APW7073
Application Information (Cont.)
PWM Compensation (Cont.)
GAIN AMP
= V COMP
V OUT
=
1
sC1
// R2
+
1
sC2
R1//
R3
+
1
sC3
=
R1 + R3
×
s
+
R2
1
×
C2
×
s
+
(R1
+
1
R3
)×
C3
R1 × R3 × C1
s s
+
C1 + C2
R2 × C1× C2
×
s
+
R3
1
×
C3
The poles and zeros of the transfer function are:
F Z1
=
1
2 × π × R2
× C2
FZ2
=
1
2 × π × (R1 + R3 )× C3
FP1
=
2×
π
× R2
1
×
C1 ×
C1 +
C2
C2
FP2
=
1
2 × π × R3
× C3
C1
R3 C3
R2 C2
VOUT
R1 FB
VCOMP
VREF
Figure 8. Compensation Network
The closed loop gain of the converter can be written
as:
GAINLC X GAINPWM X GAINAMP
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.
3.Place the first zero FZ1 before the output LC filter
double pole frequency F .
LC
F = 0.75 X F
Z1
LC
Calculate the C2 by the equation:
C2 =
1
2 × π × R2 × FLC × 0.75
4.Set the pole at the ESR zero frequency FESR:
FP1 = FESR
Calculate the C1 by the equation:
C1 =
C2
2 × π × R2 × C2 × FESR − 1
5.Set the second pole FP2 at the half of the switching
frequency and also set the second zero F at the
Z2
output LC filter double pole F . The compensation
LC
gain should not exceed the error amplifier open loop
gain, check the compensation gain at F with the
P2
capabilities of the error amplifier.
FP2 = 0.5 X FS
FZ2 = FLC
Combine the two equations will get the following
component calculations:
R3 =
R1
FS − 1
2 × FLC
C3 =
1
π × R3 × FS
FZ1 FZ2 FP1 FP2
20log
(R2/R1)
Compensation
Gain
20log
(VIN/Δ V OSC)
1.Choose a value for R1, usually between 1K and 5K.
2.Select the desired zero crossover frequency
FO: (1/5 ~ 1/10) X FS >FO>FESR
Use the following equation to calculate R2:
R2 = ∆ V OSC × FO × R1
V IN
FLC
FLC
FESR
PWM & Filter
Gain
Converter
Gain
Frequency(Hz)
Figure 9. Converter Gain and Frequency
Copyright © ANPEC Electronics Corp.
17
Rev. A.1 - Apr., 2006
www.anpec.com.tw