Datasheet

+
V
REF
C
7
R
8
R
10
R
6
C
8
P
1
P
2
Z
1
Slope = –1
f
1
f
2
Frequency
Gain (dB)
TPS40200
SLUS659F –FEBRUARY 2006–REVISED MARCH 2012 www.ti.com
Figure 37 shows the feedback network used in this application. This is a Type II compensation network which
gives a combination of good transient response and phase boost for good stability. This type of compensation
has a pole at the origin causing a -20dB/decade (-1) slope followed by a zero that causes a region of flat gain
followed by a final pole that returns the gain slope to -1 . The bode plot in Figure 38 shows the effect of these
poles and zeros.
The procedure for setting up the compensation network is as follows:
1. Determine the break frequency of the output capacitor.
2. Select a zero frequency well below this break frequency.
3. From the gain bandwidth of the error amplifier select a cross over frequency where the amplifier gain is large
relative to expected closed loop gain
4. Select a second zero well above the crossover frequency, that returns the gain slope to a -1 slope.
5. Calculate the required gain for the amplifier at crossover.
Be prepared to iterate this procedure to optimize the pole and zero locations as needed.
The frequency response of this converter is largely determined by two poles that arise from the LC output filter
and a higher frequency zero caused by the ESR of the output capacitance. The poles from the output filter cause
a 40 dB/decade roll off with a phase shift approaching 180 degrees followed by the output capacitor zero that
reduced the roll off to -20 dB and gives a phase boost back toward 90 degrees. In other nomenclature, this is a -
2 slope followed by a -1 slope. The two zeros in the compensation network act to cancel the double pole from
the output filter The compensation network’s two poles produce a region where the error amplifier is flat and can
be set to a gain such that the overall gain of the system is zero dB. This region is set so that it brackets the
system crossover frequency.
Figure 37. Error Amplifier Feedback Elements Figure 38. Error Amplifier Bode Plot
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