Datasheet

G
EA
x OPG
H
EA
=
1 + G
EA
+ OPG
2S x 9 MHz
OPG =
s
G
EA
= A
EA
x
s
2Sf
Z1
+ 1
s
2Sf
Z2
+ 1
s
2Sf
P1
+ 1
s
2Sf
P2
+ 1
s
LM2745, LM2748
SNOSAL2E –APRIL 2005–REVISED APRIL 2013 www.ti.com
The double pole at 4.5 kHz causes the phase to drop to approximately -130° at around 10 kHz. The ESR zero, at
20.3 kHz, provides a +90° boost that prevents the phase from dropping to -180º. If this loop were left
uncompensated, the bandwidth would be approximately 10 kHz and the phase margin 53°. In theory, the loop
would be stable, but would suffer from poor DC regulation (due to the low DC gain) and would be slow to
respond to load transients (due to the low bandwidth.) In practice, the loop could easily become unstable due to
tolerances in the output inductor, capacitor, or changes in output current, or input voltage. Therefore, the loop is
compensated using the error amplifier and a few passive components.
For this example, a Type III, or three-pole-two-zero approach gives optimal bandwidth and phase.
In most voltage mode compensation schemes, including Type III, a single pole is placed at the origin to boost DC
gain as high as possible. Two zeroes f
Z1
and f
Z2
are placed at the double pole frequency to cancel the double
pole phase lag. Then, a pole, f
P1
is placed at the frequency of the ESR zero. A final pole f
P2
is placed at one-half
of the switching frequency. The gain of the error amplifier transfer function is selected to give the best bandwidth
possible without violating the Nyquist stability criteria. In practice, a good crossover point is one-fifth of the
switching frequency, or 60 kHz for this example. The generic equation for the error amplifier transfer function is:
In this equation the variable A
EA
is a ratio of the values of the capacitance and resistance of the compensation
components, arranged as shown in Figure 29. A
EA
is selected to provide the desired bandwidth. A starting value
of 80,000 for A
EA
should give a conservative bandwidth. Increasing the value will increase the bandwidth, but will
also decrease phase margin. Designs with 45-60° are usually best because they represent a good trade-off
between bandwidth and phase margin. In general, phase margin is lowest and gain highest (worst-case) for
maximum input voltage and minimum output current. One method to select A
EA
is to use an iterative process
beginning with these worst-case conditions.
1. Increase A
EA
2. Check overall bandwidth and phase margin
3. Change V
IN
to minimum and recheck overall bandwidth and phase margin
4. Change I
O
to maximum and recheck overall bandwidth and phase margin
The process ends when the both bandwidth and the phase margin are sufficiently high. For this example input
voltage can vary from 3.0 to 3.6V and output current can vary from 0 to 4A, and after a few iterations a moderate
gain factor of 101dB is used.
The error amplifier of the LM2745/8 has a unity-gain bandwidth of 9 MHz. In order to model the effect of this
limitation, the open-loop gain can be calculated as:
The new error amplifier transfer function that takes into account unity-gain bandwidth is:
The gain and phase of the error amplifier are shown in Figure 31.
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