dm00061859

AN4149
Application note
Designing a CCM PFC pre-regulator based on the L4984D
By Hiroshi Andrea Fusillo
Introduction
Two methods of controlling power factor corrector (PFC) pre-regulators based on boost
topology are currently in use: the fixed-frequency (FF) PWM and the transition mode (TM)
PWM (fixed on-time, variable frequency).
With the first method the boost inductor works in a continuous conduction mode (CCM) and
employs average current-mode control, a relatively complex technique requiring
sophisticated controller ICs (e.g. the L4981A/B from STMicroelectronics) and a
considerable component count.
The second one uses the more simple peak current-mode control and makes the inductor
work on the boundary between continuous and discontinuous mode, which is implemented
with cheaper controller ICs (e.g. the L6562A, L6563x and L6564x from STMicroelectronics),
and much fewer external parts, making it far more cost efficient. For a given power
throughput, TM operation involves higher peak currents compared to FF-CCM (see the
figures below).
Figure 1. Line and inductor currents in
CCM PFC
Figure 2. Line and inductor currents in TM
PFC
AM13300v1
AM13301v1
This demonstration, consistent with the above-mentioned cost considerations, suggests the
use of TM in a lower power range, while FF-CCM is recommended for higher power levels.
In the power range of around 150-300 W, assessing which approach gives the better cost/
performance trade-off needs to be done on a case-by-case basis, considering the cost and
stress of both power semiconductors and magnetic components, but also of the EMI filter.
At the same power level, the switching frequency component to be filtered out in a TM
system is twice the line current, whereas it is typically 1/3 or 1/4 in a CCM system. In this
document the CCM using a fixed-off-time (FOT) control mode, fully integrated in the
controller, is proposed, coupling simplicity and low port count similar to a TM control. The
design procedure is explained too.
June 2013
DocID023523 Rev 2
1/43
www.st.com
Contents
AN4149
Contents
1
CCM PFC using FOT control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2
Designing a CCM FOT-controlled PFC . . . . . . . . . . . . . . . . . . . . . . . . . 10
3
2.1
Input specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2
Operating conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3
Power section design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1
Bridge rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2
Input capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.3
Output capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.4
Boost inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.5
Power MOSFET selection and power dissipation calculation . . . . . . . . 18
2.3.6
Boost diode selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
L4984D biasing circuitry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1
Feedback and OVP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2
Current sense resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3
Mult divider and VFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4
Gate driver (GD) and VCC pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4
FOT PFC boost control loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5
Layout hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6
Design example using the L4984D-CCM PFC excel spreadsheet . . . 38
7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2/43
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AN4149
List of figures
List of figures
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
Figure 19.
Figure 20.
Figure 21.
Figure 22.
Figure 23.
Figure 24.
Figure 25.
Figure 26.
Line and inductor currents in CCM PFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Line and inductor currents in TM PFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Block diagram of an FOT-controlled PFC preregulator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Line-modulated FOT modulator internal block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Line-modulated FOT modulator key waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Boundary between DCM and CCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Typical frequency change along a line half-cycle in a boost PFC operated in LM FOT . . . . 8
Typical frequency change along a line half-cycle in a boost PFC operated in TM . . . . . . . . 8
LM FOT controlled boost PFC: current waveforms (line current) . . . . . . . . . . . . . . . . . . . . . 8
LM FOT controlled boost PFC: current waveforms (boost inductor current envelope). . . . . 8
Line-modulated, FOT controlled boost PFC: input current harmonic contents . . . . . . . . . . . 9
Total MOSFETs losses in the 350 W FOT PFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Multiplier characteristics family for VFF = 1 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Multiplier characteristics family for VFF = 3 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Small signal model of a PFC stage with a constant-power load (DC-DC converter) . . . . . 30
Bode plots of the control-to-output transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Schematic diagram of a type II compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Bode plots of a type II amplifier's transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Bode plots of the closed-loop transfer function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
115 Vac step load (50 % to 100 %): improper compensation . . . . . . . . . . . . . . . . . . . . . . . 36
115 Vac step load (50 % to 100 %): good compensation . . . . . . . . . . . . . . . . . . . . . . . . . . 36
EVL4984-350W PCB layout (SMT side view). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Excel spreadsheet design specification input table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Other design data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
CCM PFC schematic based on the L4984D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Excel spreadsheet BOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
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CCM PFC using FOT control
1
AN4149
CCM PFC using FOT control
Fixed-frequency PWM is not the only alternative when CCM operation is desired. An
additional approach that couples the simplicity and affordability of TM operation with the
high-current capability of CCM operation can be a solution to the problem.
Fixed-frequency PWM modulates both switch ON and OFF times (their sum is constant by
definition), and a given converter operates in either CCM or DCM depending on the input
voltage and the loading conditions. Exactly the same result can be achieved with FOT
approach: a conventional "peak" current mode control, where the ON-time TON of the
external power switch is determined by the peak inductor current reaching the programmed
value and the OFF-time TOFF is determined by a special Fixed-off-time (FOT) modulator in
such a way that the resulting switching period is constant as long as the boost converter is
operated in CCM (i.e. the current in the boost inductor remains greater than zero in a
switching cycle).
In Figure 3 a block diagram of an FOT-controlled CCM PFC pre-regulator is shown. An error
amplifier (VA) compares a portion of the boosted output voltage Vout with a reference VREF
and generates an error signal VC proportional to their difference, a DC voltage by
hypothesis, which is fed into an input of the multiplier block and multiplied by a portion of the
rectified input voltage VMULT.
The multiplier output (VCSREF) is a rectified sine wave whose amplitude is proportional to
that of VMULT and to VC, and is used as a reference for PWM modulation. The multiplier
output is fed into the inverting input of a PWM comparator that, on the non-inverting input,
receives the voltage VCS from the sense resistor Rsense, proportional to the current flowing
through the switch M (typically a MOSFET) and the inductor L during the ON-time of M.
When the two voltages are equal, the comparator resets the PWM latch and M is turned off.
As a result, the multiplier output determines the peak current through the switch and the
inductor, and as, it is a rectified sinusoid, the inductor peak current is also enveloped by a
rectified sinusoid.
When VCSREF and VCS are equal the PWM latch output Q going high activates the timer
that, after a predetermined time in which TOFF has elapsed, sets the PWM latch, therefore
turning the switch on and starting another switching cycle.
If TOFF is such that the inductor current does not fall to zero, the system operates in CCM.
For the CCM PFC controller, please refer to Figure 4.
To understand how TOFF needs to be modulated to achieve a fixed switching frequency
independent of the instantaneous line voltage and the load, it is useful to consider the V·s
balance equation for the boost inductor under the assumption of CCM operation:
Equation 1
TON Vpk sin θ = TOFF ( Vout −Vpk sin θ )
where Vpk is the peak line voltage, Vout is the regulated output voltage, and θ is the
instantaneous phase angle of the line voltage. Solving for TON we get:
Equation 2

 Vout
TON = 
− 1  TOFF
Vpk
sin
θ


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AN4149
CCM PFC using FOT control
then, the switching period TSW will be:
Equation 3
 Vout

