Input Current Distortion of CCM Boost PFC Converters Operated in DCM
K. De Gussem´e
, D.M. Van de Sype, A.P. Van den Bossche and J.A. Melkebeek
Electrical Energy Laboratory
Department of Electrical Energy, Systems and Automation, Ghent University
Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium
E-mail: koen.degusseme@rug.ac.be
Abstract— Power factor correction (PFC) converters for the
higher power range are commonly designed for continuous
conduction mode (CCM). Nevertheless, operation in the discon-
tinuous conduction mode (DCM) occurs for light load in a zone,
close to the crossover of the line voltage. This zone will gradually
expand with decreasing load to finally encompass the entire line
cycle. Whereas in CCM the parasitic capacitances of the switches
only cause switching losses, in DCM they are a source of converter
instability, resulting in significant input current distortion. In this
paper, this source of input current distortion is analyzed and a
solution is proposed. Experimental results are obtained using a
digitally controlled boost PFC converter, designed to operate in
CCM for 1kW.
I. INTRODUCTION
For single phase power factor correction (PFC) converters,
two main approaches are followed for the converter and control
design. For low power applications, PFC converters are often
operated in the discontinuous conduction mode (DCM) as they
behave more or less as voltage followers [1]–[3]. As a result,
no input current controller is required. On the other hand,
higher power applications ask for operation in the continuous
conduction mode (CCM) [4]–[9], since in DCM the device
stresses and the conducted emissions become too high. An
input current controller is now required, since the input current
does not inherently track the input voltage.
For PFC, a boost converter is the most commonly employed
topology. It is shown in Fig. 1 together with its typical two-
loop control scheme. With this topology, a power factor near
unity can be achieved when operating in CCM. Nevertheless,
operation in DCM occurs for light load in a zone, close to
the crossover of the line voltage [10], [11]. This zone will
gradually expand with decreasing load to finally encompass
the entire line cycle. When this occurs, the input current
waveform is distorted due to the change in converter dynamics
[10]–[13] or to errors on the input current samples when digital
control is applied [11].
This paper deals with another cause of input current dis-
tortion, the influence of parasitic capacitances of the switches
on the converter waveforms in DCM. Whereas in CCM these
parasitic capacitances only cause switching losses, in DCM
they cause oscillations in the converter waveforms. When
input current control is applied, these oscillations may be a
source of converter instability, resulting in significant input
current distortion. This source of input current distortion will
be analyzed and some possible solutions will be discussed. The
Fig. 1. The boost PFC converter, together with its control loops.
Fig. 2. Black: Equivalent network for the boost converter when both diode
and switch
are blocked; Gray: snubber
theoretical analysis and a possible solution will be verified by
experimental results, using a digitally controlled boost PFC
converter, designed to operate in CCM at nominal power.
II. I
NFLUENCE OF PARASITIC CAPACITANCES ON THE
BOOST CONVERTER WAVEFORMS
In this section, after a short study of the waveforms of a
boost converter in the case of ideal switches, the effect of
the parasitic capacitances of the switches on the converter
16850-7803-7754-0/03/$17.00 ©2003 IEEE
Fig. 3. Theoretical inductor current and switch voltage in DCM, high input
voltage, black: ideal switches, gray: real switches
waveforms will be discussed. The converter is shown in Fig. 1,
together with its control scheme, typically used for PFC.
A. Converter waveforms for ideal switches
In continuous conduction mode, the switch voltage
(Fig. 1) is either zero or equal to the output voltage
,
corresponding to a closed or open switch S, respectively. As
a result, the voltage across the inductor
will be alternately
positive and negative, leading to a triangular inductor current
waveform.
At reduced load, the inductor current may become zero
before the end of the switching period (at
, Figs. 3 and
4, gray traces), resulting in discontinuous conduction mode.
Assuming that both switch
and diode
are ideal, the switch
voltage
adopts the value of the input voltage
as soon as
the inductor current
reaches zero. During the remainder of
the switching period ([
,
]), the switch voltage and the input
voltage are equal while the inductor current is zero (Figs. 3
and 4).
