LM2746MXAX datasheet(17/24 Pages) NSC

17 / 24 page

Application Information (Continued)

One popular method for selecting the compensation compo-

nents is to create Bode plots of gain and phase for the power

stage and error amplifier. Combined, they make the overall

bandwidth and phase margin of the regulator easy to see.

Software tools such as Excel, MathCAD, and Matlab are

useful for showing how changes in compensation or the

power stage affect system gain and phase.

The power stage modulator provides a DC gain A

DC that is

equal to the input voltage divided by the peak-to-peak value

of the PWM ramp. This ramp is 1.0VP-P for the LM2746. The

inductor and output capacitor create a double pole at fre-

quency f

DP, and the capacitor ESR and capacitance create a

single zero at frequency f

ESR. For this example, with VIN =

3.3V, these quantities are:

In the equation for f

DP, the variable RL is the power stage

resistance, and represents the inductor DCR plus the on

resistance of the top power MOSFET. R

O is the output

voltage divided by output current. The power stage transfer

function G

PS is given by the following equation, and Figure

13 shows Bode plots of the phase and gain in this example.

a=LC

O(RO +RC)

b=L +C

O(RORL +RORC +RCRL)

c=R

O +RL

The double pole at 4.5kHz causes the phase to drop to

approximately -130˚ at around 10kHz. The ESR zero, at

20.3kHz, provides a +90˚ boost that prevents the phase from

dropping to -180o. If this loop were left uncompensated, the

bandwidth would be approximately 10kHz 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 un-

stable 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

20147764

FIGURE 12. Power Stage and Error Amp

20147769

20147770

FIGURE 13. Power Stage Gain and Phase

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