Vout
Tsw = TON + TOFF = 
− 1 TOFF + TOFF =
TOFF
Vpk sin θ
 Vpk sin θ 
In the end, if TOFF is changed proportionally to the instantaneous line voltage, i.e. if:
Equation 4
TOFF = K t Vpk sin θ
then TSW will be equal to Kt·Vout and, since Vout is regulated by the voltage loop, also TSW
(and fSW=1/TSW) will be fixed. This result is based on the sole assumption that the
instantaneous line voltage and the output load are such that the boost inductor operates in
CCM.
Figure 3. Block diagram of an FOT-controlled PFC preregulator
DocID023523 Rev 2
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CCM PFC using FOT control
AN4149
Figure 4. Line-modulated FOT modulator internal block diagram
0
COMP
MULT
CS
+
-
Multiplier
-
ITimer
PWM
Comparator
S
+
Q
GD
TIMER
Driver
R
ON
OFF
PWM Latch
CT
AM13303v1
Figure 5. Line-modulated FOT modulator key waveforms
MULT
TIMER
S
TOFF
TON
t
t
R
t
Q
t
GD
t
Multiplier output
CS
t
AM13304v1
With reference to the block diagram (Figure 4) and the relevant key waveforms in Figure 5,
an OFF-time proportional to the instantaneous line voltage is achieved by charging the
capacitor CT with a constant current ITIMER, accurately fixed internally and temperature
compensated, while the MOSFET is off and commanding MOSFET's turn-on (and resetting
CT at zero) as the voltage across CT equals that on the pin MULT. The voltage on this pin is:
Equation 5
VMULT = K P Vpk sin θ
where KP is the divider ratio of the resistors biasing pin MULT. As a result:
Equation 6
TOFF =
6/43
CT
ITIMER
K P Vpk sin θ
DocID023523 Rev 2
→
Kt =
CT
I TIMER
KP
AN4149
CCM PFC using FOT control
and the switching frequency will be:
Equation 7
f sw =
I TIMER
1
1
=
=
Tsw K P CT Vout K t Vout
The timing capacitor CT, therefore, will be selected with the following design formula:
Equation 8
CT =
I TIMER
K P Vout f sw
Vout and fsw are design specifications, KP is chosen so that the voltage on pin MULT is
within the multiplier's linearity range (0 to 3 V) and ITIMER is specified in the "Electrical
characteristics" section of the L4984D datasheet.
Along a line half-cycle, TOFF goes all the way from nearly zero to the maximum on the
sinusoid peak. It is important to check that the OFF-time occurring on the peak of the
sinusoidal voltage at minimum input voltage is greater than the minimum programmable
value:
Equation 9
TOFF min =
CT
I TIMER
K P Vpk min > 1.2 μ s
This constraint limits the maximum programmable frequency at:
Equation 10
f sw. max = 833
Vpkmin
Vout
[KHz]
As the line RMS voltage is increased and/or the output load is decreased the boost inductor
current tends to become discontinuous starting from the region around the zero-crossings.
As a result, in the DCM regions the switching frequency is no longer constant and tends to
increase.
Figure 6. Boundary between DCM and CCM
AM13305v1
DocID023523 Rev 2
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CCM PFC using FOT control
AN4149
However, the frequency rise is significantly lower as compared to that of a transition-mode
(TM) operated boost PFC stage, as illustrated in Figure 7 and 8 .
Figure 7. Typical frequency change along Figure 8. Typical frequency change along
a line half-cycle in a boost PFC operated a line half-cycle in a boost PFC operated
in LM FOT
in TM
9
1.6
1.4
Vin=230 Vac
1.2
1
Vin= 88 Vac
0.8
Vin=230 Vac
8
Normalized switching frequency
Normalized switching frequency
Vin=264 Vac
Vin= 115 Vac
0.6
7
6
5
4
Vin= 115 Vac
3
Vin= 88 Vac
2
1
0.4
0
0.52
1.05
1.57
2.09
2.62
0
3.14
Line voltage phase angle (rad)
Vin=264 Vac
0
0.52
1.05
1.57
2.09
2.62
3.14
Line voltage phase angle (rad)
AM13306v1
AM13307v1
Due to the peak current vs. average current error which becomes much worse at low current
levels (especially in DCM), the current that the boost PFC pre-regulator draws from the
power line will not be exactly sinusoidal but will be affected by a distortion that will be lower
as the current ripple in the boost inductor is smaller as compared to its peak value.
Figure 9 and 10 show some theoretical waveforms, relevant to full load condition, in a line
cycle at different input voltages.
Figure 9. LM FOT controlled boost PFC:
current waveforms (line current)
Vin = 88 Vac
Line current
Inductor current (A)
Line current (A)
Vin = 88 Vac
Figure 10. LM FOT controlled boost PFC:
current waveforms (boost inductor
current envelope)
Vin = 190 Vac
Vin = 264 Vac
Vin = 230 Vac
Line voltage phase angle (rad)
rad)
Boost inductor
current envelope
Vin = 264 Vac
Line voltage phase angle (rad)
AM13308v1
AM13309v1
In Figure 9 the line (input) current waveform is shown for different line voltages, while
Figure 10 illustrates the envelope of the inductor current at minimum and maximum line
voltage.
The input current waveform relevant to Vin = 88 Vac shows no visible sign of distortion; the
operation of the boost inductor is CCM throughout the entire line cycle as shown by the
8/43
DocID023523 Rev 2
AN4149
CCM PFC using FOT control
inductor current envelope. The brown waveform is relevant to Vin=190 Vac, which is the
condition where CCM operation no longer occurs at zero-crossings (this voltage value, for a
given power level, depends on the inductance value of the boost inductor); a certain degree
of distortion is already visible. The waveform relevant to Vin = 264 Vac shows the highest
degree of distortion and the largest portion of the line cycle where the boost inductor
operates in discontinuous mode (DCM). However, its harmonic content, shown in Figure 9
and 10, is still so low that is not an issue for EMC compliance. Almost all the distortion is
concentrated in the third harmonic, whose amplitude is 17% of the fundamental one, while
the THD is 17.7%.
% Harmonic amplitude
(normalized to fundamental)
Figure 11. Line-modulated, FOT controlled boost PFC: input current harmonic
contents
Vin = 264Vac
THD = 17.7%
Harmonic order (n)
AM13310v1
The compliance with conducted EMI emission regulations is also facilitated by the voltage
ripple appearing across the output capacitor CO , at twice the line frequency fL, which has
peak amplitude ΔVout proportional to the output current IOUT. As a consequence, fsw is not
constant but is modulated at 2fL, spreading the spectrum of the electrical noise injected
back into the power line. The relative frequency change due to the output voltage ripple is:
Equation 11
Δf sw
=
f sw
ΔVout
Vout
ΔVout
1+
Vout
where ΔVout can be found with the following expression:
Equation 12
ΔVout =
Iout
4 π f L Cout
DocID023523 Rev 2
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Designing a CCM FOT-controlled PFC
AN4149
2
Designing a CCM FOT-controlled PFC
2.1
Input specification
The following is a possible design procedure for a CCM FOT-controlled PFC using the
L4984D. This first part is a detailed specification of the operating conditions of the circuit that
is needed for the calculations of the design steps in the following sections.
In this example a 350 W wide-input range mains PFC circuit has been considered. Some
design criteria are also given.
Mains voltage range (Vacrms) :
Equation 13
V A C m ax = 26 5V
V A C m in = 9 0V
Minimum mains frequency:
Equation 14
f l = 47 H z
Rated output power (W):
Equation 15
Pout = 3 50 W
Typically the output for a boost PFC output voltage is 400 Vdc as it has to be higher than the
maximum rectified input voltage:
Equation 16
2 ⋅V A C max
In cases where the maximum AC input voltage VACmax is higher than 265 V, as typical in
ballast applications, the output voltage must be set higher accordingly. As a rule of thumb
the output voltage must be set 6 or 7% higher than the maximum input voltage peak.
Regulated DC output voltage (Vdc):
Equation 17
V out = 400 V
The target efficiency and PF are set for the following calculations based on the operating
condition of the PFC, here at minimum input voltage and maximum load. An efficiency of
92%, at minimum input voltage and maximum load, could be a starting point for a typical
PFC.
Expected efficiency (%):
Equation 18
η=
10/43
Pout
= 92%
Pin
DocID023523 Rev 2
AN4149
Designing a CCM FOT-controlled PFC
Expected power factor:
Equation 19
PF = 0 .99
Because of the narrow loop voltage bandwidth of the E/A to reject the ripple at twice the line
frequency on the E/A output, the PFC output may experience overvoltage at startup or
during load transients. In order to protect the controller from excessive output voltage that
can overstress the output components and the load, in the L4984D a pin (PFC_OK, pin #6)
has been dedicated to monitor the output voltage with a separate resistor divider. The
divider is selected so that the voltage at the pin reaches 2.5 V if the output voltage exceeds
a preset value (VOVP) larger than the maximum Vout that can be expected, also including
worst-case load/line transients.
Maximum output voltage (Vdc):
Equation 20
V OVP = 430 V
The output voltage has a ripple Vout at twice the line frequency (2fL), and whose amplitude is
proportional to the load and depends on the impedance of the output capacitor. The ripple
amplitude determines the AC current flowing into the output capacitor and the ESR. The
value of the maximum output voltage ripple accepted should be below a certain level to
keep the output voltage far from the VOVP limit during normal operating conditions, to
increase hold-up time, and to reduce the AC losses on the output capacitor. The peak-topeak voltage ripple Vout is usually selected in the range between 2-8% of the output voltage.
Here a ratio of 5% is chosen for the output voltage ripple, that is 20 V.
Maximum output low frequency ripple (peak-to-peak):
Equation 21
Δ V o u t = 20V
The desired ripple on the output voltage is not the only parameter used to select the bulk
capacitor. The hold-up time, if requested, should also be taken into account. The hold-up
time is defined as the duration of time that a power supply's output will remain above a
minimum level in case of mains dips.
The hold-up time (tHold) is measured from the time when the line voltage disappears to the
time when the output voltage reaches the required minimum voltage value (Voutmin). A holdup time of 10-20 ms is often required for today’s offline power supplies. Values of 300 V and
15 ms for the minimum output voltage after line drop and hold-up time, respectively, are
chosen here:
Minimum output voltage after line drop (Vdc):
Equation 22
V out min = 300 V
Hold-up time (ms):
Equation 23
t Ho l d = 15 m s
DocID023523 Rev 2
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Designing a CCM FOT-controlled PFC
AN4149
The design will be done on the basis of a maximum admitted ripple factor Kr , that is the ratio
of the maximum peak-to-peak current ripple amplitude to the inductor peak current, at
minimum line voltage and rated load. In the continuous conduction mode converters, the
acceptable current ripple factor is typically fixed in a range between 20% and 35%. Low
values for the Kr keep the peak-to-peak ripple current and the input current distortion low,
but lead to larger inductor physical size. Choosing higher values for Kr , the inductor size
can be smaller, but the input current distortion is increased. For this design, the maximum
specified current ripple factor is chosen equal to 27%, as a trade-off between the inductor
size and the input current distortion.
Ripple factor:
Equation 24
K r = 0 .2 7
In order to properly select the power components of the PFC and size the heat sinks, the
maximum operating ambient temperature around the PFC circuitry must be known. Please
note that this is not the maximum external operating temperature of the entire equipment,
but it is the local temperature at which the PFC components are working. The power
dissipation leading to a temperature rise combined with the ambient temperature must not
result in any temperature exceeding the operating temperature rating of the components.
Maximum ambient temperature ( °C):
Equation 25
T ambx = 50 °C
2.2
Operating conditions
The first step is to define the main parameters of the circuit, using the specifications given in
Section 2.1.
Rated DC output current:
Equation 26
I out =
Pout
V out
I ou t =
350W
= 0 . 875 A
400V
Maximum input power:
Equation 27
Pin =
12/43
Pout
Pin =
η
DocID023523 Rev 2
350 W
⋅ 100 = 380 .4 W
92
AN4149
Designing a CCM FOT-controlled PFC
The maximum value of the RMS current circulating in the boost cell at the minimum line
voltage of the selected range is equal to:
Maximum RMS input current:
Equation 28
I in =
Pin
I in =
VAC m in ⋅ PF
380 .4W
= 4 .27 A
90Vac ⋅ 0 .99
In order to describe the energy and relevant equations concerning a boost PFC, the ratios of
the voltage inputs of the boost converter to the regulated output voltage are defined. In
particular kmin and kmax refer to the ratio of the minimum and the maximum input voltage to
the output voltage, respectively.
Equation 29
k min =
2
VAC min
V out
k m ax =
2
90Vac
= 0 . 32
400V
k max =
2
VAC max
V out
k max =
2
2 65Vac
= 0 .94
400V
Combining equation 28 and equation 29 the maximum line peak current can be found.
Maximum line peak current:
Equation 30
I P K max =
2 ⋅ Pin
I P K max =
k m in ⋅ V out
2 ⋅ 380 .4W
= 5 .98 A
0 .32 ⋅ 400V
Maximum inductor peak current:
Equation 31
IL PK max =
K 
2 ⋅ Pin