B. Converter waveforms for real switches, high input voltage
For most applications in this power range,
MOSFETs or
IGBTs are employed as switching devices. One of their inher-
ent parasitic elements, which has an important influence on the
waveforms in DCM, is the output capacitance
(
for
MOSFETs,
for IGBTs). The value of this capacitance is
not only dependent on the type and the rating of the switch, but
is also a non-linear function of the switch voltage
. Another
component whose parasitic capacitance causes similar effects
is the output diode
. Its parasitic capacitance
is generally
lower than the parasitic capacitance
of the switch.
At the instant
, where the inductor current reaches zero
in DCM, the converter can be represented by the network of
Fig. 2 (black lines), with as initial conditions:
"!#$%'&
,
(!#)
and
*!,+
A. As the voltages across the capacitances
of this circuit are not in equilibrium, this results in oscillation.
Fig. 4. Theoretical inductor current and switch voltage in DCM, low input
voltage, black: ideal switches, gray: real switches
If the input capacitor
-
has a small value compared to
the capacitances
and
-
, the switch voltage remains
at
)
during [
,
] and the input voltage oscillation can be
approximated by:
(!.)-/.01)2/3$%'&'4576890;:<>= ?@01A/3B44DC
(1)
with
:AE>= F
the angular frequency of the oscillation. Note that
the input voltage may become twice as high as the output
voltage for low
>$%'&
, leading to a high voltage stress across
the bridge rectifier diodes (Fig. 1). Therefore, the capacitance
value of the input capacitance
-
is chosen to be at least an
order of magnitude larger than the combined capacitance of
and
-
.
If
2
is much larger than
and
-
, the input voltage
is constant and equal to
>$%'&
. Hence, the oscillation in
the interval [
,
] is dominated by the inductor
and the
capacitances
G
and
. Assuming that
G
and
are
linear capacitances, the switch voltage
and inductor current
can be approximated by (Fig. 3):
H014I!#$%'&J,01)-/3$%'&'4576890;:<K01A/3B44
(2)
014I!L/
)2/3$%'&
M
8N OP0;:<K01A/3B44KC
(3)
with
:<Q!
R
S
T2 U
O@V
M
Q!
W
22X
(4)
The capacitance
-
in these expressions is equal to the
parallel connection of the switch capacitance and the diode
capacitance. The natural impedance
M
is much larger than
the parasitic resistances of the network, so the oscillation will
be hardly attenuated. The oscillation is ended when the switch
is turned on again (
). For low duty-ratios, this interval may
take several oscillation cycles.
1686
Fig. 5. Positive duty-ratio step, yielding a positive input current step
C. Converter waveforms for real switches, low input voltage
The converter waveforms in the case of low values of the
input voltage
>
, are presented in Fig. 4. In (2), the switch
voltage
, will exhibit negative values if the input voltage is
lower than half the output voltage. If no reverse diode
Y$Z
(Fig. 2) is integrated in the converter circuit, this may cause
a breakdown of the switching device. Therefore, a reverse
diode should be integrated in the circuit if the switch cannot
withstand negative voltages and if it does not contain one
intrinsically.
If a reverse diode is present and for a large input capacitor
2
, at
the switch voltage swings down to
+
V as
> \[
F
)
(2) (a non-linear capacitance results in a different condition).
From this moment awards, the switch voltage will be clamped
to zero, allowing the energy stored in the inductor
to flow
to the input capacitor
-
. As a result, the input voltage
will rise until the current becomes positive again (
]
).
The value of the input voltage at this instant is not equal to
the rectified voltage
>$%'&
, as the energy stored in the input
capacitor
2
and the combined parasitic capacitance
G
at
is now completely stored in the input capacitor
G
at
]
.
The resulting input voltage can be calculated using an energy
balance
R
^
2
!
R
^
2 )
$%'&
J
R
^
2
C
(5)
yielding
"!
W
$%'&
J
2
X
(6)
The non-linearity of the switch and diode capacitances can
be expressed by replacing the second term in the right hand
side of (5) by the total energy stored in the switch and output
diode capacitances at the instant
. The resulting increase of
the input voltage is important for low values of the line voltage
only, since the second term in the right hand side of (5) is not
depending on the input voltage.
