Critical conduction mode boost power factor correction converters operating at the boundary of continuous conduction mode and discontinuous conduction mode have been widely used for power applications lower than 300W. This paper proposes an enhanced variable ontime control method for the critical conduction mode boost PFC converter to improve the total harmonic distortion characteristic. The inductor current, which varies according to the input voltage, is analyzed in detail and the optimal ontime is obtained to minimize the total harmonic distortion with a digital controller using a TMS320F28335. The switch ontime varies according to the input voltage based on the computed optimal ontime. The performance of the proposed control method is verified by a 100W PFC converter. It is shown that the optimized ontime reduces the total harmonic distortion about 52% (from 10.48% to 5.5%) at 220V when compared to the variable ontime control method.
I. INTRODUCTION
Along with the remarkable developments in power electronics, the usage of nonlinear loads has drastically increased. The increase usage of nonlinear loads generates more harmonic current than in the past. The harmonic components of an input current are not involved in power transfer, but just circulate through transmission lines and increase the RMS value of the input current, which increases the conduction losses of the transmission lines and generates heat
[1]
. Because of these problems, international regulations on harmonic currents such as IEC6100032 have been established. To satisfy these regulations, ACDC converters should contain power factor correction (PFC) circuits as a preregulator.
For power applications less than 300W, a critical conduction mode (CRM) boost PFC converter has been widely used
[2]

[5]
. The main advantages of the CRM boost PFC converter, when compared to the continuous conduction mode (CCM) boost PFC converter, are that it has no reverse recovery problem in the diode and it is easy to achieve zero voltage switching (ZVS) or quasiZVS without auxiliary circuits. When compared to the discontinuous conduction mode (DCM) boost PFC converter, it has less current stresses on the active and passive components, and a smaller input filter.
The current mode control method has been widely used to control CRM boost PFC converters. The current mode control method senses the rectified line voltage and generates a current reference signal by multiplying the sensed information with the output voltage of the error amplifier
[6]
. Then the current reference signal is compared with the sensed inductor current information to make the peak inductor current follow the waveform of the rectified line voltage. This is the best way for the power factor correction, because the inductor current is directly controlled to follow the sinusoidal reference waveform. The most popular control IC using the current mode control for the CRM boost PFC converter is the L6561/2 from STMicroelectronics. However, many semiconductor companies have started developing control ICs using the voltage mode control method for CRM boost PFC converters to reduce both the external components and the power loss
[7]

[9]
. The voltage mode CRM PFC control IC compares a ramp signal with the output voltage of the error amplifier and then the switch ontime is controlled to be constant irrespective of the line voltage. Because the inductor current is zero when the switch is turned on, the peak inductor current is proportional to the rectified line voltage. Therefore, the line current can follow the line voltage waveform achieving a unity power factor. In addition, the voltage mode CRM PFC control IC does not need a multiplier to generate the sinusoidal reference that is necessary for the current mode control IC. Because of this benefit, the internal IC circuit is simpler and the external circuit design is easier than those of the current mode CRM PFC ICs. Therefore, many applications including LCD TVs and notebook adapters are using the voltage mode CRM PFC IC and the number of applications adopting the voltage mode CRM PFC IC is increasing.
The conventional control method of the voltage mode CRM boost PFC converter is a constant ontime (COT) control.
Fig. 1
shows a voltage mode CRM boost PFC converter circuit, which determines the switch turnoff instant by comparing the internal ramp signal and the output voltage of the error amplifier. Theoretically, the input current should follow the input line voltage waveform if the switch is turned on right after the inductor current reaches zero. However, there is some delay time before the switch is turned on because of the zero current detection (ZCD) circuit. The ZCD circuit is necessary to sense the instant that the inductor current reaches zero and an auxiliary winding coupled with the inductor is used for zero current detection. As shown in the waveforms of
Fig. 2
, the switch output capacitor (C
_{oss}
) starts to be discharged resonating with the inductor after the diode is turned off. Then, the auxiliary winding voltage drops starting from n·(V
_{o}
V
_{in}
). If this voltage is lower than the threshold voltage (V
_{ON}
_
_{ZCD}
), the switch is turned on. The ZCD circuit introduces some delay time before the switch is turned on after the inductor current reaches zero and this delay time can be controlled to achieve zero voltage switching (ZVS) or quasiZVS by using R
_{ZCD}
and C
_{ZCD}
as shown in
Fig. 1
. However, this delay time causes some distortion of the input line current. Several methods have been proposed to solve this problem
[6]
,
[10]

[16]
. However, some of these methods are empirical and one method is analytical. However, it cannot be applicable to wide input voltage applications.