⋅ 1 + r 
V AC min ⋅ PF 
2 
IL P K max =
2 ⋅ 380 .4W 
0 .27 
⋅ 1 +
 = 6 .8 5 A
90V ⋅ 0 .99 
2 
Inductor peak-to-peak ripple current :
Equation 32
Δ IL PK max = K r ⋅ IL P K max
ΔIL PK ma x = 0 .27 ⋅ 6 .85 A = 1 .85 A
In order to calculate the losses of the switches, the RMS current flowing through the
MOSFET and through the boost output diode are found.
Maximum RMS switch current:
DocID023523 Rev 2
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Designing a CCM FOT-controlled PFC
AN4149
Equation 33
Pin
ISW rm s =
ISW rm s =
2 ⋅ V AC min ⋅ PF
38 0 .4W
2 ⋅ 90V ⋅ 0 .99
⋅ 2−
⋅ 2−
1 6 ⋅ k min
3π
16 ⋅ 0 .318
= 3 .65 A
3π
Maximum RMS diode current:
Equation 34
IDr m s =
ID rms =
Pin
2 ⋅ V A C min ⋅ PF
380.4W
2 ⋅ 90V ⋅ PF
⋅
⋅
1 6 ⋅ k min
3π
16 ⋅ 0.32
= 2.22 A
3π
It is worth reminding that the accuracy of the equations developed here is quite good at low
line voltage and worsens at high line and as the power throughput is reduced. As the current
stresses of the switches are calculated at maximum load and minimum line voltage, the
previous expressions are acceptable for design purposes.
2.3
Power section design
2.3.1
Bridge rectifier
The input rectifier bridge can use standard slow recovery, low-cost devices. Typically a
600 V device is selected in order to have good margin against mains surges. An NTC
resistor limiting the current at turn-on is required to avoid overstressing the bridge diodes.
The rectifier bridge power dissipation can be calculated starting from the input RMS current
and the input average current through the bridge diodes.
Equation 35
I in _ rm s _ b ri d ge =
2 ⋅ I in
=
2
2 ⋅ 4 . 36 A
= 3 . 02 A
2
2 ⋅ I in
2 ⋅ 4 . 36 A
Equation 36
I in _ avg _ b ri dg e =
π
=
π
= 1 . 92 A
The power dissipated on a D15XB60 bridge can be estimated combining equation 35 and
equation 36 with the threshold voltage (Vth) and dynamic resistance (Rdiode) of a single
diode of the bridge, the values of which can be found in the datasheet of the diode.
Equation 37
Pbridge = 4 ⋅ R diode ⋅ I 2 inrms + 4 ⋅V th ⋅ I in _ avg
Pbridge = 4 ⋅ 0 .025 Ω ⋅ (3 .02 A) 2 + 4 ⋅ 0 .7V ⋅ 1 .92 A = 6 .29 W
14/43
DocID023523 Rev 2
AN4149
Designing a CCM FOT-controlled PFC
From this number and the given maximum ambient temperature Tambx the total maximum
thermal resistance required to keep the junction temperature below 125 °C is:
Equation 38
R th =
2.3.2
125 °C − T a m b x
P b r id g e
R th =
125 ° C − 50 ° C
°C
= 11 . 92
6 . 29W
W
Input capacitor
The input filter capacitor, Cin, is placed across the output of the bridge diodes. This capacitor
must smooth the high-frequency ripple and must sustain the maximum instantaneous input
voltage. In a typical application an EMI filter is placed between the mains and the PFC
circuit. In this application the EMI filter is reinforced by a differential mode Pi-filter after the
bridge to reject the differential noise coming from the whole switching circuit. The design of
the EMI filters (common mode and differential mode) is not described here.
For wide-range operation the minimum value of the input filter capacitor can be calculated
as follows, using a practical formula based on the output power that the PFC delivers at full
load:
Equation 39
C in = 2 . 5 ⋅ 10 −3 ⋅
μF
W
C in = 2 . 5 ⋅ 10 − 3 ⋅
⋅ Pout
μF
W
⋅ 350W = 875 nF
The maximum value of this capacitor has to be not much higher than the minimum value to
avoid the distortion of the input mains current, due to the residual voltage retained by the
capacitor that causes the diodes of the bridge rectifier to be reverse-biased and the input
current flow to temporarily stop. The selected value for the input filter capacitor of this
design is 1 μF.
2.3.3
Output capacitor
The output bulk capacitor (CO) selection depends on the regulated DC output voltage, the
output power, the RMS current into the capacitor, the output voltage ripple and hold-up time
(if requested).
The value of the output capacitor to meet the output voltage ripple requirements can be
defined using the following expression (equation 40). ΔVout has to be intended as twice the
mains frequency peak-to-peak voltage ripple, function of the capacitor impedance and the
peak capacitor current. The contribution of the ESR (equivalent series resistance) is
neglected here as the capacitive reactance is dominant.
Equation 40
Co ≥
I ou t
Pou t
=
2 π ⋅ f l ⋅ Δ V ou t
2 π ⋅ f l ⋅ V o u t ⋅ Δ V o ut
Co ≥
350 W
= 148 . 1μ F
2π ⋅ 47 Hz ⋅ 400 V ⋅ 20V
where fl is the minimum line frequency. Although ESR usually does not affect the output
ripple, it should be taken into account for power loss calculation. The total capacitor RMS
ripple current, including the mains frequency and switching frequency components, is:
DocID023523 Rev 2
15/43
Designing a CCM FOT-controlled PFC
AN4149
Equation 41
I Crms =
I Crms =
ID 2 rms − I 2 out
(2. 22 A ) 2 − ( 0 .87 A ) 2 = 2 .04 A
Reading the ESR value of the datasheet of the output capacitor chosen, the power losses
associated to this ripple current can be easily calculated by:
Equation 42
PCrms = I Crms ⋅ ESR
2
If the PFC stage has to guarantee a specified hold-up time, the calculation of the output
capacitor is different. The value of the capacitor when the line voltage drops out, needed to
deliver the output power for a certain time (tHold) until the output voltage reaches the
required minimum voltage value (Voutmin), depends on the load and the value of the ripple.
When Voutmin is reached, a 'power fail' is detected, stopping the downstream system
supplied by the PFC. The worst case for the hold-up time is at minimum input voltage and
full load, with the line drop starting at the valley of the sine-varying ripple of the output
voltage.
Equation 43
Co =
2 ⋅ Pout ⋅ t H old
Co =
2
Δ V out 

2
 − V out min
 V out −
2


2 ⋅ 350 W ⋅ 15 ms
(400 V
− 10V
)2 − (300V )2
= 169 μ F
Considering a 20% tolerance on the electrolytic capacitors, a value of 200 μF has been
chosen, using two capacitors of commercial value of 100 μF placed in parallel. The actual
hold-up time and ripple voltage with the selected value are:
Actual hold-up time:
Equation 44
t Hold
t Hold =
2


