Simplifying Power Factor Correction in SMPS

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Simplifying Power Factor
Correction in SMPS
By Jon Mark Hancock, Senior Applications Engineer,
Infineon Technologies NA, San Jose, Calif.
A high-performance controller integrates
protection functions using failure mode error
analysis combined with the predictable switching
behavior of superjunction MOSFETs and SiC
Schottky diodes.
ne “component” in the quest for improved energy efficiency and power
quality is the use of active harmonic
filter power factor correction (PFC)
in switched-mode power supplies
(SMPSs) for computing and industrial applications.
Active PFC offers several well-known benefits, including
automatic line-voltage adjustment, marked improvement
of ac mains power quality in medium- and high-power
applications, and stabilization of the SMPS bulk bus voltage. These features, in turn, improve cost factors and the
holdup time of the isolated PWM converter.
Though the basic implementation of active PFC with a
boost converter is topologically quite simple, the devil is
in the details. One challenge is managing surge current at
startup and during brownouts due to cycle skip. It’s also
difficult to achieve high efficiency and compact size simultaneously at higher power levels where continuous current
mode (CCM) operation is preferred for the boost inductor because of the lower EMI and switch/diode stress associated with CCM.
To demonstrate how these various requirements may
be met, a design example for a 650-W power supply will be
presented using a new high-integration PFC controller for
continuous conduction mode PFC. This controller will be
combined with a very low switching loss superjunction
MOSFET and a SiC Schottky diode in hard switching. The
basis of this design, the ICE1PCS01 controller, is the first
CCM PFC with enhanced protection and management
features integrated into compact 8-pin DIP or SOIC.
This controller replaces other larger package types usually used for this application with no loss in functionality.
The integration level of the ICE1PCS01 and the simplification of the PFC implementation are reflected in a simplified design process aided by an available XL design tool.
While the PFC boost converter is a simple topology in
principle, the inherently wide range of operating input
voltage (85 Vac to 265 Vac in this example) requires evaluation in the design process. In particular, the wide input
range relates to stress factors such as brownout and cycle
skip recovery, when switch and diode current max out.
Simple calculations can be used to establish the basic operating conditions and component values. Using a calculation program like MathCAD makes it feasible to estimate
the operating waveforms and losses based on the waveforms expected over the complete ac operating cycle. This
analysis makes possible a more complete design synthesis
in the first pass before building and testing hardware.
With this approach, we’ll explore two variants on a
650-W PFC design. One version uses a 250-kHz clock to
achieve component size reduction, while the other trades
size for other benefits with a more typical 100-kHz
version. Requirements for the proposed design are listed
in the table.
About 10% extra power is budgeted to compensate for
the efficiency loss of the PWM stage following the PFC
O
Power Electronics Technology
October 2004
Name
Input voltage range
Value
90 Vac to 265 Vac
Nominal output voltage
Vout
400 V
Rated output power to
PWM
Pout
650 W
h
92% +
Target efficiency
Minimum bus operating
voltage
Inductor ripple current
Operating pulse
frequency
26
Symbol
VINmin - VINmax
VBUSmin
300 V
IRipple
20% to 30% IPk
fS
250 kHz
Minimum holdup time
THoldup
20 msec
Line dropout voltage
(effective min low line)
VIN_rms
75 Vac
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Power Electronics Technology October 2004
POWER FACTOR CORRECTION
boost converter. “Brownout” holdup voltage is the worstcase electrical performance required but not for sustained
thermal capability. It also considers the requirement to
provide full output power while charging/recharging the
bulk bus cap (such as during cycle skip recovery). For this
reason, we’ll use 75 Vac as the effective low-line value for
power limiting.
Next, the MOSFET tON time is calculated for fS = 250 kHz
(6)
And finally, estimate nominal inductor value as follows:
Passive Component/Rectifier Parameters
First, we’ll estimate the peak input current based on Pout,
target efficiency h, and VIN_rms,
(7)
For 100-kHz, the inductance calculated is about 270 µH.
How do these two inductors compare, using equivalent
cores and design practices? Using standard methods for
synthesizing SMPS inductor design,[1] assume a no loadto-full load inductance/permeability drop of 30% to 40%
with a powdered MPP core.
