LM2745 datasheet(17/23 Pages) NSC

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Application Information (Continued)

as high as possible. Two zeroes f

Z1 and fZ2 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 fre-

quency. The gain of the error amplifier transfer function is

selected to give the best bandwidth possible without violat-

ing 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 compo-

nents, arranged as shown in Figure 13.A

EA is selected to

provide the desired bandwidth. A starting value of 80,000 for

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 mini-

mum output current. One method to select A

EA is to use an

iterative process beginning with these worst-case conditions.

Increase A

Check overall bandwidth and phase margin

Change V

IN to minimum and recheck overall bandwidth

and phase margin

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 band-

width 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 15.

In VM regulators, the top feedback resistor R

FB2 forms a part

of the compensation. Setting R

FB2 to 10 k

Ω±1%, usually

gives values for the other compensation resistors and ca-

pacitors that fall within a reasonable range. (Capacitances >

1 pF, resistances <1M

Ω)C

C1,CC2,CC3,RC1, and RC2 are

selected to provide the poles and zeroes at the desired

frequencies, using the following equations:

20137474

20137475

FIGURE 15. Error Amp. Gain and Phase

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