Datasheet

100 1k 10k 100k 1M 10M
-20
0
20
40
60
80
100
-180
-135
-90
-45
0
45
90
GAIN (dB)
FREQUENCY (Hz)
PHASE (°)
GAIN
PHASE
s
2Sf
Z1
+1
s
2Sf
Z2
+1
s
s
2Sf
P1
+1
s
2Sf
P2
+1
G
EA
= K
m
100 1k 10k 100k 1M 10M
-80
-60
-40
-20
0
20
40
60
-360
-320
-280
-240
-200
-160
-120
-80
-40
0
GAIN (dB)
FREQUENCY (HZ)
PHASE (°)
GAIN
PHASE
LM21215A
SNOSB87B –MARCH 2011–REVISED MARCH 2013 www.ti.com
Figure 34. Power Train Bode Plot
The complex poles created by the output inductor and capacitor cause a 180° phase shift at the resonant
frequency as seen in Figure 34. The phase is boosted back up to -90° because of the output capacitor ESR zero.
The 180° phase shift must be compensated out and phase boosted through the error amplifier to stabilize the
closed loop response. The compensation network shown around the error amplifier in Figure 33 creates two
poles, two zeros and a pole at the origin. Placing these poles and zeros at the correct frequencies will stabilize
the closed loop response. The Compensated Error Amplifier transfer function is:
(12)
The pole located at the origin gives high open loop gain at DC, translating into improved load regulation
accuracy. This pole occurs at a very low frequency due to the limited gain of the error amplifier; however, it can
be approximated at DC for the purposes of compensation. The other two poles and two zeros can be located
accordingly to stabilize the voltage mode loop depending on the power stage complex poles and Q. Figure 35 is
an illustration of what the Error Amplifier Compensation transfer function will look like.
Figure 35. Type 3 Compensation Network Bode Plot
As seen in Figure 35, the two zeros (f
LC
/2, f
LC
) in the comensation network give a phase boost. This will cancel
out the effects of the phase loss from the output filter. The compensation network also adds two poles to the
system. One pole should be located at the zero caused by the output capacitor ESR (f
ESR
) and the other pole
should be at half the switching frequency (f
SW
/2) to roll off the high frequency response.
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