The realized design for 250 kHz uses a 55439-A2 core
with 34 turns of two strands of AWG 15 wire, resulting in a
net loaded inductance of ~108 µH, with a no load inductance of 165 µH, and estimated core losses of 2.4 W and
copper losses of 3.6 W, for a total estimated loss of 6 W at a
75-Vac input. In contrast, the 270-µH 100-kHz inductor
was realized with two stacked 55439-A2 cores and 38 turns
of two strands of AWG 15, resulting in estimated core loss
of 1.6 W, estimated copper loss of 7.5 W (including
the effect of longer path length) and total estimated losses
of 9.1 W.
This loss is almost 50% higher than that achieved with
the 250-kHz 112-µH inductor. However, the argument for
lower operating frequency usually is reduced losses with
a focus on semiconductors. The inductor losses can be
reduced, but only with a larger, more expensive construction. The issue for the designer, then, is how much the
change in operating frequency affects the semiconductor
losses and EMI filter, and if with the total losses the overall
reduction in magnetics volume and cost is worthwhile.
(1)
Next, estimate dissipation of power rectifier for total loss
calculation and heatsink sizing:
(2)
Calculate the thermal impedance to ambient RthHS required
for power rectifier; assume maximum junction temperature TJmax = 150°C, maximum ambient temperature TAmax
of 70°C, Junction to HS RthJHS = 2 K/W,
(3)
The boost inductor is sized based on the ripple currentto-line current ratio, which has a typical range of 20% to
30%. The inductance value depends on the chosen switching frequency and the tolerable current ripple. Space limitations preclude a detailed discussion of the tradeoff, but
let’s examine two possibilities: One will be at 100-kHz
reflecting typical industry practice with standard semiconductor components, and the other will be at 250 kHz,
which is easily achieved with superjunction MOSFETs and
silicon carbide Schottky rectifiers.
The worst-case ripple current will be determined by the
duty cycle of the switch at the peak voltage of low line and
the clock frequency used. This won’t be the point of highest duty cycle in the switch, but it will reflect the highest
current and current ripple in the inductor.
Considering the basic input-to-output duty cycle (D)
transfer function of the boost converter:
Bulk Capacitor
The bulk capacitor selection process is driven primarily
by the required ripple current capability, hold-up time requirements and operating voltage. For a nominal bulk bus
of 400 V, a 450-V capacitor should provide adequate margin considering the overvoltage protection (OVP) response
characteristics of the ICE1PCS01.[2]
Holdup time is dependent on the range of bulk bus
operation for the PWM isolation converter. The wider
the range over which the converter can operate, the smaller
the bulk capacitor possible. However, at the same time,
this widening of input voltage range compromises the
efficiency and transformer utilization of the output converter. A typical compromise might be an operating range
extending down to 300 V. Then, the necessary value can be
calculated:
(4)
Then, calculate the duty cycle at the peak of the waveform
(substituting root of 2, times the ac value) in the equation:
(5)
Power Electronics Technology
October 2004
28
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POWER FACTOR CORRECTION
Fig. 1. Boost switch and boost diode duty
cycle for 75 Vac in, 400 V out.
Fig. 2. Average and min/max inductor current.
Fig. 3. Average input current and switch/diode
average current.
Next, taking a data point at one quarter of the ac period
interval should yield the peak input current:
(8)
The bulk capacitor was realized in the demonstration
design using two 180-µF caps. This parallel combination
of two capacitors provides a higher total ripple current rating and better cooling (from increased surface area) than
would a single capacitor.
Iin_max = 13.93 A
(12)
This agrees with the value calculated in equation (1).
Using the same range variables, the duty cycle for the switch
and diode can be calculated and plotted (see Fig. 1) over
one ac mains period:
Boost Switch and Boost Rectifier
Estimating the operating conditions and losses for the
boost switch and diode are difficult to do with any accuracy if only simplified expressions are used to define the
operating conditions. In particular, the switching loss is
dependent on instantaneous current and clock frequency.
