 0:
L
'
nL
>z
M
The equation (16) is the limit condition that equation (9) is
valid. The ripple current i, (figure 3) is:
Using (3), (9) and (17), the desired relation between average
current and ripple current in a switching period can be obtained:
The same comment made to equation (18) is valid to equation
(22). Using equations (6), (lo), (12) and (22) inductor L, and L,
are designed for CUK converter as PFP in DCM.
2.3. Some comements about the intermedium capacitor C,
In conventional CUK and SEPIC converters, the capacitor C, is
assumed to have a constant voltage. When operating as PFP, the
capacitor voltage has two constraints: to have a nearly constant
value in a switching period; and follows the input voltage in a line
period. Its value has a great influence in the input current
waveform. The resonant frequency of C,, L, and
must be much
greater than line frequency, to avoid input current oscilations each
half cycle. Besides, if the resonant frequency is near the switching
frequency, the characteristic of good power factor is lost achieving
distorted waveforms. As a general rule, we can use:
As the relation of equation (18) is an inverse fuction of the duty
cycle, some applications can require to calculate it for minimum
load.
Using equations (6), (IO), (12) and (18), we can design
inductors L, and
for SEPIC converter as PFP in DCM.
where component values are referred to primary side and 2, = 2 ~ f .
From (23) we can choose an initial value for capacitor C, and,
by simulation, to adjust it to obtain a better response.
2.2. CUK Converter
2.4.
Figure 4 shows the CUK converter with an isolation transformer
[12]. The operation in DCM without transformer can be seen in
When operating with a little ripple, the current of input diodes
and inductor L, are easily aproximated. To the input diodes:
Some comments about other components
~31.
Ll
Ca
Cll
12
Figure 4. CUK converter with an isolation transformer.
Equations (1-2) and (4-14) are the same for SEPIC and CUK
converter, as well as figure 3. For CUK converter, the equivalent
inductance is:
Le*
=
L, L2
n2L, + L~
To the inductor L,:
4%
ZL,w =
'8
(9). (14) and (19) in (13):
The turn-on of the switch is with zero-current, but the turn-off
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is dissipative. The maximum current and voltage are:
Using K, = 0,05 and from equations (3), (6) and (10):
=
Vs-
d = 0,632
v, + v,
(31)
At the turn-off of the switch spikes can be present.
L, = 75 p H
The output diode presents a dissipative turn-on, and non
dissipative turn-off. The maximum value of current and voltage
L, = 150pH
are:
From (23), choosing a resonant frequency about 5 KHz:
C, = 4,7pF
VD.3,
=
v, + v,
=
"Smax
A simulation using Analog Workbench was performed for this
situation. In figure 5.a the line current during a line cycle is
shown, and in figure 5.b a detail at maximum current can be seen,
demonstrating the operation at discontinuity limit.
(33)
The peak-to-peak current is high. The average current is:
............................................
...........................
Also the inductor L, presents a high peak-to-peak current value.
Its maximum and minimum current values are:
............ .A..?&&..
(35)
..........
.___
..........................
rms mi-142 3 . 2 4 a
.......................................
a)
4
The equations were derived for non-isolated converters, and
must be adapted if a transformer is used. Other values of current
and voltage in the components can be obtained by simulation.
3. DESIGN EXAMPLE AND SIMULATION RESULTS
I,"
As an example, a SEPIC converter with the following
characteristics will be designed:
v, = 50 sin 2aft V
f = 50 Hz
v = 1oov
P o = l W W ( R = loon)
fs = 50 KHz, T, = 20 ps
n = l
3
Mal"
. . .
Figure 5. (a) Input current with limit condition of DCM; @) A
detail.
Another simulation is performed considering K, = 0,02. From
(6) and (10):
To operate in DCM, we must have (equation 12):
L,
=
20 pH
d = 0,4
Using a relation of 0 , l in equation (18) (considering nominal
load):
3.1. Analysis of inductors' influence
First, will be used the limit condition (16):
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L, = 1 mH
L, = 20,4 pH
resonant frequency of 10 KHz, C, = 0,22 pF, and a distorted
input current is obtained (figure 7.b)
Choosing a resonant frequency about 2500 Hz:
C, = 3,9 p F
The input current is shown in figure 6.a, and a detail at
maximum current is shown in figure 6.b, where can be seen the
ripple obtained as well the operation in DCM. The good frequency
spectrum can be seen in figure 6.c. The power factor obtained by
simulation is > 0.99.
2 4/dl"
a)
I-
I
11"
h)
I
'
I
J
l
'
1 ~
10 m
[
'
1
~
1
'
1
~
15m
'I I ' ~I
~
' I
'
I
'
I
~
I
'
I
~
20m
9
x
AX?-:
me
A
m
I l -b-I
Figure 7. Influence of capacitor C, (a) w , = 500 Hz, C ,
(b) w , = 10 KHz, C , = 0 2 2 pF
= m ms
=
100 pF;
4. EXPERIMENTAL RESULTS
1. 1.
..I.
....
. .....
. ..
.
......
. .
1 A/div
. ..
.