ΔVout 
2
Co ⋅ Vout −
 − Vout
min 
2 


=
2 ⋅ Pout
[
]
200 μF ⋅ (400V − 10V )2 − (300V )2
= 18 ms
2 ⋅ 350W
Peak-to-peak output voltage ripple:
Equation 45
Δ V out =
2.3.4
I out
2 ⋅ π ⋅ f l ⋅ Co
Δ V out =
0 . 87 A
= 14 . 81V
2 ⋅ π ⋅ 47 Hz ⋅ 200 μ F
Boost inductor
As indicated in the specs in Section 2.1: Input specification, the maximum current ripple
factor Kr , that is the ratio of the maximum peak-to-peak current ripple amplitude to the
16/43
DocID023523 Rev 2
AN4149
Designing a CCM FOT-controlled PFC
inductor peak current at minimum line voltage and rated load, is 27%, as a trade-off
between the inductor size and the stress on the switches.
This choice led to the inductor peak-to-peak ripple current (ILPK) equal to 1.89 A (equation
32).
The value of the inductance L required for the boost inductor can be calculated starting from
the volt-second balance of the inductor. The minimum value of L is then a function of the
duration of the OFF-time, the voltage across the inductor during TOFF, and the inductor
peak-to-peak ripple current.
Equation 46
L=
V out − 2 ⋅ V AC
⋅ TOFF (V AC )
Δ IL pk (V AC )
The latter expression should be calculated at low line and the value found is the minimum
inductance value of the PFC inductor. To find the value of L, first TOFF needs to be
calculated.
In a fixed-off-time control using the L4984D, the off-time (TOFF) is changed proportionally to
the instantaneous line voltage in order to make the switching frequency (fSW) constant. The
switching frequency is determined by a capacitor connected between the TIMER pin and
ground, charged by an accurate internal generator (ITIMER) of 156 μA (typ.), during the OFFtime, generating a voltage ramp.
When the voltage ramp equals the voltage on the MULT pin, connected through a resistive
divider to the rectified mains to get a sinusoidal voltage reference, the OFF-time of the
power MOSFET is terminated, the gate driver (GD) pin is driven high and the ramp resets at
zero. The timing capacitor CT is then selected with the following formula:
Equation 47
CT =
I TIM ER
k p ⋅ V out ⋅ f SW
where fsw is the switching frequency and kp the maximum required divider ratio, calculated
considering the maximum value of the multiplier input, that is, the voltage measured on the
MULT pin at maximum mains voltage. According to the datasheet of the L4984D, the linear
operating range is between 0 to 3 V, so the maximum value of the multiplier input
(VMULTmax) is equal to 3 V.
The maximum required divider ratio kp can be now found as:
Equation 48
kp =
V MULT
max
2 ⋅ VA C max
=
3 . 00V
= 8 ⋅ 10 − 3
2 ⋅ 265 Vac
DocID023523 Rev 2
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Designing a CCM FOT-controlled PFC
AN4149
The switching frequency chosen for this design is around 70 kHz, so the capacitor on the
TIMER pin needed to obtain the desired frequency is (equation 47):
Equation 49
CT =
8 ⋅1 0
−3
1 56 μ A
= 6 95 pF
⋅ 40 0 V ⋅ 70 kH z
A commercial value of 680 pF has been selected. An NP0 capacitor has to be used.
Now TOFF can be finally calculated. Along a line half-cycle, TOFF varies from nearly zero to
the maximum value, occurring at the MULT peak voltage. To calculate the boost inductor the
value at the MULT peak should be considered, found simply from the product of the
maximum required divider ratio kp and the peak of the rectified input voltage at low mains
voltage (Vpkmin).
The maximum OFF-time at VACmin is then:
Equation 50
T OFF (V AC min ) =
680 pF
⋅ 8 ⋅ 10 −3 ⋅ 2 ⋅ 90V = 4 .4 μ s
156 μ A
The value of the inductance L required for the boost inductor at VACmin can now be
calculated with equation 46.
Equation 51
L (VAC min ) =
L (VAC min ) =
Vout − 2 ⋅ V AC min
⋅ TOFF (V AC min )
ΔIL pk (V AC min )
400V − 2 ⋅ 90V
⋅ 4 .4 μ s = 654 μ H
1 .85 A
The value chosen for the inductor is 700 μH.
2.3.5
Power MOSFET selection and power dissipation calculation
The selection of the MOSFET concerns mainly RDS(on), that should be low in order to
minimize conduction losses, without increasing the switching losses due to the MOSFET 's
equivalent output capacitance Coss. To achieve high efficiency both RDS(on) and Coss have
to be taken into account, and the trade-off between cost vs. performance must also be
considered.
The MOSFET breakdown voltage is needed, considering the PFC nominal output voltage
and adding some margin (20%) to guarantee reliable operation. Therefore, a minimum
voltage rating of 500 V (1.2 · Vout = 480 V) is selected.
In this 350 W CCM PFC application, two STF21N65M5 (placed in parallel) have been
chosen, to improve robustness against surges and burst tests, and 650 V MOSFETs have
been chosen, having a good balance between RDSon and Coss. In order to calculate the
contribution of the MOSFETs to the total efficiency of the system, the power losses have
been calculated, which are mainly the sum of the conduction, switching and capacitive
losses.
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DocID023523 Rev 2
AN4149
Designing a CCM FOT-controlled PFC
The conduction losses at maximum load and minimum input voltage are calculated by:
Equation 52
Pcond (VAC ) = RDS on ⋅ (ISW rms (VAC ) )
2
Because normally in a MOSFET datasheet RDS(on) is given at ambient temperature (25 °C),
in order to properly calculate the conduction losses at 100 °C (typical MOSFET junction
operating temperature), a factor KTEMP between 1.5 to 2, which can be found in the device
datasheet, should be taken into account. In the case of the STF21N65M5, looking at the
normalized ON resistance vs. temperature graph, a factor of 1.7 should be considered at
100 °C.
Equation 53
R DSon _@ 100°C =
RDS on _@ 25 °C
Num _ of _ paralleled _ MOSFETs
⋅ K TEMP =
0 .179 Ω
⋅ 1 .7 = 0 .152 Ω
2
where the RDSon value is divided by two since two MOSFETs are placed in parallel. The
maximum RMS switching current, at minimum VAC, has been found from equation 33. Now,
from equation 52 and equation 53, and considering that two MOSFETs in parallel have been
used, the maximum conduction losses at low line and full load can be calculated as:
Equation 54
Pcond (VAC ) = R DSon _@ 100 ° C ⋅ (ISW rms (VAC ) )2
Pcond (90V ) = 0 . 152 Ω ⋅ (3 . 65 A ) = 2 . 02 W
2
The switching losses are difficult to predict as they depend on the particular switching
waveform, determined by many factors (driving current, gate resistors, MOSFET gate
internal resistance, Vth, gate charge, total capacitance on the drain node including parasitic
capacitances etc.). A good approximation to determine the generic switching losses due to
the MOSFET commutation occurring at turn-on and turnoff can be basically expressed by:
Equation 55
Psw (VAC ) =
1
⋅ V DS ⋅ I D ⋅ (t rise + t fall )⋅ f sw
2
where VDS is the drain-to-source of the MOSFET, ID the average drain current and trise and
tfall refer to the rising and the falling edge of VDS . To estimate the rising and falling times of
the drain voltage, datasheet values of the switching performance of the MOSFET can be
used.
First the average rising times of the drain voltage can be calculated considering the total
drain node capacitance and the average value of the peak current flowing through the
inductor.
DocID023523 Rev 2
19/43
Designing a CCM FOT-controlled PFC
AN4149
The exact value of the MOSFET's COSS is indicated in the datasheet looking at the graph
representing COSS vs. VDS. At VDS equal to 400 V, COSS is 40 pF. This value should be
multiplied by two as two MOSFETs have been used in parallel, and adding a rough 100pF of
all other contributions, CD can be found:
Equation 56
C D = 2 ⋅ C OSS + C stray = 2 ⋅ 40 pF + 100 pF = 180 pF
Then the average rising time of the drain voltage is:
Equation 57
t rise =
C D ⋅ V DS
C D ⋅ V DS
=
≈ 17 ns
π
ID
1
⋅  IL pk max
π
0
However, the average falling time depends on the driving current IG (limited by the resistor