Voltage mode CRM boost PFC converter circuit.
ZCD circuit related waveforms.
This paper first describes some of the existing methods in section II. Then, an enhanced variable ontime (eVOT) control method is proposed in section III. Unlike the conventional control methods, the proposed method computes the switch ontime by analyzing key waveforms of the CRM boost PFC converter. The switch ontime is derived from the computation for compensating the zerocrossing distortion and the input current shaping at every switching instant. The performance of the proposed method is verified with a 400V, 100W boost PFC rectifier controlled by a digital signal controller (DSC) in section IV. Section V provides some conclusions.
II. EXISTING CONTROL METHODS TO IMPROVE CURRENT DISTORTION
 A. Variable OnTime (VOT) Control Method
The CRM boost PFC converter circuit shown in
Fig. 1
is analyzed when the input voltage has a positive value. As the CRM boost PFC converter has a zerocrossing detection (ZCD) circuit to detect the turnon instant, the switching frequency of the CRM boost PFC converter is variable depending on the input voltage and the output power. The ZCD circuit is set when the inductor current is zero. A switch SW is turned on at every zerocrossing event and is turned off when the ramp signal meets the output voltage of the error amplifier. In the CRM boost PFC converter, the input current over a switching period is expressed as (1).
If the ontime of the switch,
t_{on}
, is constant, the input current follows the waveform of the input voltage as shown in (1).
This allows for a unity power factor with a sinusoidal input voltage. However, to achieve ZVS or quasiZVS, the turnon instant of the switch is delayed until the switch drainsource voltage reaches zero or valley to minimize the switching loss. Because the delay time is almost constant and the t
_{off}
shown in
Fig. 2
decreases as the input voltage decreases, the effect of the delay time is dominant around the zero crossing of the input voltage so that the THD of the input current can increase. A variable ontime control (VOT) method has been proposed to improve the THD of the input current by controlling the switch ontime as shown in
Fig. 3
[6]
. It simply adds a resistor R
_{2}
between the auxiliary winding and the MOT pin. The MOT pin is for setting the internal ramp slope to control the ontime. The voltage of the MOT pin, V
_{MOT}
, is constant and if a resistor R
_{1}
is used, an internal current source that is proportional to V
_{MOT}
/R
_{1}
charges an internal capacitor to make a ramp signal. Without R
_{2}
, the ramp slope is constant and the switch ontime is controlled to be constant. However, if R
_{2}
is used, (V
_{MOT}
V
_{AUX}
)/R
_{2}
current is added to V
_{MOT}
/R
_{1}
. Then, the internal ramp slope changes according to the input voltage because V
_{AUX}
is negatively proportional to the input voltage when the switch is turned on. The ramp signal generated by I
_{2}
varies according to the input voltage, and this signal is added to the constant ramp signal generated by I
_{1}
as shown in
Fig. 4
. The internal ramp signal consists of the constant ramp signal and a ramp signal that varies according to the input voltage as shown in (2).
Variable ontime CRM boost PFC converter.
Internal ramp signal of the VOT control method.
where, C
_{Ramp}
is the internal capacitor for ramp generation, and
n
is the turn ratio of the inductor.
As the input voltage decreases, the ontime increases from t
_{on1}
to t
_{on3}
. Therefore, t
_{on}
is at its maximum near the AC line zero crossing point and is at its minimum at the AC line peak point. This method is very simple and effective. However, R
_{2}
should be obtained based on experiments to find the value that minimizes the THD.
 B. Perturbation OnTime (POT) Control Method
Another variable ontime control method has been proposed as shown in
Fig. 5
[16]
. The inductor current information and the internal ramp signal are added to be compared with the output voltage of the error amplifier. This method is another implementation of
[6]
, because the inductor current information is proportional to the input voltage. In addition, the current limiting circuit might be triggered if too high a R
_{CS}
is used to improve the THD performance. This method is also empirical.
Perturbation ontime CRM boost PFC converter.