To address this reality, the operating ripple current and
pulse-by-pulse operation is calculated to estimate the total
loss. These operating points are determined by the input
voltage and current over one complete ac cycle. First, functions specifying the ac operating period and the input voltage and an indexed variable for the period are defined as:
(13)
Next, the ripple current DI as a function of input voltage and operating duty cycle is calculated for the on time
(switch) and off time (diode):
(14)
(9)
(15)
A plot of the estimated minimum and maximum inductor current for 110 µH inductor and 250- kHz switching frequency is shown in Fig. 2. These are the currents
which have to be handled by the boost switch and boost
rectifier. The average and RMS switch current can be calculated by integration (see Fig. 3):
(10)
Using the previously calculated values for RMS input
current, a waveform for the PFC input current is calculated:
(11)
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(16)
29
Power Electronics Technology October 2004
POWER FACTOR CORRECTION
IS _ rms :=
1
⋅∫
Tmain
0 ⋅ms
Tmain
IS (tmain ) dtmain
2
The turn-off calculation is a complex function of current amplitude, RG and device type, which isn’t shown in
detail here for space limitations:
IS _ rms = 7.645 A (17)
PS _ off (tmain ) := Eoff _ type (tmain )⋅ fS
Waveforms of maximum and minimum switch current
peak current are used to determine the switching losses:
1

 1
iS _ max (tmain ) := iin (tmain ) + ⋅ ∆L _ on (tmain ) ⋅

 NS
2


1
1
iin (tmain ) − ⋅ ∆L _ on (tmain ) if iin (tmain ) ⟩ ⋅ ∆L _ on (tmain )
2
2
0 ⋅ A otherwise
iS_min (tmain ) := 
 1
 ⋅ NS
PS _ off _ avg :=
(18)
Tmain
⋅∫
Tmain
0⋅ms
(19)
The peak diode
currents, of course,
are at the same
amplitude as the
peak switch currents. Considering
the average and
RMS values, some
care should be taken
because of the high
crest factor of peak
current to average
current in the boost
rectifier. Under
surge conditions as
when recovering
from cycle skip, the
duty cycle ratios can
flip while very high
peak current exits in
the diode. This ac- Fig. 4. Plots of conduction, switching losses for
tion raises the surge boost transistor, both instantaneous and
power dissipation averaged.
dramatically for up to several ac mains cycles unless protective measures are taken by the controller.
The diode conduction losses depend on the forward
characteristic of the diode, which must be considered in
the loss calculation. The silicon carbide Schottky rectifier
can be modeled as a junction potential with a negative temperature coefficient combined with a drift region resistance
with a positive temperature coefficient. The operating
waveform of diode current can be calculated over one ac
mains period as follows:
(20)
Switching Losses in MOSFET
Using data that is also incorporated in the data sheets
regarding switching loss behavior for turn-on (Eon) and
turn-off (Eoff), and switching behavior as a function of gate
resistance and load current, functions have been defined
in MathCAD, which calculate the turn-on and turn-off
losses in joules per switching event (space limitations preclude including full details here).
These switching event losses are multiplied based on
the SMPS switching frequency to calculate the total loss.
Switching loss behavior in superjunction MOSFETs such
as CoolMOS is often much lower than for conventional
vertical DMOS transistors because of the effect of the
nonlinear output capacitance, which acts as a nonlinear
snubber capacitor, reducing turn-off losses over those
expected.[3]
PS _ on (tmain ) :=
ND
NSiC _ test
Eon _ type (tmain )⋅ fS
(21)
Integration gives the average turn-on losses:
PS _ on _ avg :=
1
Tmain
⋅∫
Tmain
0⋅ms
PS _ on (tmain )dtmain
PS _ on _ avg = 3.251W
Power Electronics Technology
ID (tmain ) := iin (tmain )⋅ dD (tmain )⋅
(22)
October 2004
(25)
Conduction and Switching Losses in Diode
PS _ cond (tmain )dtmain
PS _ cond _ avg = 12.191W
PS _ off (tmain )dtmain
PS := PS _ cond _ avg + PS _ on _ avg + PS _ off _ avg
PS = 22.953W
Integration of momentary values gives average conduction losses.
1
Tmain
(24)
In comparison, at 100 kHz the turn-on losses are estimated at 1.3 W and turn-off at 3 W. This amounts to a
difference of ~7 W, partially offset by lower inductor losses
by 3 W.
