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100 100 k10 k1 k 1 M
10
−20
−10
20
30
40
0
Frequency − Hz
Gain − dB
High Frequency Gain
f
Z1
f
Z2
f
P2
f
P1
V
O
+ V
FB
R
Z1
) R
SET
R
SET
(49)
R
SET
+
R
SET1
R
SET2
R
SET1
) R
SET2
(50)
GAIN +
R
PZ2
ǒ
R
Z1
R
P1
R
Z1
)R
P1
Ǔ
(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)
TPS40075
SLUS676A – MAY 2006 – REVISED SEPTEMBER 2007
A typical bode plot to this type of compensation network is shown in Figure 32 .
Figure 32. Type III Compensation Bode Plot
The high frequency gain and the break (pole and zero) frequencies are calculated using the following equations.
Using this PWM and L-C bode plot the following actions ensure stability.
1. Place two zero ’ s close to the double pole, i.e. f
Z1
= f
Z2
= 3559 Hz
2. Place a pole at one octave below the desired crossover frequency. The crossover frequency was selected as
one quarter the switching frequency, f
CO
= 100 kHz, f
P1
= 50 kHz
3. Place the second pole about an octave above f
co
. This ensures that the overall system gain falls off quickly to
give good gain margin, f
P2
= 200 kHz
4. The high-frequency gain is sufficient to ensure 0 dB at the required crossover frequency, GAIN = -1  GAIN
of PWM and LC at the crossover frequency, GAIN = 17.6 dB, or 7.586
32 Submit Documentation Feedback Copyright © 2006 – 2007, Texas Instruments Incorporated
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