Datasheet

f − Frequency − kHz
−20
−10
0
10
20
30
40
Gain − dB
G029
0.1 1 10 1k100
High-Frequency Gain
f
Z1
f
Z2
f
P1
f
P2
VOUT + VREF
R
Z1
) R
SET
R
SET
(50)
GAIN + R
PZ2
R
Z1
) R
P1
R
Z1
R
P1
(51)
f
P1
+
1
2p R
P1
C
PZ1
(52)
f
P2
+
C
P2
) C
Z2
2p R
PZ2
C
P2
C
Z2
[
1
2p R
PZ2
C
P2
(53)
f
Z1
+
1
2p R
Z1
C
PZ1
(54)
f
Z2
+
1
2p
ǒ
R
PZ2
) R
P1
Ǔ
C
Z2
[
1
2p R
PZ2
C
Z2
(55)
TPS40077
SLUS714D – JANUARY 2007 – REVISED APRIL 2009 ..................................................................................................................................................... www.ti.com
Figure 33. Type-III Compensation Typical Bode Plot
The high-frequency gain and the break (pole and zero) frequencies are calculated using the following equations.
Looking at the PWM and LC bode plot, there are a few things which must be done to achieve stability.
1. Place two zeros close to the double pole, e.g., f
Z1
= f
Z2
= 4.3 kHz
2. Place both poles well above the crossover frequency. The crossover frequency was selected as one sixth the
switching frequency, f
co1
= 50 kHz, f
P1
= 66 kHz
3. Place the second pole at three times f
co1
. This ensures that the overall system gain falls off quickly to give
good gain margin, f
p2
= 150 kHz
4. The high-frequency gain should be sufficient to ensure 0 dB at the required crossover frequency, GAIN = – 1
× gain of PWM and LC at the crossover frequency, GAIN = 16.9 dB
Using these values and Equation 50 through Equation 55 , the Rs and Cs around the compensation network can
be calculated.
1. Set R
Z1
= 51 k Ω
2. Calculate R
SET
using Equation 50 , R
SET
= 32.4 k Ω
3. Using Equation 54 and f
z1
= 4.3 kHz, C
PZ1
can be calculated to be 726 pF, C
PZ1
= 680 pF
4. f
P1
and Equation 52 yields R
P1
to be a standard value of 3.3 k Ω .
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