APW7068 Datasheet, PDF (16/26 Pages) Anpec Electronics Coropration – Synchronous Buck PWM and Linear Controller with 0.8V Reference Out Voltage

APW7068
Application Information (Cont.)
PWM Compensation (Cont.)
The PWM modulator is shown in Figure 8. The input
is the output of the error amplifier and the output is the
PHASE node. The transfer function of the PWM
modulator is given by:
GAIN_PWM
=
V_IN1
∆V_OSC
VOSC
OSC
PWM
Comparator
Driver
Output of
Error Amplifier
VIN
PHASE
Driver
Figure 8. The PWM Modulator
The compensation network is shown in Figure 9. It
provides a close loop transfer function with the highest
zero crossover frequency and sufficient phase margin.
The transfer function of error amplifier is given by:
GAIN_AMP
=
V_COMP
V_OUT1
=
sC1 1//^{R2}
+
1
sC2


R1//R3 + ¹ 
 ^sC3 
=
R1 + R3
R1 × R3 × C1
×


s
+
R2
1
×
C2


×

s
+
s s

+
C1 + C2
R2 × C1× C2


1
(R1 + R3 )×
×


s
+
R3
1
×
C3
C3



The poles and zeros of the transfer function are:
F _Z1
=
1
2 × π × R2
× C2
F_Z2
=
1
2 × π × (R1 + R3 )× C3
F_P1
=
2
×
π
×
R2
1
× 

C1×
C1 +
C2
C2


F_P2
=
1
2 × π × R3
× C3
C1
R3 C3
R2 C2
VOUT1
R1 ^FB
VCOMP
VREF
Figure 9. Compensation Network
The closed loop gain of the converter can be written
as:
GAIN_LC X GAIN_PWM X GAIN_AMP
Figure 10. 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.
1.Choose a value for R1, usually between 1K and 5K.
2.Select the desired zero crossover frequency F :
O
(1/5 ~ 1/10) X F_S >F_O>F_ESR
Use the following equation to calculate R2:
R2 = ^∆VOSC × ^FO × R1
V_IN
F_LC
3.Place the first zero F before the output LC filter
Z1
double pole frequency F .
LC
F = 0.75 X F
Z1
LC
Calculate the C2 by the equation:
C2 =
1
2 × π × R2 × F_LC × 0.75
4.Set the pole at the ESR zero frequency F :
ESR
F =F
P1
ESR
Calculate the C1 by the equation:
C1 =
C2
2 × π × R2 × C2 × F_ESR − 1
Copyright © ANPEC Electronics Corp.
16
Rev. A.2 - Jun., 2006
www.anpec.com.tw