Optimizing the Feedback Loop

A very high phase margin may be very stable, with almost no ringing, but there will be greater undershoot/overshoot. 

We should also have realized by now that intuitively, poles are generally responsible for making matters worse — since they always introduce a phase lag, leading us closer to the danger level of —180°. On the other hand, zeros boost the phase angle (phase lead), and thereby help increase the phase margin away from the danger level. 

Note that in terms of the asymptotic approximation, the open-loop gain crosses the 0 dB axis with a slope of —1, but then immediately thereafter falls off at a slope of—2. But since the pole is very close to the crossover frequency, the gain in reality falls by 3 dB at this break point (as compared to the asymptotic approximation). So the actual crossover occurs a little earlier. The reason the phase is affected by almost 45° at the crossover frequency is that phase starts changing a decade below where the pole really is. 

Note that engineers use various tricks to improve the response further. For example, they may spread the two zeros symmetrically around the LC double pole (rather than coinciding with it). One reason to put a zero (or two) slightly before the LC pole location is that the LC pole can produce a very dramatic 180° phase shift, and this can sometimes lead to conditional stability. So the zero absorbs some of that abruptness in a sense. 

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We have presented the computed gain-phase plots in Figure 7-22. We see we have a generous 78° of phase margin and a crossover frequency of 100 kHz. Based on the logic presented for the Type 3 compensation scheme (nonoptimized case, see section optimizing the feedback loop ), the phase margin in this case is also expected to be around 90°. 

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