placed on the gate), the MOSFET's total gate charge QG and the driving voltage Vdr,
supposed here equal to VCC (for example, 15 V) applied for simplicity. In the resistor
calculation the intrinsic gate resistance should also be considered. In the case of the
STF21N65M5, RG is 2.5 Ω which has to be added to the externally placed resistor RGext
(3.3 Ω in this design).
Equation 58
t Cfall =
QG
=
IG
QG
50 nC
=
≈ 19 ns
V dr
15V
R Gext + R G
3 .3Ω + 2 .5 Ω
Finally, the MOSFET’s switching losses can be estimated with equation 55:
Equation 59
PSW (90 V ) =
1
⋅ 400 V ⋅ 4 .36 A ⋅ (17 ns + 19 ns )⋅ 70 kHz = 2 .2W
2
To estimate the capacitive losses, that is, the losses due to the discharge of the total drain
capacitance through the MOSFET at turn-on, this simple expression can be considered:
Equation 60
Pcap (VAC ) =
Pcap (90V ) =
20/43
1
2
⋅ C D ⋅ V DS ⋅ f sw (VAC )
2
1
2
⋅ 180 pF ⋅ (400 V ) ⋅ 70 kHz = 1W
2
DocID023523 Rev 2
AN4149
Designing a CCM FOT-controlled PFC
The MOSFET total losses at minimum input voltage (VACmin) is the sum of the three
previous losses from equation 54, equation 55, and equation 60:
Equation 61
Ploss (VAC ) = Pcond (VAC ) + Psw (VAC ) + Pcap (VAC )
Ploss (90V ) = 2 .02W + 2 .2W + 1W = 5 .23W
From equation 61, using the data relevant to the MOSFET selected, it can be observed that
the maximum total losses, occurring at VACmin and full load, is around 5 W. From this
number and the given maximum ambient temperature, the total maximum thermal
resistance required to keep the MOSFET's junction temperature below 125 °C is:
Equation 62
R th =
125 °C − T ambx
Ploss (VAC )
R th =
125 °C − 50 °C
°C
= 14 . 3
5 . 23W
W
As the result of equation 62 is much lower than the junction-ambient thermal resistance
given in the MOSFET datasheet for the selected device package (62.5 °C/W), a heatsink
must be used.
Figure 12 shows the trend of the total losses on the line voltage for the two selected
STF21N65M5 MOSFETs.
Figure 12. Total MOSFETs losses in the 350 W FOT PFC
Power losses vs Input voltage (full load)
6
MOSFET losses (W)
5
4
3
2
1
0
80
100
120
140
160
180
Input voltage (Vac)
200
220
240
260
Conduction losses
Switching losses
Capacitive losses
Total losses
AM13311v1
DocID023523 Rev 2
21/43
Designing a CCM FOT-controlled PFC
2.3.6
AN4149
Boost diode selection
Following criteria similar to those used for the calculation of the MOSFET losses, the output
rectifier can be properly selected. A minimum breakdown voltage of 1.2·(Vout) and a
minimum current rating higher than 5·Iout (equation 26) can be considered for an initial
rough selection of the rectifier. The correct selection is then confirmed by the thermal
calculation, as the diode junction temperature must be below 125 °C.
Since this circuit operates in the continuous current mode, reverse recovery is experienced
by the diode, and the MOSFET at turn-on has to carry also the boost diode minority carrier
charge. Then, to minimize the recovery losses, an ultra-fast diode with low trr (reverse
recovery time, the time required to deplete the stored charge) and Qrr (reverse recovery
charges, the charge that must be dissipated on the MOSFET) or a SiC rectifier has to be
selected.
In this 350 W application the STTH8S06 (600 V, 8 A) has been selected and shows very fast
reverse recovery time, 12 ns typical (measured for IF =1 A). The rectifier AVG (equation 26)
and RMS (equation 33) current values, the Vth (rectifier threshold voltage) and Rd (dynamic
resistance) given in the datasheet allow calculating the rectifier losses.
From the STTH8S06 datasheet, Vth is 1.2 V, and Rd is 0.087 Ω, the conduction losses are
equal to:
Equation 63
Pdiode = Vth ⋅ I out + Rd ⋅ ID 2 rms
Pdiode = 1.2V ⋅ 0.87 A + 0.087 Ω ⋅ (2.22 A ) = 1.48W
2
Since the converter is working in continuous conduction mode the losses in the MOSFETs
due to the recovery of the boost diode have to be taken into account. The energy loss due to
the reverse recovery effect of the diode is:
Equation 64
E rr = V R ⋅ Q rr
Where VR is the reverse voltage across the output diode, when it stops conducting, that is
400 V, and Qrr the reverse recovery charges, the charge that must be dissipated through the
MOSFET. On the datasheet the graph of Qrr vs. dIF/dt is represented. Following the
0.5 xIF(AV) curve at Tj = 125 °C a value of 80 nC is found assuming the typical case of
200 A/us.
Then the recovery energy is:
Equation 65
E rr = 400 V ⋅ 80 nC = 32 μ J
And the reverse recovery losses are:
Equation 66
Prr = E rr ⋅ f sw = 32 μ J ⋅ 70 kH z = 2 . 24W
22/43
DocID023523 Rev 2
AN4149
Designing a CCM FOT-controlled PFC
If a single heatsink for the MOSFETs and diode is used, the maximum total losses of the
switches should be considered:
Equation 67
Pswitch = Ploss (90 V ) + Pdiode ( 90V ) + Prr = 5 .84 W + 1 .48 W + 2 .24 W = 9 .56 W
From this number and the given maximum ambient temperature, the total maximum thermal
resistance required can be found as:
Equation 68
R th =
125 °C − T ambx
Pswitch
R th =
125 °C − 50 °C
°C
= 7 .85
9 .56W
W
In this design in order to keep the junction MOSFET temperature below 100 °C (around
90 °C measured on the package) and to ensure a higher degree of reliability, the thermal
resistance has been chosen equal to:
Equation 69
R th =
100 °C − 50 °C
°C
= 5 .23
W
9 .57 W
DocID023523 Rev 2
23/43
L4984D biasing circuitry
3
AN4149
L4984D biasing circuitry
The following sections describe the selection of the circuitry around the L4984D.
3.1
Feedback and OVP
Pin 1 (INV): this pin is connected both to the inverting input of the E/A and to the OVP
circuitry. A resistive divider has to be connected between the boost regulated output voltage
and this pin. The internal reference on the non-inverting input of the E/A is 2.5 V (typ.), the
output voltage (Vout) of the PFC pre-regulator is set at the nominal value by the resistor ratio
of the feedback output divider. RoutH and RoutL will be then selected considering the desired
nominal output voltage and the desired output power dissipated on the output divider.
For example for a 25 mW output divider dissipation:
Equation 70
R outH =
(V out
− 2 .5V )
25 mW
2
R outH =
(400 V
− 2 .5V )2
= 6 .320 M Ω
25 mW
Please note that for RoutH a resistor with a suitable voltage rating (> 400 V) is needed, or
more resistors in series have to be used. Here three 2.2 MΩ resistors in series have been
selected.
Equation 71
R outH
400V
=
− 1 = 159
RoutL
2 .5V
R outH
V
= out − 1
R outL
2 .5V
Equation 72
R outL =
V out
159
R outL =
6 .6 M Ω
= 39 .7 kΩ
159
For RoutL a value of 160 kΩ in parallel to a 56 kΩ has been selected.
Pin 2 (COMP): this pin is the output of the E/A that is fed to one of the inputs of the
multiplier. A feedback compensation network is placed between this pin and INV. It has to be
designed in with a narrow bandwidth in order to avoid that the system rejects the output
voltage ripple (100 Hz) that would bring high distortion of the input current waveform. A
theoretical criterion to define the compensation network value is to set the E/A bandwidth
(BW) below 20 Hz. The compensated two-pole feedback network selection for this 350 W
FOT PFC has been described in detail in Section 4: FOT PFC boost control loop.
Pin 6 (PFC_OK - Feedback failure protection): PFC_OK pin has been dedicated to
monitor the output voltage of a separate resistor divider. This divider is selected so that the
voltage at the pin reaches 2.5 V if the output voltage exceeds a preset value (Vovp), usually
larger than the maximum Vout that can be expected, also including worst-case load/line
transients. For a maximum output voltage Voutmax of 430 V and selecting a 50 μA current
flowing in to the divider:
24/43
DocID023523 Rev 2
AN4149
L4984D biasing circuitry
Equation 73
RL =
V REF _ PFC _ OK
RL =
I divider
2 .5V
= 50 k Ω
50 μ A
By selecting a commercial value of 56 kΩ:
Equation 74
 V OUT _ MAX