Combining conduction and switching power losses in
the boost switch (see Fig. 4):
⋅RdsON _ type (TJ _ S )⋅ dS (tmain )
PS _ cond _ avg :=
⋅∫
Tmain 0⋅ms
PS _ off _ avg = 7.511W
Then the switch conduction losses can be calculated,
considering the RON, conduction time and current:
2


iS_min (tmain )
1 

PS _ cond (tmain ) := ⋅ +iS _ max (tmain )⋅ i S_min (tmain )


3
2


+iS_max (tmain )
1
(23)
30
1
ND
(26)
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POWER FACTOR CORRECTION
The average and RMS current are then calculated by integration:
(32)
In comparison, at 100 kHz, the estimated turn-off losses
are 0.42 W, not a significant difference.
Then the total power losses in the boost diode are the
sum of conduction and switching loss:
(27)
PD: = PD_cond_avg + PD_off PD = 6.897W
Heatsink Calculations
(28)
Heatsink calculations for the boost switch and diode
must account for the thermal interface material between
the transistor and diode package and the heatsink. This
varies by type, but for popular TO-220 materials it’s in the
range of 1.5 K/W, and for the TO-247 package, the greater
area yields about 1 K/W. If one uses a maximum ambient
of 50°C and a maximum junction temperature target of
130°C, for conservative derating practice, the heatsink to
ambient impedance follows:
Next, minimum and maximum diode currents can be
calculated over one mains period:
(29)
(33)
The instantaneous conduction loss is calculated from:
At this thermal impedance, forced air flow will make a
substantial size reduction possible for the heatsink. With
different requirements for junction temperature or ambient, the parameters can be modified accordingly. The diode heatsink requirements can be calculated similarly:
(30)
(34)
From integration of the results of this function the averaged loss over the mains period is calculated:
PD _ cond _ avg = 5.847W
Calculation of Other Component Parameters
The ICE1PCS01 PFC controller integrates functions for
soft-start, open-loop protection, brownout protection, enhanced dynamic loop response, soft and hard overcurrent
protection [7]. It operates with duty cycle capability exceeding 95% and can be used over a wide switching frequency
range, up to 250 kHz. The built-in totem pole driver can
supply up to 1.5 A for driving a MOSFET or IGBT boost
switch.
Only a few external parts are required to define functionality for the output voltage set point, operating frequency, maximum power output, soft-start, voltage control loop bandwidth and average mode current loop (Fig.
5). Components to determine include the current sense
resistor, the frequency setting resistor, the average current
mode compensation and the voltage loop compensation.
The compensation network design for a PFC controller
is critical because of the influence on main performance
(31)
Diode Switching Loss
In the case of conventional ultrafast silicon diodes,
calculating the switching losses is quite complex, if
possible at all, due to the several nonlinear effects on Qrr
behavior. These effects include rising effective Qrr with rising di/dt and rising temperature. For SiC Schottky diodes,
the matter is greatly simplified, as there is no Qrr per se,
only a displacement charge exists due to the depletion capacitance, for which loss is easily estimated per switching
cycle.[4, 5, 6]
For the proposed 6-A SiC Schottky rectifier:
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31
Power Electronics Technology October 2004
POWER FACTOR CORRECTION
D6 IN4746
D7
IN4746
Shutdown
RLY1
G2RL-DC12
CY1 SIOV1
TB2
F1
L2
L3
T5A
SMV-10
D8
4n7
CX1
u68
u68
CMV-60
CY2
L4 110uH
BR1
GBJ2506
4n7
220R
C15 01u C10
+
22uF
1N
4
VSENSE
GND
ICOMP
180uF
+C18 R12
201K
180uF
C18
u68
R17
5K11
VCOMP
1
R24
22K6
+VO
TB3
GND-Vo
OR1
Gate H
GATE
2
ISENSE FREQ
C21
SPW35N60C3 Q2
C17
1u5 R5
R15
R25 6R8
12K
OR1
R18
650W CCM-PFC
8
3
C1
SDT068S60
OR1
R19
R20
IC1
ICE1PCS01
V+12
7
VCC
R11
C22 +201K
D9
6A6-T
CX2
6
Shutdown
2N3904
Q1
5
R23
10K
R1
1K
C11
u22
C20
1u0
R2
1K
Fig. 5. Schematic of PFC design example.
this resistor can be generated at initial charge of the bulk
capacitor, it’s required to include a series resistor of
~200 V on the current sense pin to prevent damage from
excess voltage to the ISENSE input.