 C. Analytical OnTime Adjustment Scheme
There is an attempt to adjust the ontime analytically in
[14]
. This scheme senses the switch
v_{ds}
voltage to determine the ZVS instant. However, it cannot be applicable if the input voltage is higher than half of the output voltage, because the switch voltage does not become zero after the inductor current reaches zero. In addition, the analysis is performed only when the input voltage is lower than half of the output voltage.
III. PROPOSED CONTROL METHOD
Several methods have been proposed to improve the THD performance of the voltage mode CRM boost PFC converter but the methods are empirical and the analysis does not cover all the operating conditions as described in section II. In this section, a new control method is proposed based on an analysis of the input current.
 A. Analysis of the Input Current
An analysis of the inductor current is necessary to determine the variations of the switch ontime. The waveform of the inductor current during the ZCD delay time varies according to the rectified input voltage. If the rectified input voltage of the CRM boost PFC converter is higher than half of the output voltage
V_{o}
, the energy stored in the inductor when the current is negative is not sufficient to make the switch voltage
v_{ds}
zero. On the other hand, if the rectified input voltage of the CRM boost PFC converter is lower than half of the output voltage, the inductor is charged sufficiently so that the switch voltage drops to zero. This results in a difference in the waveform of the inductor current and the compensated ontime is determined by separate equations according to the magnitude of the input voltage.
Fig. 6
shows the waveforms of the switch gating signal, the inductor current
i_{L}
, the inductor voltage
v_{L}
, and the MOSFET drainsource voltage
v_{ds}
during one switching period, when
V_{in}
is higher than
V_{o}/2
. As shown in
Fig. 6
, the switch is turned on when the drainsource voltage reaches the valley by resonance between the switch parasitic capacitor and the boost inductor to achieve the minimum voltage switching. In this condition, the inductor current during one switching period is divided into three periods; the switch conduction period (t
_{0}
t
_{1}
), the diode conduction period (t
_{1}
t
_{2}
) and the LC resonance period (t
_{2}
t
_{3}
). The input current of the CRM boost PFC converter is equal to the average inductor current over one switching period. The average input current considering the delay time is expressed as (3).
Key waveforms when V_{in} > V_{o}/2.
where,
S_{neg1}
is the area of the inductor current for
t_{d1}
.
S_{neg1}
is obtained from the integral of the inductor current over a half of the resonance period after the inductor current has become zero.
S_{neg1}
is obtained by (4).
where,
t_{d1}
is onehalf of the resonance period,
, and ω
_{r}
is the frequency of the resonance,
.
Equation (5) can be obtained by substituting (4) into (3) to get the average input current over one switching period.
where,
M=V_{o}/V_{in}
.
When
V_{in}
is lower than
V_{o}/2
, the waveforms of the switch gating signal, the inductor current
i_{L}
, the inductor voltage
v_{L}
, and the MOSFET drainsource voltage
v_{ds}
during one switching period are shown in
Fig. 7
.
Key waveforms when V_{in}<V_{o}/2.
The waveforms in
Fig. 7
have one more mode when compared to
Fig. 6
. While the drainsource voltage falls down to the valley at t
_{3}
when
V_{in}
>
V_{o}/2
, it reaches zero at t
_{4}
when
V_{in}
<
V_{o}/2
. After t
_{4}
, the MOSFET body diode starts conducting and the inductor current increases linearly during t
_{4}
t
_{6}
. The time duration from t
_{2}
to t
_{4}
, the instant that the drainsource voltage reaches zero, is given by (6).
And the inductor current at t
_{4}
is obtained by (7).
Because the magnitude and the slope of the inductor current when the inductor current increases linearly are known, the instant that the inductor current reaches zero can be obtained. The period when the inductor current increases linearly is shown in (8).
where,
t_{lin}
is the period from t
_{4}
to t
_{6}
. Therefore, when the input voltage is lower than half of the output voltage, the area that the inductor current has a negative value,
S_{neg2}
, is divided into two parts; the LCresonance period (t
_{2}
t
_{4}
) and the linearly increasing period (t
_{4}
t
_{6}
).
The area of the inductor current during
t_{res}
(t
_{2}
t
_{4}
) is
and during
t_{lin}
(t
_{4}
t
_{6}
), it is shown in (10).
Then, the total area when the inductor current has a negative value is obtained by (11).
The total area that the inductor current has a negative value increases as the input voltage decreases. Substituting
S_{neg2}
into (3) instead of
S_{neg1}
results in (12).
