Closed-Form Critical Conditions of Instabilities for Constant On-Time Controlled Buck Converters

A general instability critical condition in terms of the loop gain is derived for the constant on-time controlled buck converter. The instability is associated with a discrete-time pole at -1. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition, which also shows the required ramp slope to stabilize the converter. Different control schemes are shown to have similar forms of critical conditions. Some previously known critical conditions become special cases in this generalized framework, and their inaccuracies are identified.