LM3477 datasheet(21/23 Pages) NSC

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Compensation (Continued)

Choosing C

C1 = 88x10

−9 F will set f

Z2 =fP1, canceling out

the power pole and insuring a −20dB/decade slope in the

low frequency magnitude response. In other words, the

phase margin below the crossover frequency will always be

higher than the phase margin at the crossover frequency.

If better transient response times are desired, a second

method is to set f

Z2 between fP1 and

⁄2 decade before f

C, the

target crossover frequency. This trades more low frequency

gain for less phase margin, which translates to faster but

more oscillatory step responses. We pick C

C1 = 49nF (use

47nF).

If the esr zero of the output capacitor (f

ESR) is too low or if

more phase margin is required, additional components may

be added to increase the flexibility of the compensator.

Use C

C2 if fESR <

⁄2 f

S, that is if:

For this example, f

ESR = 159 kHz, so use CC2.

The equations used here for R

C,CC1, and CC2 are approxi-

mations valid when C

C2 << CC1. For exact equations, see

Plotting Open Loop Response earlier in this section. In some

cases, the desired inductance is several times higher than

the optimal inductance set by the internal slope compensa-

tion. This results in a Q lower than 0.15, in which case

additional methods of compensating are presented (see

SAMPLING POLE QUALITY FACTOR section).

Sampling Pole Quality Factor

In a current mode control architecture, there is an inherent

resonace at half the switching frequency. The LM3477/A

internally compensates for this by adding a negative slope to

the PWM control waveform (see DEFAULT/ADJUSTABLE

SLOPE COMPENSATION section). The factor in the power

stage equations above, Q, describes how much resonance

will be observed. Q is a function of duty cycle and m

c. Figure

16 shows how the power stage bode plot is affected as Q is

varied from 0.01 to 10. The resonance is caused by two

complex poles at half the switching frequency. If m

c is too

low, the resonant peaking could become severe coinciding

with subharmonic oscillations in the inductor current. If m

c is

too high, the two complex poles split and the converter

begins to act like a voltage mode converter and the compen-

sation scheme used above should be changed.

If Q>2, the sampling poles are imaginary and are approach-

ing the right half of the imaginary plane (the system is

becoming unstable). In this case, Q must be decreased by

either increasing the inductance, or more preferably, adding

more slope compensation through the R

SL resistor (see

DEFAULT/ADJUSTABLE SLOPE COMPENSATION sec-

tion).

If Q<0.15, it means that one of the sampling poles is de-

creasing in frequency towards the dominant power pole, f

p1.

There are three ways to compensate for this. Decrease the

crossover frequency, add a phase lead network, or use the

output capacitor’s ESR to cancel out the low frequency

sampling pole.

One option is to decrease the crossover frequency so that

the phase margin is not as severely decreased by the sam-

pling pole. Decreasing the crossover frequency to between

1kHz to 10kHz is advisable here. As a result, there will be a

decrease in transient response performance.

Another option is the use of the feed-forward capacitor, Cff.

This will provide a positive phase shift (lead) which can be

used to increase phase margin. However, it is important to

note that the effectiveness of Cff decreases with output

voltage. This is due to the fact that the frequencies of the

zero f

zff and pole fpff get closer together as the output voltage

is reduced.

The frequency of the feed-forward zero and pole are:

200033J3

FIGURE 15. Open Loop Frequency Response for

LM3477 Compensation Design Example

200033J5

FIGURE 16. The Quality Factor Q of the Two Complex

Poles is used to qualify how much resonant peaking is

observed in the Power Stage Bode Plot

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