RH = R L ⋅ 
− 1
 V REF _ PFC _ OK



 430V

R H = 56 k Ω ⋅ 
− 1  = 9 . 623 M Ω
2
.
5
V


Three resistors 3.3 MΩ in series provide the calculated value for the PFC_OK high resistor.
Notice that both feedback dividers connected to the L4984D pin #1 (INV) and pin #6
(PFC_OK) can be selected without any constraints. The unique criterion is that both dividers
have to sink a current from an output bus which needs to be significantly higher than the
current biasing the error amplifier and the PFC_OK comparator. The OVP function handles
"normal" overvoltage conditions, i.e. those resulting from an abrupt load/line change or
occurring at startup. In case the overvoltage is generated by a feedback failure, for instance
when the upper resistor of the output divider (R1) fails open, eventually the error amplifier
output (COMP) will saturate high and the voltage on its inverting input (INV) will drop from its
steady-sate value (2.5 V).
An additional comparator monitors the voltage on pin INV, comparing it against a reference
located at 1.66 V. When the voltage on pin PFC_OK exceeds 2.5 V and, simultaneously, the
voltage on pin INV falls below 1.66 V, the FFD function is triggered: the gate drive activity is
immediately stopped, the device is shut down and its quiescent consumption reduced. This
condition is latched and in order to restart the L4984D it is necessary to recycle the input
power, so that the Vcc voltage falls below 6 V (VCCrestart).
The pin PFC_OK doubles its function as a non-latched IC disable: a voltage below 0.23 V
shuts down the L4984D, reducing its consumption below 2.2 mA. To restart simply let the
voltage on the pin rise above 0.27 V. Note that these functions offer complete protection
against not only feedback loop failures or erroneous settings, but also against a failure of
the protection itself. Either resistor of the PFC_OK divider failing short or open or a pin
PFC_OK floating will result in shutting down the L4984D and stopping the pre-regulator.
DocID023523 Rev 2
25/43
L4984D biasing circuitry
3.2
AN4149
Current sense resistor
Pin 4 (CS): The pin #4 is the inverting input of the current sense comparator. Through this
pin, the L4984D senses the instantaneous inductor current, converted in a proportional
voltage by an external sensing resistor (RS). As this signal crosses the threshold set by the
multiplier output, the PWM latch is reset and the power MOSFET is turned off. The threshold
is defined by:
Equation 75
V CS = V CS _ OFF SE T + k m ⋅
(V COM P − 2 . 5V ) ⋅ V MU LT
V F2F
where:
–
VCS (multiplier output) is the reference for the current sense (VCS_OFFSET is its
offset).
–
km=0.23 (typ.) is the multiplier gain.
–
VCOMP is the voltage on pin 2 (E/A output).
–
VMULT is the voltage on pin 3.
–
VFF is the second input to the multiplier for 1/V2 function. It compensates the
control loop gain dependence on the mains voltage. The voltage at this pin is a DC
level equal to the peak voltage on pin MULT (pin 3).
The sense resistor value (RS) can be calculated as follows. For the 350 W PFC it will be:
Equation 76
Rs <
0 .84 V
= 0 .12 Ω
7 .0 A
Where:
–
ILpk is the maximum peak current in the inductor, calculated with
–
Vcsm in = 0.84 V is the minimum value of the L4984D current sense reference
clamp (VCSclamp in the datasheet).
According to the result, three parallel resistors of 0.33 Ω with 1 W of power rating have been
selected.
Because the internal current sense clamping sets the maximum current that can flow in the
inductor, the maximum peak of the inductor current will be calculated considering the
maximum Vcsclamp admitted on the L4984D:
Equation 77
IL pkx =
0 .93 V
= 8 .45 A
0 .11 Ω
The calculated ILpkx will be the value at which the boost inductor shall not saturate and it will
be used for calculating the inductor number of turns and air gap length. The power
dissipated by RS is given by:
Equation 78
Ps = 0 .11Ω ⋅ (3 .73 ) = 1 .53W
2
2
Ps = R s ⋅ ISW rms
26/43
DocID023523 Rev 2
AN4149
Mult divider and VFF
Pin 3 (MULT): the MULT pin is the second multiplier input. It will be connected, through a
resistive divider, to the rectified mains to get a sinusoidal voltage reference.
Figure 13. Multiplier characteristics
family for VFF = 1 V
Figure 14. Multiplier characteristics
family for VFF = 3 V
500
1.2
VCOMP
VCOMP
1.1
450
VFF = 3 V
1.0
400
Upper voltage clamp
Upper Voltage
0.9
5.5 V
350
0.8
5.5 V
5.0 V
300
4.5 V
0.6
0.5
Vcs (mV)
0.7
Vcs (V)
3.3
L4984D biasing circuitry
4.0 V
5.0 V
250
4.5 V
200
0.4
3.5 V
4.0 V
150
0.3
3.5 V
100
0.2
3.0 V
3.0 V
50
0.1
2.6 V
2.6 V
0
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0
0.5
1
1.5
2
2.5
3
3.5
VMULT (V)
VMULT (V)
AM13313v1
AM13314v1
A complete illustration is given by the diagrams of Figure 13 and Figure 14 which show the
typical multiplier characteristics family. The linear operation of the multiplier is guaranteed
within the range 0 to 3 V of VMULT and the range 0 to 0.82 V (typ.) of Vcs, while the minimum
guaranteed value of the maximum slope of the characteristics family (typ.) is:
Equation 79
dV CS
V
= 1 .4
dV MULT
V
The voltage on the MULT pin is used also to derive the information on the RMS mains
voltage for the VFF compensation and the brownout function:
Pin 5 (VFF): the power stage gain of PFC pre-regulators varies with the square of the RMS
input voltage. This applies as well to the crossover frequency fc of the overall open-loop
gain because the gain has a single pole characteristic. This leads to large trade-offs in the
design. For example, setting the gain of the error amplifier to get fc = 20 Hz at 264 Vac
means having fc about 4 Hz at 88 Vac, resulting in sluggish control dynamics. Additionally,
the slow control loop causes large transient current flow during rapid line or load changes
that are limited by the dynamics of the multiplier output. This limit is considered when
selecting the sense resistor to let the full load power pass under minimum line voltage
conditions, with some margin. But a fixed current limit allows excessive power input at high
line, whereas a fixed power limit requires the current limit to vary inversely with the line
voltage.
Voltage feed-forward can compensate for the gain variation with the line voltage and allow
overcoming all of the above-mentioned issues. It consists of deriving a voltage proportional
to the input RMS voltage, feeding this voltage into a squarer/divider circuit (1/V2 corrector)
and providing the resulting signal to the multiplier that generates the current reference for
the inner current control loop.
DocID023523 Rev 2
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L4984D biasing circuitry
AN4149
In this way a change of the line voltage will cause an inversely proportional change of the
half sine amplitude at the output of the multiplier (if the line voltage doubles, the amplitude of
the multiplier output will be halved and vice versa) so that the current reference is adapted
to the new operating conditions with (ideally) no need for invoking the slow dynamics of the
error amplifier. Additionally, the loop gain will be constant throughout the input voltage
range, which improves significantly dynamic behavior at low line and simplifies loop design.
Actually, with other PFC embedding the voltage feed-forward, deriving a voltage
proportional to the RMS line voltage implies a form of integration, which has its own time
constant. If it is too small, the voltage generated will be affected by a considerable amount
of ripple at twice the mains frequency that will cause distortion of the current reference
(resulting in high THD and poor PF). If it is too large, there will be a considerable delay in
setting the right amount of feed-forward, resulting in excessive overshoot and undershoot of
the pre-regulator's output voltage in response to large line voltage changes. Clearly a tradeoff was required.
The L4984D implements an innovative voltage feed-forward which, with a technique that
makes use of just two external parts, overcomes this time constant trade-off issue
whichever voltage change occurs on the mains, both surges and drops. A capacitor CFF and
a resistor RFF, both connected from the pin VFF (pin #5) to ground, complete an internal
peak-holding circuit that provides a DC voltage equal to the peak of the rectified sine wave
applied on pin MULT (pin #3). In this case following values have been selected:
Equation 80
C FF = 1μF
R FF = 1M Ω
In this way, in case of sudden line voltage rise, CFF will be rapidly charged through the low
impedance of the internal diode. In case of line voltage drop, an internal "mains drop"
detector enables a low impedance switch which suddenly discharges CFF avoiding a long
settling time before reaching the new voltage level. Consequently, an acceptably low
steady-state ripple and low current distortion can be achieved without any considerable
undershoot or overshoot on the preregulator's output like in systems with no feed-forward
compensation. This pin is internally connected to a comparator in order to provide the
brownout (AC mains undervoltage) protection. A voltage below 0.8 V shuts down (does not
latched) the L4984D and brings its consumption to a considerably lower level. The L4984D
restarts as the voltage at the pin rises above 0.88 V. These data have to be considered
during the MULT divider selection, setting the minimum operating voltage.
Please find here following the procedure to set properly the operating point of the multiplier
and the divider resistor values. Supposing a 60 uA (IMULT) current flowing into the multiplier
divider, the lower resistor value can be calculated:
Equation 81
RmultL =
VMULT max 3.00V
=
= 50 kΩ
I MULT
60μA
A commercial value of 51 kΩ for the lower resistor is selected. The upper resistor value can
now be calculated:
Equation 82
R multH =
28/43
1− kp
kp
⋅ R multL =
1 − 8 ⋅ 10 −3
⋅ 56 kΩ = 6 .944 M Ω
8 ⋅ 10 −3
DocID023523 Rev 2
AN4149
L4984D biasing circuitry
In this application example a RmultH = 6.9 MΩ and a RmultL = 51 kΩ have been selected.
Please note that for RmultH a resistor with a suitable voltage rating (> 400 V) is needed, or
more resistors in series will have to be used.
The voltage on the multiplier pin with the selected component values re-calculated at
minimum line voltage is 0.93 V and at maximum line voltage is 2.74 V, so the multiplier will
work correctly within its linear region. Finally, depending on the MULT resistors the brownout
functions also have to be checked, calculating the VSTART and VSTOP voltages:
Equation 83
0 .88 V
V START =
2
⋅
R multH + R multL
R multL
V START =
0 .88V
⋅
R multH + R multL
R multL
V STOP =
0 .80V
2
⋅
6 .9 M Ω + 56 k Ω
= 77 .29V
56 k Ω
⋅
6 .9 M Ω + 51 kΩ
= 70 .2V
51 k Ω
Equation 84
V STOP =
0 .80 V
2
2
Start and stop PFC voltages are suitable for correct operation by the PFC; the MULT divider
has to be set considering these two voltages, in order to disable the PFC with an anomalous
input low mains voltage that could cause an overheating of the PFC due to the higher input
mains current. In order to set the required voltage startup threshold reiterations could be
required by selecting MULT resistors and checking the actual PFC start voltage.
3.4
Gate driver (GD) and VCC pins
Pin 8 (GND): this pin acts as the current return both for the signal internal circuitry and for
the gate drive current. When laying out the printed circuit board, these two paths should run
separately.
Pin 9 (GD): is the output of the driver. The pin is able to drive an external MOSFET with
600 mA source and 800 mA sink capability.
The high-level voltage of this pin is clamped at about 12 V to avoid excessive gate voltages
in case the pin is supplied with a high Vcc. To avoid undesired switch-on of the external
MOSFET because of some leakage current when the supply of the L4984D is below the
UVLO threshold, an internal pull-down circuit holds the pin low. The circuit guarantees 1.1 V
maximum on the pin (at Isink=2mA), with Vcc > VCC_ON. This allows omitting the "bleeder"
resistor connected between the gate and the source of the external MOSFET used for this
purpose.
Pin 10 (VCC): is the supply of the device. This pin will be externally connected to the startup
circuit (usually, one resistor connected to the rectified mains) and to the self-supply circuit.
Whatever the configuration of the self-supply system, a capacitor will be connected between
this pin and ground. To start the L4984D, the voltage must exceed the startup threshold (12
V typ.). Below this value the device does not work and consumes around 65 µA (typ.) from
VCC. This allows the use of high value startup resistors (in the hundreds of kΩ), which
reduces power consumption and optimizes system efficiency at low load, especially in widerange mains applications. When operating, the current consumption (of the device only, not
considering the gate drive current) rises to a value depending on the operating conditions
but never exceeding 6 mA. The device keeps on working as long as the supply voltage is
over the UVLO threshold (13 V max). If the VCC voltage exceeds 22.5 V, an internal Zener
DocID023523 Rev 2
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FOT PFC boost control loop
AN4149
diode, 20 mA rated, will be activated in order to clamp the voltage. Please remember that
during normal operation the internal Zener will not have to clamp the voltage, because in
that case the power consumption of the device will increase considerably and its junction
temperature will also increase. The recommended operating condition for safe operation of
the device is below the minimum clamping voltage of the pin.
4
FOT PFC boost control loop
In order to find a compensation network ensuring stability over a large variety of operating
conditions and to prevent dangerous oscillations of the output voltage as a result of load
changes, it is necessary to have a correct understanding of the control loop of FOT PFC
systems.
The loop gain of PFC pre-regulators must have a very low crossover frequency (fc) so as to
keep VCOMP (error amplifier output) fairly constant over a given line cycle, filtering twice the
line frequency ripple on the output of the error amplifier, in order to ensure low THD (total
harmonic distortion). As a rule of thumb, fc should not exceed 20 Hz.
The small signal model of a PFC stage with a constant power load (the regulated DC-DC
converter) can be represented as a controlled current source delivering power to the output
capacitor.
Figure 15. Small signal model of a PFC stage with a constant-power load (DC-DC
converter)
Io
Co
Vo
AM13315v1
The current generator:
îo
is controlled by the small-signal AC control voltage:
v̂c
and the system acts as a pure integrator and the resulting control-to-output transfer function
is:
Equation 85
v̂ o
G
= G ( jω ) = o
v̂ c
jω
30/43
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AN4149
FOT PFC boost control loop
where the unity gain factor Go is given by the following expression regardless of the control
method and the characteristics of the control IC:
Equation 86
Go =
V out
Pout
⋅ (V C − V C 0 ) ⋅ C o
In the previous expression Vc is the error signal of the voltage control loop (voltage on the
COMP pin for the L4984D), that is, the output of the error amplifier, and VCO the "zeropower" level of the control voltage, that is, the burst mode threshold of COMP voltage (2.4 V,
typ.).
The effective control voltage Vcomp - VC0, can be expressed for the L4984D starting from the
expression of the variation of signal out from the modulator with respect to the E/A output
(COMP) change, using the formula indicated in the datasheet of the L4984D (equation 87).
Equation 87
V CS = VCS _ OFFSET + k m ⋅
(V COMP
− 2 .4V ) ⋅ V MULT
2
V FF
Where km is the small signal multiplier gain assumed here equal to the large single gain km
(typ. 0.304). From this expression, replacing:
Equation 88
V CS = R S ⋅ I Lpk
V FF =
2 ⋅ V AC ⋅ K
p
and rewriting equation 31 which describes the maximum inductor peak current as:
Equation 89
IL pk =
K 
2 ⋅ I out ⋅ V out 
⋅ 1 + r 
2 
η ⋅ V AC ⋅ PF 
the effective control voltage Vcomp-VCO can be found:
Equation 90
V COM P − VC 0 =
2 ⋅ R S ⋅ K p ⋅ Pin 
K 
⋅ 1 + r 
2 
Km

