APW7098
Application Information (Cont.)
PWM Compensation (Cont.)
4. Set the pole at the ESR zero frequency FESR
FP1 = FESR
:
The pole and zero frequencies of the transfer function
Calculate the C1 by the following equation:
are:
1
FZ1
FZ2
=
2´ p ´ R2´ C2
C2
C1=
2´ p ´ R2´ C2´ FESR - 1
1
=
=
2´ p ´
(R1+R3
)
´ C3
5. Set the second pole FP2 at the half of the switching
frequency and also set the second zero FZ2 at the output LC
filter double pole FLC. The compensation gain should not
exceed the error amplifier open loop gain, check the
compensation gain at FP2 with the capabilities of the
error amplifier.
1
F
P1
C1´ C2
æ
ö
÷
ø
2´ p ´ R2´
ç
C1+ C2
è
1
F
=
P2
2´ p ´ R3´ C3
C1
FP2 = 0.5 X FSW
R3
C3
R2
C2
FZ2 = FLC
VOUT
Combine the two equations will get the following
component calculations:
FB
VCOMP
R1
R1
R3 =
VREF
FSW
- 1
Figure 8. Compensation Network
2´ F
LC
The closed loop gain of the converter can be written as:
GAINLC X GAINPWM X GAINAMP
1
C3 =
p ´ R3´ FSW
Figure 9. shows the asymptotic plot of the closed loop
converter gain, and the following guidelines will help to
design the compensation network. Using the below
guidelines should give a compensation similar to the
curve plotted. A stable closed loop has a -20dB/ decade
slope and a phase margin greater than 45 degree.
FZ1 FZ2
FP1
FP2
Compensation Gain
20log
(R2/R1)
20log
(VIN/ΔVOSC
)
1. Choose a value for R1, usually between 1K and 5K.
2. Select the desired zero crossover frequency
FO= (1/5 ~ 1/10) X FSW
FLC
Use the following equation to calculate R2:
FESR
Converter Gain
DVOSC FO
R2 =
´
´ R1
PWM & Filter Gain
V
F
LC
IN
Frequency(Hz)
3. Place the first zero FZ1 before the output LC filter double
pole frequency FLC.
Figure 9. Converter Gain and Frequency
Output Inductor Selection
FZ1 = 0.75 X FLC
Calculate the C2 by the equation:
The duty cycle (D) of a buck converter is the function of
the input voltage and output voltage. Once an output volt-
age is fixed, it can be written as:
1
C2 =
2´ p ´ R2´ FLC ´ 0.75
Copyright ã ANPEC Electronics Corp.
22
www.anpec.com.tw
Rev. A.6 - Oct., 2009
ANPEC [ ANPEC ELECTRONICS COROPRATION ]
