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 the origin, a pole, and a zero. Supposedly, the zero of the compensation network 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 network zero at the LC pole location then gives a -2...but if the ESR zero is then canceled with a pole in the compensation network, how does one obtain the required -1 slope?