The current loop is controlled by a transconductance
amplifier OTA2, which has two inputs: a signal from the
nonlinear gain block and a signal from the current-sense
pin. The main variable from a design viewpoint is the
switching frequency of the converter. Due to the influence
of the nonlinear gain block, it is necessary to add an additional capacitance in the range of 0.5 nF to the calculated
value:
areas, including loop transient response, THD for input
current and the net power factor.[7] The maximum average
input current, Iin_max, was previously calculated in equation
12. However, for the current-sense resistor calculation
the effect of inductor ripple current, as shown in Fig. 2,
must be used. Considering the soft limiting threshold of
700 mV for the current sense input to determine the maximum output power, the current sense resistor value is found
from:
IS _ peak = 15.321A
RCS : + =
0.7V
(35)
IS _ peak
GOTA 2 := 1.1 ⋅ 10
RCS = 0.046Ω
fSW := 250 ⋅ 10
The current sense resistor should be a low-inductance
type. Paralleled high-current surface-mount devices
(SMDs) work better in this application than axial-leaded
resistors because of the much lower inductance of the
SMDs. In the design shown, SMD resistors were paralleled
with a slightly lower resistance than the calculated value, as
this is offset by the PCB trace resistance.
Because a high surge current and voltage drop across
Power Electronics Technology
October 2004
C10 :=
−3
3
GOTA 2
2 ⋅ p fSW
+ 0.5 ⋅ 10
−9
C10 = 1.2 × 10
−9
(36)
Output voltage setting (feedback loop) is determined
by the internal VREF and R17 and
R11+R12 externally; targeting 400 V, and assuming a
value of 5.11 kO for the shunt resistor R17,
32
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POWER FACTOR CORRECTION
the lines voltage from the current fed through
the boost rectifier (Fig. 3). The voltage-loop
compensation must be set so that this ripple
is not amplified through the control loop. Instead, it should be well suppressed, by setting
the error amp loop gain to unity in the neighborhood of one-tenth the mains frequency.
For stability reasons, a phase lead is used to
improve the phase margin. The chosen values for R23, C11 and C20 are shown in Fig. 5.
C11 = 1 × 10-7
C20 = 1 × 10-6
R23 = 1 × 104
The response of combination of OTA1
Vcomp output (with nominal GOTA1 = 40
µS or microsiemens) can be described for the
frequency dependent variable S jv :
K1 (s ) :=
1 + s ⋅ R 23 ⋅ C 20
s ⋅ (C11 + C20 ) + s ⋅ R 23 ⋅ C11 ⋅ C20 
⋅ GOTA1
(39)
and the phase in degrees of this function
calculated from this equation in MathCAD:
K1phase :=
arg (K1 (si ))
i
p
The amplitude and phase transfer function
are shown in Fig. 6, which shows a nominal
loop bandwidth of ~6 Hz and ~20° phase
margin.
Fig. 6. Compensated error amplifier response.
RSeries :=
Vout − VREF
VREF
IC Protection Functionality
⋅ R17
The key to operational robustness, in addition to sizing
the active and passive components correctly, is the protection and startup control functions of the controller. These
functions have been designed according to failure mode
error analysis (FMEA) and are managed by the inputs from
just a few pins. Specifically, those pins are VSENSE, ISENSE
and VCC, with VCOMP used to set loop compensation and
manage soft-start-related protection functions. (For a basic
state diagram, see Application Note AN-PFC-ICE1PCS01-1,
available at www.infineon.com.)
There are several off-state modes related both to safe
startup conditions and protective shutdown. These include:
● OFF—before VCC reaches 11 V or when VCC drops
below 10 V (UVLO)
● OFF—if VSENSE is below 0.8 V , due to external pull
down (standby mode), VIN does not reach VIN(MIN)
(undervoltage protection or UVP), or open loop protection (OLP), loss of feedback connection
● OFF—if VOUT drops below 50% of rated voltage
(brownout protection or BOP) with ISENSE ~0.7 V
● OFF—when peak current limit is exceeded (peak
(37)
RSeries = 403690Ω
RSeries is split into two resistors R11 and R12 for reason of
power handling and voltage withstanding; two 201K 1%
resistors are suggested. This yields a calculated output of
VOUTnom :=
⋅ 180
(R11+ R12 ) + R17
R17
⋅ VREF
(38)
VOUTnom = 398.346V
The feedback signal from the output voltage divider is
fed to OTA1 at pin 6 (VSENSE). OTA1 is a transconductance amplifier and charges the compensation network at
VCOMP pin 5, consisting of R23, C11 and C20. Note that
this current charge rate into the compensation network
also determines the soft-start time.