Then this expression can be used to find the unity gain factor (equation 86):
DocID023523 Rev 2
31/43
FOT PFC boost control loop
AN4149
Equation 91
Go =
Go =
km
K 

2 ⋅ η ⋅ Vout ⋅ R S ⋅ k p ⋅ 1 + r  ⋅ C o
2 

0. 23
0 .27 

2 ⋅ 0 .92 ⋅ 400V ⋅ 0 .11Ω ⋅ k p ⋅ 1 +
 ⋅ 200 ⋅ μ F
2 

= 955 .7
Looking at Figure 16, related to the gain and the phase of the control-to-output transfer
function, it is possible to notice that it has just one pole at the origin. The gain falls with a
slope -20 dB/dec and the phase shift is -90 ° at all frequencies.
It can also be noted that the crossover frequency is much higher than the one required for a
PFC (lower than 20 Hz). To make the gain roll off at low frequency (so as to cross the 0 dB
axis at low frequency) and to boost the phase in the neighborhood of the crossover
frequency (so as to increase phase margin), type II compensation is usually used, which
adds a pole-zero couple.
Figure 16. Bode plots of the control-to-output transfer function
AM13316v1
Figure 17. Schematic diagram of a type II compensation
C1
R2
C2
R1
VOUT
Vref
VCOMP
AM13317v1
32/43
DocID023523 Rev 2
AN4149
FOT PFC boost control loop
The transfer function of the compensated error amplifier is:
Equation 92
G EA ( s ) =
1+
1
R INV
_H
⋅ C1
⋅
1
s ⋅ R2 ⋅ C 2

C1 + C 2
s ⋅  1 +
s ⋅ R 2 ⋅ C1 ⋅ C 2




In order to calculate the values of the components of the compensation network, the
Venable K-Factor calculation is used, starting from the amount of phase margin needed at
the crossover frequency and the desired maximum 3rd harmonic distortion level D3.
Phase margin is defined as the difference between 180 ° and the actual phase lag at the
frequency where the open-loop gain is unity. The higher the phase margin, the more overdamped the system is. As rule of thumb, to ensure fast transient response with a good level
of ringing, a phase margin of 60 ° has to be chosen.
Φ m = 60 °
D 3 = 2%
The Venable K-factor is defined as:
Equation 93
 π

⋅φm 
1 + sin 
 180
 = 3 . 732
K =
π


⋅φm 
cos 
 180

The required E/A gain (at 2fL) in order to keep the distortion below the desired maximum 3rd
harmonic distortion (D3) is:
Equation 94
H 2f =
2 ⋅ D 3 ⋅ (V COM P − V C 0 )
=
Δ V ou t 2
2 ⋅ 0 .02 ⋅
H 2f =
2 ⋅ D3 ⋅
2 ⋅ R S ⋅ k p ⋅ Pin 
K 
⋅ 1 + r 
km
2 