In addition, because the period that the inductor current increases linearly is infinite when the input voltage is close to zero as shown in (8), energy is seldom transferred in this region. For these reasons, the input current distortion deteriorates especially near the AC line zero crossing point. Therefore, a proper variable ontime control is necessary for the control of the CRM boost PFC converter to alleviate the current distortion.
 B. Enhanced Variable OnTime Control Method
In this section, based on the analysis of the inductor current in the previous section, a proper ontime for the CRM boost PFC converter is computed. In (5) and (12), the variable
k
is defined as follows.
Equation (13) is a quadratic equation related to
t_{on}
. By applying this variable in (5) and (12), the relationship between the input voltage and the input current can be obtained by (14).
where,
t
_{d}
_{1}
=
,
t
_{d2}
=
(
θ
+(
M
1)sin
θ
.
where,
R_{eq}
is
2L/k
. If the variable
k
is constant, the waveform of the input current follows that of the input voltage. The resulting ontime of the CRM boost PFC converter is computed using (13). By solving (13), the ontime is obtained as shown in (15).
For the COT control,
k
can be obtained from (16) using (14) because the ontime is proportional to the output voltage of the error amplifier, v
_{c}
[7]
.
The same equation can be applied to the eVOT control, because
v_{c}
is almost constant over one AC line period and it changes according to the output load condition.
Fig. 8
shows the calculated ontime of the CRM boost PFC converter controlled by the eVOT control method when the output power is 100W. When applying the eVOT control method, it is necessary to limit the maximum switch ontime because the compensated ontime goes infinite if there is no limiter in (15). Therefore, the ontime is limited to be less than 40㎲ in
Fig. 8
. As shown in
Fig. 8
, the ontime variation near the AC line zero crossing point is much larger than the variation when the input voltage is higher than half of the output voltage. In addition, it looks like that the ontime is almost constant when the input voltage is higher than half of the output voltage. The variation of the switch ontime is 16.4% when the input voltage is higher than half of the output voltage and that of the switch ontime is 1639% when the input voltage is lower than half of the output voltage. The effect of the ontime compensation when the input voltage is higher than half of the output voltage is little when compared to the effect when the input voltage is lower than half of the output voltage.
Computed ontime and scaled input voltage of the CRM boost PFC converter over half of line period.
IV. EXPERIMENTAL RESULTS
The proposed control method is verified by a 100W prototype, as shown in
Fig. 9
. The circuit parameters for the prototype are listed in
Table I
. In
Table I
, C
_{oss}
is 380pF, which includes the MOSFET and diode junction capacitances. The line voltage is universal and the frequency is 60Hz. The maximum ontime is 40㎲.
Experimental circuit diagram.
CIRCUIT PARAMETERS
When the input voltage is close to zero, the switch offtime is reduced and the switching period can be shorter than the computation time of the DSC. Therefore, it is necessary to reduce the computation time of the DSC so that it is as short as possible. In the eVOT control method, a phase extraction and trigonometric function for the switch ontime calculation increase the computation time of the DSC. To solve this problem,
t_{d}
_{2}
in equation (15) can be approximated as below if it is assumed that
t_{res}
is π/2.
Fig. 10
shows the error between the exact delay time and the approximate delay time, and
Fig. 11
shows the error between the exact switch ontime and the switch ontime while adopting the approximate delay time. Although the error between the exact delay time and the approximate delay time has a maximum value of 18%, the switch ontime error has a maximum value of 4.7% and it is reasonable to use the approximate delay time.
Fig. 12
,
Fig. 13
, and
Fig. 14
show the waveforms of a CRM boost PFC converter controlled by the COT, VOT, and eVOT control methods respectively when the AC line voltage is 220V. The periods during which the zero crossing distortion exists are about 1.48ms, 1.17ms, and 0.661ms, respectively.
Fig. 15
,
Fig. 16
and
Fig. 17
show the line voltage and current of a PFC converter controlled by the COT, VOT, and eVOT control methods when the AC line voltage is 110V. When the line voltage is 110V, the periods during which the line current has zero value are about 1.28ms, 1.07ms, and 0.431ms, respectively. As mentioned previously, this period is caused because the switch ontime is not enough to transfer power to the load.
Error between the exact delay time and the approximate delay time.
Error between the exact ontime and the approximate ontime.
Waveforms of input current and input voltage with COT control at 220V.
Waveforms of input current and input voltage with VOT control at 220V.
