LM2744 datasheet(21/32 Pages) TI1

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100

10k

100k

FREQUENCY (Hz)

GEA x OPG

HEA =

1 + GEA + OPG

2S x 9 MHz

OPG =

GEA = AEA x

2SfZ1

+ 1

2SfZ2

+ 1

2SfP1

+ 1

2SfP2

+ 1

LM2744

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SNVS292E – SEPTEMBER 2004 – REVISED JANUARY 2012

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 fZ1 and fZ2 are placed at the double pole frequency to cancel the double

pole phase lag. Then, a pole, fP1 is placed at the frequency of the ESR zero. A final pole fP2 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 60kHz for this example. The generic equation for the error amplifier transfer function is:

(26)

In this equation the variable AEA is a ratio of the values of the capacitance and resistance of the compensation

components, arranged as shown inFigure 14. AEA is selected to provide the desired bandwidth. A starting value

of 80,000 for AEA 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 tradeoff

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 AEA is to use an iterative process

beginning with these worst-case conditions.

1. Increase AEA

2. Check overall bandwidth and phase margin

3. Change VIN to minimum and recheck overall bandwidth and phase margin

4. Change IO 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 110,000 is used.

The error amplifier of the LM2744 has a unity-gain bandwidth of 9MHz. In order to model the effect of this

limitation, the open-loop gain can be calculated as:

(27)

The new error amplifier transfer function that takes into account unity-gain bandwidth is:

(28)

The gain and phase of the error amplifier are shown in Figure 15.

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