Δ V out 2
2 ⋅ 0. 011Ω ⋅ 8 ⋅ 10 − 3 ⋅ 380.4W 
0. 27 
⋅ 1 +

0.23
2 

= 0 .018
14. 81V 2
while the unity frequency gain is:
Equation 95
H0 =
4π ⋅ f LINE _ min ⋅ H 2 f
K2
H0 =
4π ⋅ 47 Hz ⋅ 0 .018
= 0 .763
3 .732 2
The frequency of the zero and the pole of the compensation network can be found with the
following two expressions, where Go is the unity gain factor (equation 91).
DocID023523 Rev 2
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FOT PFC boost control loop
AN4149
Equation 96
z=
1
⋅
2π
Go ⋅ H o
K
z =
1
⋅
2π
955 .7 ⋅ 0 .763
= 2 . 2 Hz
3. 732
Equation 97
p=
K
⋅ Go ⋅ H o ⋅ K
2π
p=
3 .732
⋅ 955 .7 ⋅ 0 .763 ⋅ 3 .732 = 30 .9 Hz
2π
Then the values of the components can be calculated as follows.
Feedback parallel capacitor:
Equation 98
C1 =
1
z
⋅
H o ⋅ R outH p
C1 =
1
2.2 Hz
⋅
= 14 .1nF
0 .763 ⋅ 6 .6 M Ω 30 . 9 Hz
A value of 22 nF has been selected for the parallel feedback capacitor.
Feedback series capacitor:
Equation 99
 p− z
C 2 = C1 ⋅ 

 z 
 30 .9 Hz − 2. 2 Hz 
C 2 = 22 nF ⋅ 
 = 287 nF
2 .2 Hz


A value of 220 nF has been selected for the series feedback capacitor.
Feedback series resistor:
Equation 100
R2 =
1
2π ⋅ z ⋅ C 2
R2 =
1
= 328 .8 k Ω
2 π ⋅ 2 .2 Hz ⋅ 220 nF
A value of 330 kΩ has been selected for the series feedback resistor.
The gain and the phase of the transfer function of the type II amplifier are represented in the
bode plots in Figure 19.
Figure 18. Bode plots of a type II amplifier's transfer function
AM13318v1
34/43
DocID023523 Rev 2
AN4149
FOT PFC boost control loop
The closed-loop transfer function is the product of the control-to-output transfer function
(equation 85) and the E/A transfer function (equation 92):
Equation 101
D3 =
D3 =
D3 =
H 2 fL ⋅ Δ V out 2 100
⋅
V COM P − V C 0
2
H 2 fL ⋅ Δ V out 2
100
⋅
2 ⋅ R S ⋅ k p ⋅ Pin 
K  2
⋅ 1 + r 
2 
km

0 .0 11 ⋅ 14 .81 / 2
1 00
⋅
= 1 .286
−3
2 ⋅ 0 .011 Ω ⋅ 8 ⋅ 10 ⋅ 380 .4W 
0 .27  2
⋅ 1 +

0 .23
2 

The gain and the phase of the closed-loop transfer function is represented in the Bode plots
in Figure 20.
Figure 19. Bode plots of the closed-loop transfer function
AM13319v1
Finally all the parameters describing the actual closed-loop transfer function are calculated.
Crossover frequency:
Equation 102
f c = root ( F (2 πf − 1, f
))
f c = 5 . 9 Hz
Phase margin:
Equation 103
Φ = 180 ° + Φ F (2 ⋅ π ⋅ f c )
Φ = 56 .4 °
E/A gain at 2fL:
DocID023523 Rev 2
35/43
FOT PFC boost control loop
AN4149
Equation 104
(
)
H 2 fL = H 4 ⋅ π ⋅ f LINE _ min = 0 . 011
From equation 90 and equation 104 the actual 3rd harmonic distortion can be found:
Equation 105
D3 =
H 2 fL ⋅ Δ V out 100
⋅
= 1 .253
V COMP − V ref
2
The comparison between Figure 20 and Figure 21 shows the practical difference between
two different configurations of compensation network. In the first case, where the series
resistor R2 is such to move the "phase boost" far from the crossover frequency, the phase
margin is very low (around 22 °) then the system is underdamped, experiencing large
overshoots and ringings. In the second case where the phase margin is around 56 ° the
response of the system to the load variation is fast and without ringing, thus with limited
deviations.
Figure 20. 115 Vac step load (50 % to 100
%): improper compensation
36/43
Figure 21. 115 Vac step load (50 % to 100
%): good compensation
DocID023523 Rev 2
AN4149
5
Layout hints
Layout hints
The layout of any converter is a very important phase in the design process which is
sometimes neglected by the designers. Even if the layout phase sometimes looks to be
time-consuming, a good layout undoubtedly saves time during the functional debugging and
the qualification phases. Additionally, a power supply circuit with a correct layout needs
smaller EMI filters or less filter stages, allowing consistent cost saving.The L4984D does not
need any special attention to the layout, just requiring that the general layout rules for any
power converter be carefully applied. Basic rules are listed here below, using the EVL4984350W PCB layout as a reference (Figure 23).
–
Keep the power and signal RTN separated. Connect the return pins of the
components carrying high current such as the input filter, sense resistors or output
capacitors as close as possible. This point is the RTN star point. A downstream
converter must be connected to this return point.
–
Minimize the length of the traces relevant to the boost inductor, MOSFET's drain,
boost rectifier and the output capacitor.
–
Keep signal components as close as possible to each relevant pin of the L4984D.
Specifically, components and traces relevant to the error amplifier have to be
placed far from traces and connections carrying signals with high dV/dt, such as
the MOSFET's drain.
–
Connect heatsinks to power GND.
–
Add an external shield to the boost inductor and connect it to power GND.
–
Please connect the RTN of the signal components including the feedback,
PFC_OK and MULT dividers close to pin 8 (GND) of the L4984D.
–
Connect a ceramic capacitor (100÷470 nF) close to pin #10 (VCC) and to pin #8
(GND) of the L4984D. Connect this point to the RTN star point (see rule 1).
Figure 22. EVL4984-350W PCB layout (SMT side view)
AM13320v1
DocID023523 Rev 2
37/43
Design example using the L4984D-CCM PFC excel spreadsheet
6
AN4149
Design example using the L4984D-CCM PFC excel
spreadsheet
An excel spreadsheet has been created for a quick and easy reference in order to design a
boost CCM PFC pre-regulator using the L4984D.
Figure 22 shows the first sheet already precompiled with the input design data used in
Section 2.1.
Figure 23. Excel spreadsheet design specification input table
Figure 24. Other design data
The spreadsheet generates a complete list of parts of the PFC schematic represented in
Figure 25 on page 39 including the power dissipation calculation of the power components,
following the calculation procedure described in this document .
38/43
DocID023523 Rev 2
AN4149
Design example using the L4984D-CCM PFC excel spreadsheet
Rs
MOS
D
COUT
ROUTL
ROUTH
Vout
RH
RL
Figure 25. CCM PFC schematic based on the L4984D
2
6
L4984D
PFC-OK
VFF
RFF
5
7
TIMER
CS
GND
MULT
3
CcompS
~
~
CFF
_
RmultH
90-264Vac
CcompP
RmultL
+
BRIDGE
4
8
9
GD
COMP
2
1
INV
CIN
VCC
10
VCC
L
C_TIMER
1
3
RcompS
AM13324v1
DocID023523 Rev 2
39/43
Design example using the L4984D-CCM PFC excel spreadsheet
AN4149
The bill of material for Figure 25: CCM PFC schematic based on the L4984D is
automatically compiled by the excel spreadsheet. It summarizes all selected components
and some pertinent data.
Figure 26. Excel spreadsheet BOM
350
BRIDGE RECTIFIER
W FOT PFC BASED ON L4984D
BILL OF MATERIAL
Selected
Value
D15XB60
MOSFET P/N
2 x STF21N65M5
DIODE P/N
STTH8S06
Inductor
Max peak Inductor current
L
Ilpkx
700
7.91
μH
A
Pin 4 – CS Sense resistor
Power dissipation
Rsx
Ps
0.11
1.53
Ω
W
INPUT Capacitor
Cin
1
μF
OUTPUT Capacitor
Cout
330
μF
Pin 3 - MULT Divider
Rmult L
Rmult H
100
12500
kΩ
kΩ
CT
680
pF
fs
72.26
kHz
RoutH
RoutL
6600
41.5
kΩ
kΩ
RL
RH
56
9900
kΩ
kΩ
Pin 1,2 - Compensation
Network
CcompP
CcompS
RcompS
22
220
390
nF
nF
kΩ
Voltage Feedforward
CFF
RFF
1000
1000
nF
kΩ
Pin 7 - TIMER capacitor
Switching frequency
Pin 1 - Feedback Divider
Pin 6 - Output divider for
PFC_OK
IC Controller
40/43
Unit
[]
L4984D
DocID023523 Rev 2
AN4149
7
References
References
–
L4984D, CCM PFC controller", datasheet.
–
A new continuous-time model for current-mode control with constant frequency,
constant On-time and constant Off-time, in CCM and DCM", IEEE power
electronics specialists conference record, San Antonio, Texas, pp. 382-389, 1990.
–
Current mode control, venable technical paper #5, www.venableind.com.
–
Fixed-Off-Time control of PFC pre-regulators", 10th European conference on
power electronics and applications, EPE2003, Toulouse France, paper 382.
–
A systematic approach to frequency compensation of the voltage loop in boost
PFC pre-regulator", abstract.
DocID023523 Rev 2
41/43
Revision history
8
AN4149
Revision history
Table 1. Document revision history
42/43
Date
Revision
Changes
07-Mar-2013
1
Initial release.
06-Jun-2013
2
Updated title in cover page and Figure 26: Excel spreadsheet BOM.
Minor text changes.
DocID023523 Rev 2
AN4149
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