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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
30103740
FIGURE 9. Power Train Bode Plot
The complex poles created by the output inductor and ca-
pacitor cause a 180° phase shift at the resonant frequency as
seen in
Figure 9. The phase is boosted back up to -90° due
to 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 compen-
sation network shown around the error amplifier in
Figure 8creates 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:
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 ze-
ros can be located accordingly to stabilize the voltage mode
loop depending on the power stage complex poles and Q.
Figure 10 is an illustration of what the Error Amplifier Com-
pensation transfer function will look like.
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
30103741
FIGURE 10. Type 3 Compensation Network Bode Plot
LC/2, fLC) in the comen-
sation network give a phase boost. This will cancel out the
effects of the phase loss from the output filter. The compen-
sation 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. The
dependancy of the pole and zero locations on the compen-
sation components is described below.
An example of the step-by-step procedure to generate
comensation component values using the typical application
setup, (see
Figure 15), is given. The parameters needed for
the compensation values are given in the table below.
Parameter
Value
V
IN
5.0V
V
OUT
1.2V
I
OUT
15A
f
CROSSOVER
100 kHz
L
0.56 H
R
DCR
1.8 m
C
O
150 F
R
ESR
1.0 m
ΔV
RAMP
0.8V
f
SW
500 kHz
where
ΔV
RAMP is the oscillator peak-to-peak ramp voltage
(nominally 0.8V), and f
CROSSOVER is the frequency at which
17
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LM21215