I'm working through the excellent text on SMPS design "Switching Power Supplies A to Z", by Sanjaya Maniktala. Right now I'm reading the section on the feedback loop and stabilization. As a first-order rule of thumb to achieve stability, Mr. Maniktala suggests that the loop gain transfer function of the switcher intersect the 0 dB point at approximately 1/6th the switching frequency, with a slope of -1. To achieve this, one needs a compensation network transfer function that has a pole at the origin, and at least two zeros to cancel the double pole of the switcher's equivalent LC output network.

A type 2 compensation network consists of a pole at zero, a pole, and a zero. Supposedly, the zero of the compensation netowrk plus the zero created in the loop transfer function by the output capacitor ESR is used to cancel the double pole created by the equivalent output network. However, in one of the diagrams the author suggests the Type 2 compensation be set up this way: set the compensation network zero at the LC pole, and set the compensation network pole at the approximate position of the ESR zero.

I'm not sure I understand how this will work. The pole at zero gives a slope of -1. Plus the LC double pole, gives a slope of -3. The compensation zero at the LC pole location then gives a -2...but if the ESR zero is then cancelled with a pole in the compensation network, how does one obtain the required -1 slope?


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The first point is correct. As a general rule of thumb, the loop crossover frequency should be a fraction of the converter switching frequency. I've heard both one-fifth and one-sixth cited as the maximum.

Crossing over at -1 is not a firm requirement for stability. If the closed-loop response at the crossover frequency has sufficient phase margin (typically 45 degrees or more) and gain margin (-10 dB or more when the phase is at 0 degrees), the converter is stable.

The reason -1 slope is cited as the target for gain crossover is that, in general, the phase is small and isn't changing rapidly during that part of the curve. When the gain slope is -2, the phase shift is greater and changes rapidly, making it difficult to ensure phase margin if the crossover frequency shifts (due to component tolerances, etc.) That doesn't make it impossible to choose a compensation network, but it does make it more sensitive to changes.


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