Fig. 6. Positive duty-ratio step, yielding a negative input current step
An oscillation is now initiated at
]
, which is ended at
the start of the on-time of the next switching period (
).
Assuming a linear switch capacitance
, the switch voltage
and inductor current can be approximated
Y!. _
R
/`5768901:<K01A/3]a44b
(7)
*!
M
8N OP0;:<K01A/3]a44KC
(8)
which means that the switch voltage will oscillate between
+
V
and twice the value of the input voltage
at the instant
]
.
In (7) and (8),
:I
and
M
are given by expression (4). Due
to the non-linearity of the switch and diode capacitances, the
oscillation will not be sinusoidal (see Fig. 4).
III. C
ONSEQUENCES FOR AVERAGED INPUT CURRENT
WAVEFORMS
While in the previous section, the converter waveforms for
a boost converter operated in DCM with a constant duty-
ratio and constant rectifier voltage were discussed, in this
section, the consequences of these waveforms, on the averaged
input current waveforms of a boost converter, operated as PFC
converter, are studied.
In the case of ideal switches, the input current averaged
over one switching cycle is proportional to the square of the
duty-ratio for DCM [11],
c
>dI!
^
fe
)
)2/3 `ehg
hi
C
(9)
so an increase of the duty-ratio will cause an increase of
the input current, while a lower duty-ratio will lead to a
lower averaged input current. Nevertheless, in the case of real
switches, a positive step in the duty-ratio does not inherently
lead to a positive step in the inductor current
j
. After all,
though a step
k
g
leads to an increase in inductor current
(Fig. 5), a different step
k
g
F
can result in a lower inductor
current (Fig. 6). Consequently, the gain of the duty-ratio-to-
input-current transfer function is depending on the magnitude
of the step in the duty-ratio, and, due to the parasitic nature
1687
10us/divCH3=500mA
CH4=200V
Fig. 7. Input current (upper trace) and switch voltage (lower trace) for high
input voltage, experimental results
of the oscillation, unpredictable. Moreover, this gain can be
both positive or negative at every moment, depending on the
instantaneous value of the input current at the beginning of
the on-time of the switch. This effect results in unpredictable
inductor current behavior, causing inductor current loop insta-
bility and, as a result, input current distortion.
On the other hand, the variation of the input voltage can also
result in averaged input current distortion, even when the duty-
ratio remains constant (voltage follower operation), or varies
very slowly (due to a low current controller gain). The reason
is that the fraction of the switching cycle where the inductor
current flows,
0
g
J
gal
4
, not only depends on the duty-ratio,
but also on the input voltage [11]
g
J
gml
!
g
)014
)n014A/3 H014X
(10)
As a result, the length of the time interval [
,
] will vary
as a function of the input voltage, and consequently, the
phase of the oscillation at the start of the on-time of the next
switching cycle (
) will change during a grid cycle. Hence,
the oscillation during the switch off-time in DCM may cause
severe distortion in the averaged input current waveform.
IV. P
OSSIBLE SOLUTIONS
In section III. the effect of the input current oscillation on
the averaged input current waveform and the input current
control loop stability has been demonstrated. As the average
input current depends strongly on the instantaneous input
current at the beginning of the on-time of the transistor, any
solution, resulting in a lower amplitude of the oscillation
of the inductor current, will diminish this effect. Expression
(3) reveals that this amplitude can be reduced by choosing
switches, switch
and diode
, with a low parasitic capac-
itance, yielding a minimal value of
oE
. To achieve this, a
switch should be chosen which is as small as the application
allows, since the switch output capacitance is closely related
to the maximum switch current for a given switch type. As
the converter is designed for CCM operation at a higher power
10us/divCH3=500mA
CH4=200V
Fig. 8. Input current (upper trace) and switch voltage (lower trace) for low
input voltage, experimental results
level, demanding a high input current, large switching devices
are needed. Since the parasitic capacitance of a switch is
proportional to its current rating, this reduction is limited.