Waveforms of input current and input voltage with eVOT control at 220V.
Waveforms of input current and input voltage with COT control at 110V.
Waveforms of input current and input voltage with VOT control at 110V.
Waveforms of input current and input voltage with eVOT control at 110V.
Therefore, to improve the distortion, the switch ontime should be increased near the AC line zero crossing point.
Fig. 18
shows the measured switch ontime of a CRM boost PFC converter controlled by the COT, VOT, and eVOT control methods near the AC line zero crossing point when the voltage is 110V and 220V.
Measured switch ontime near zero crossing point of AC line voltage when AC line voltage is 110V and 220V.
As shown in
Fig. 18
, the switch ontime near the AC line zero crossing point is longest when the eVOT control method is applied. This result shows that the proposed eVOT control method compensates the zero crossing distortion of the input current properly.
Table II
shows the THD of the CRM boost PFC converter controlled by the COT, VOT, and eVOT control methods when the output power is 100W. The THD of the CRM boost PFC converter controlled by the proposed eVOT control method shows superior performance when compared to those by the COT and VOT control methods. The THD of the eVOT control method is minimized by experiments.
THD OF THE CRM BOOST PFC CONVERTER USING EACH CONTROL METHOD AT 100W
THD OF THE CRM BOOST PFC CONVERTER USING EACH CONTROL METHOD AT 100W
In low power applications, using a TMS320F28335 is not reasonable because it is too expensive. In
Fig. 19
, the operation time of the DSC is shown and compared with the gate signal near the zero crossing point of the AC line voltage. During
T
_{1}
, an analogtodigital converter (ADC) converts the analog signal to digital data. After
T
_{1}
, a toggle is set and the DSC operator computes the next gate signal ontime based on the data of the ADC during
T
_{2}
. After the DSC operation, the toggle is set to off and the DSC stands by during
T
_{3}
. As shown in
Fig. 19
, the DSC can be replaced by a cheaper one. Because the million instructions per second (MIPS) of the TMS320F28335 is 150, a DSC whose MIPS is over 30 can replace the TMS320F28335.
Operation period of DSC near zero crossing point of AC line voltage.
V. CONCLUSIONS
This paper proposes an enhanced variable ontime control method for CRM boost PFC converters to improve the current distortion. Because of the delay time of ZVS or quasiZVS after the diode is turnedoff in the CRM boost PFC converter, the input current distortion deteriorates especially near the AC line zero crossing point. To compensate this distortion, the optimized ontime is computed based on an analysis of the inductor current waveform. The performance of the CRM boost PFC converter controlled by the eVOT control method is demonstrated with experimental results. It is shown that the optimized ontime reduces the total harmonic distortion by about 52% (from 10.48% to 5.5%) at 220V and by 54% (from 6.87% to 3.74%) at 110V when compared to the variable ontime control method.
BIO
JungWon Kim received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Seoul National University, Seoul, Korea, in 1994, 1996, and 2001, respectively. He was a Senior Engineer with Fairchild Korea Semiconductor, Ltd. He was a Vice President of Silicon Mitus, Inc. from 2007 to July 2013. He is currently a Senior Researcher in the Engineering Research Institute of Seoul National University. His current research interests include power factor correction, converter parallel operation, modular converter systems, distributed power systems, and soft switching converters.
JeHyun Yi received his B.S. degree in Electrical Engineering from Seoul National University, Seoul, Korea, in 2011, where he is currently pursuing his Ph.D. degree. His current research interests include high power DC–DC converters, power factor correction circuits, and DC distribution systems.
BoHyung Cho received his B.S. and M.S. degrees from the California Institute of Technology, Pasadena, CA, USA, and his Ph.D. degree from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA, USA, all in Electrical Engineering. Prior to his research at Virginia Tech, he was a member of the Technical Staff with the Department of Power Conversion Electronics, TRW Defense and Space System Group, USA. From 1982 to 1995, he was a Professor with the Department of Electrical Engineering, Virginia Tech. In 1995, he joined the School of Electrical Engineering, Seoul National University, Seoul, Korea, where he is currently a Professor. His current research interests include power electronics, modeling, analysis, and control of spacecraft power processing equipment, and distributed power systems. Dr. Cho is a member of Tau Beta Pi. He was a recipient of the 1989 Presidential Young Investigator Award from the National Science Foundation. He chaired the 2006 IEEE Power Electronics Specialists Conference.
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