The output voltage at the bulk bus capacitors C18 and
C22 contains a ripple voltage at double the frequency of
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33
Power Electronics Technology October 2004
POWER FACTOR CORRECTION
current limit or PCL)—ISENSE > 1.05 V
● OFF—if VOUT is higher than 105% VOUT(NOM)
(overvoltage protection or OVP).
The basic soft-start functionality is used in several
modes, including power limiting while maintaining
sinusoidal current during the initial turn-on while
VSENSE>0.8 V and <4 V. In the case of output overload,
when the ISENSE pin reaches -0.7 V, the soft overcurrent
(SOC) function reduces the current-loop gain, limiting
the maximum output power.
Should the output voltage decline below 51% of rated
value, which is 2.55 V at the VSENSE pin, the soft-start
cycle is reset and a new startup will be attempted. SOC
limiting is not a cycle- by-cycle limit but maintains the sinusoidal current wave shape. Peak current limiting on a
cycle-by-cycle basis is implemented only if the ISENSE pin
exceeds -1.08 V.
An Excel tool has been created to make many of the calculations described above for designing a converter. This
tool features user-input fields for converter specifications,
drop down boxes for standard component value selection
and predefined parameters for some popular cores. The
Excel tool can be obtained from www.infineon.com.[8]
A dual-layer version of the test board was constructed
with the calculated components, as shown in the schematic
Fig. 7. Measured efficiency over line-voltage range for 600-W output
running at 250 kHz.
Smart layout for your PCB
flowPHASE 0
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Tel.: +49 (0)89 722 - 28457 • Fax: +49 (0)89 722 - 32936
www.em.tycoelectronics.com
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POWER FACTOR CORRECTION
of Fig. 5. Layout practices used a minimal size for the HF
current loop between C17 and C16, and Q2 and D9. The
performance was as expected from the design calculations,
and the measured efficiency at 600 W out over the linevoltage range is shown in Fig. 7.
Measurements showed that the rise and fall time of Q2
was limited somewhat by the 1.5-A gate drive booster in
the ICE1PCS01, and overall efficiency might be improved
slightly by using a gate drive booster. The results in switching efficiency were comparable to those achieved at both
higher and lower powers for these components in similar
PETech
applications.[9,10]
SiC-Schottky Diodes,” presented at International Conference
on SiC and Reliability Comp ’99.
5. H. Kapels, R. Rupp, L. Lorenz, I. Zverev, “SiC Schottky
diodes: A Milestone in hard switching applications,” Proceedings, PCIM 2001, Nuremberg, Germany, 2001.
6. I. Zverev, H. Kapels, R. Rupp, M. Herfurth, Silicon Carbide Schottky: “Novel Devices Require Novel Design Rules,”
PCIM 2002 Proceedings, Nuremberg, Germany.
7. W. Frank, “ICE1PCS01—Technical Description,” Application Note, Infineon Technologies AG, Munich, Germany;
Feb. 2003.
8. W. Frank, “ICE1PCS01—Calculation Tool for PFC
Preconverter using ICE1PCS01,” Application Note, Infineon
Technologies AG, Munich, Germany, 2002.
9. J. Hancock, L. Lorenz, “Comparison of Circuit Design Approaches in High Frequency PFC Converters for SiC Schottky
Diode and High Performance Silicon Diodes,” PCIM 2001
Proc., pp. 192-200.
10. Staff, “First Mass-Produced Power Supplies Featuring SiC
Diodes,” Power Electronics Europe, April 2004.
References
1. Magnetics Inc., “Inductor Design in Switching Regulators,”
Technical Bulletin SR-1A.
2. Infineon Technologies, “ICEPCS01—Standalone Power
Factor Correction Controller in Continuous Conduction
Mode,” Datasheet May 2003.
3. Wei Dong, Bing Lu, Qun Zhao and Fred C. Lee, “Performance Evaluation of CoolMOS TM and SiC Diode for PFC
Applications,” APEC 2004.
4. R. Rupp, M. Treu, A. Mauder, E. Griebl, W. Werner, W.
Bartsch, D. Stephani, “Performance and Reliability Issues of
For more information on this article,
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