Another possibility to reduce the amplitude of the oscillation
is to add a snubber. Among the numerous possible topologies
for snubbers, a simple resistive snubber is chosen to demon-
strate the principle (Fig. 2, gray lines). The capacitance value
of the snubber capacitor must be chosen large enough to in-
fluence the oscillation, which means larger than the combined
capacitance of the switch and diode parasitic capacitances. On
the other hand, the switching losses, in DCM as well as in
CCM, will increase drastically when the snubber capacitance
is chosen too large. When adding the snubber to the circuit,
the energy of the oscillation will now be dissipated in the
resistor, causing the amplitude of the input current oscillation
to fall quickly. As a result, in most cases the inductor current
will be zero when the switch starts conducting again, so
the input current will not be distorted. Nevertheless, the first
negative peak in the inductor current is hardly attenuated by
the snubber. Consequently, some input current distortion will
exist near border mode operation.
V. E
XPERIMENTAL RESULTS
For the experimental verification of the waveforms obtained
in previous sections, a 1kW boost PFC converter (Fig. 1) with
following characteristics has been used
prq)s
!
^ut
+uv*Cxw
s
!zyu+n{-|uC}wn~3!zyu+u{-|
q
!#+n+uv*C!#a+u9TC!
Rh
{
(11)
This converter operates in DCM during the entire line cycle
when it is operated at
>
W input power or lower [11]. The
switch employed is an IRF
u+
MOSFET and the output diode
is a RURP
t
+nn+
.
In Fig. 7, the instantaneous input voltage is near
^
+n+
V,
which gives large oscillations of the switch voltage. The
oscillation is nearly sinusoidal as the switch output capacitance
is quite linear in this voltage range. At low input voltage (
^
V
for Fig. 8), the switch voltage will reach
+
V, so the oscillation
1688
10us/divCH4=200mA
Fig. 9. Input current waveform without snubber
10us/divCH4=200mA
Fig. 10. Input current waveform with snubber
is not sinusoidal anymore, as the switch output capacitance
changes drastically in this range. The period where the switch
voltage is clamped to zero, is also observed in Fig. 8.
In Figs. 9 and 10, the detailed input current waveforms are
depicted for the converter without snubber and with snubber
respectively. While in the current in Fig. 9 fast changes are
observed, the input current in Fig. 10 exhibits only very
slow changes. For the influence of these oscillations on the
averaged input current waveforms, three different experiments
are performed. For the first experiment the regular CCM input
current controller is used. As the gain of the duty-ratio-to-
input-current in DCM is much lower than the gain in CCM,
the total loop gain is low, so the controller is too slow to
correct the input current oscillation. The resulting waveform
is shown in Fig. 11, displaying bulges where the on-time of
the switch starts with a positive input current and dips where
the on-time starts with a negative input current. In Fig. 12
the experiment is repeated for a converter with snubber. The
waveform is now smooth, although it is still not sinusoidal,
due to the low gain of the control loop. Therefore, the control
parameters are adapted to DCM operation. When no snubber
is applied, the loop becomes instable as the total loop gain is
now higher (Fig. 13). The input current now jumps from the
2ms/divCH1=200mA CH2=120V
Fig. 11. Input current (black) and input voltage (gray) waveforms without
snubber, controller designed for CCM
2ms/divCH1=200mA
CH2=120V
Fig. 12. Input current (black) and input voltage (gray) waveforms with
snubber, controller designed for CCM
top of the input current oscillation to the lowest point and back
in only few switching cycles. The waveform for the converter
with snubber (Fig. 14), is nearly sinusoidal.
A final experiment was done to find the influence for control
algorithms where no input current controller is employed in
DCM, such as voltage follower operation [3]. When assuming
a large output capacitor, the output voltage can be assumed
to be nearly constant and the output voltage controller will
maintain a constant duty-ratio when operating at constant
output power. Nevertheless, an important amount of input
current distortion is observed in Fig. 15, as the instantaneous
input current at the beginning of the on-time of the switch is
varying periodically with the input voltage. Fig. 16 shows that
here again the use of a simple snubber can solve the problem.
VI.
CONCLUSION
When power factor correction converters designed for op-
eration in the continuous conduction mode, are operated at
reduced load, discontinuous conduction mode will appear
during part of the line cycle or even the entire line cycle. As
these converters are designed for CCM operation, they often
use an averaged input current controller. Due to the parasitic
capacitances of both the switch and the diode, the input
1689