,
M l 4.11
..
. ~..
.
.
The situation simulated and shown in figure 6 was
experimentally performed. As there are losses in the components,
the duty cycle was adjusted to obtain nominal output voltage. Good
results were achieved, as can be seen in figure 8, where input
current and voltage (a), output voltage (b) and a detail of the
operation in DCM (c) are shown.
A
.
5. CONCLUSIONS
C)
X
11Il1~
100
Rx19: F r e o
I
I IIIII//
I
I I H I I I
fit 50
H7
I
10K
1K
Ilw
at - 2
I
lllllll
KH,
I I h
=
I I I
1
100K
SEPIC and CUK converters operating in voltage-follower
approach (discontinuous conduction mode) have advantages over
other converters that are used as Power Factor Preregulators. By
correctly choosing inductors L, and L, (considering the current
ripple) and capacitor C, (considering frequencies involved in the
converter), a line current with little harmonic content can be
achieved, in steady-state.
Comparing SEPIC and CUK converters with boost and fly-back
converters in discontinuous conduction mode as PFP, a good
current waveform is achieved without an input filter. In addition,
comparing them with converters as PFP in continuous conduction
mode, similar current waveform is obtained with only one control
loop (operation in CCM requires two control loops).
Some disadvantages can be found in the comparison. For
example, a greater number of components, with a high peak-topeak current in the indutor L, and capacitor C,. Nevertheless, a
HZ
RI9 I
KHL
3.2. Analysis of capacitor's influence
In the simulations made above, a good choice of capacitor C,
was made. Now, will be shown two other situations, both
considering the second simulation performed.
If we choose a resonant frequency of 500 Hz, we have C, =
100 pF. In figure 7.a the input current for this situation is shown,
where the transitory response obtained can be seen. Choosing a
287
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I
'
I
~
U
__
-
1
[51
M. ALBACH, "An ac-to-dc Converter with Low Mains Current
Distortion and Minimized Conducted Emissions", EPE 1989, pp.
457-460.
161
C. P. HENZE and N. MOHAN. "A Digitally Controlled ac-todc
Power Conditioner that Draws Sinusoidal Input Current", IEEE
PESC 1986. pp. 531-537.
[7]
C. A. CANESIN and I. BARBI, "A Unity Power Factor Multiple
Isolated Outputs Switching Mode Power Supply Using a Single
Switch", lEEE APEC 1991, pp. 430-436.
[8]
K. H. LIU and Y. L. LIN, "Current Waveform Distortion in
Power Factor Correction Circuits Employing Discontinuous
Mode Boost Converter", lEEE PESC 1989, pp. 825-829.
[9]
J . SEBASTIAN, J. UCEDA, J. A. COBOS, J. ARAU and F.
ALDANA, "Improving Power Factor Correction in Distributed
Power Supply Systems Using PWM and ZCS-QR SEPIC
Topologies", lEEE PESC 1991, pp. 780-791.
20 V/di.v
level 50 V
f
T
f
I
[lo]
R. P. MASSEY and E. C. SNYDER, "High Voltage
Single-Ended DC-DC Converter", lEEE PESC 1977, pp.
156-159.
[ll]
J. SEBASTIAN, J. A. COBOS, P. GIL and J. UCEDA, "The
Determination of the Boundaries between Continuous and
Discontinuous Conduction Modes in PWM dc-todc Converters
Used as Power Factor Preregulators", lEEE PESC 1992, pp.
1061 - 1070.
[12]
R.D. MIDDLEBROOK and S. CUK, "Isolation and Multiple
Output Extensions of a New Optimum Topology Switching DCto-DC converter", IEEE PESC 1978, pp. 256-264.
[I31
S. CUK, "Discontinuous Inductor Current Mode in the Optimum
Topology Switching Converter", lEEE PESC 1978, pp. 105-123.
I
1
f
level 2 A
i
Figure 8. Experimental results (a) input current and voltage; (b) Output voltage;
(c) A detail at maximum current.
good design and implementation can overcome these problems.
As shown by simulation and experimentation, the described
approach to design inductors L,,
and capacitor C,, in DCM, is
valid. Besides, the input current obtained is of high quality.
Therefore, SEPIC and CUK converters in DCM seem to be good
choices to use as PFP.
6. REFERENCES
M. J. KOCHER and R. L. STEIGERWALD, "An ac-to-dc
Converter with High Quality Input Waveforms", lEEE Trans. 1.
A., vol. IA-19, no 4, pp. 586-599, JulylAugust, 1983.
L. H. DIXON, "High Power Factor Preregulators for Off-line
Power Supplies", Unitrode Power Supply Design Seminar, pp.
6.1-6.16, 1988.
I. BARBI and S.A.O. da SILVA, "Sinusoidal Line Current
Rectification at Unity Power Factor with Boost Quasi-Resonant
Converters", lEEE APEC 1993, pp. 553-562.
C. ZHOV, R. B. RIDLEY and F. C. LEE, "Design and Analysis
of a Histerestic Boost Power Factor Correction Circuit", lEEE
PESC 19p0, pp. 800-807.
288
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