Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters

Based on a general critical condition of subharmonic oscillation in terms of the loop gain, many closed-form critical conditions for various control schemes in terms of converter parameters are derived. Some previously known critical conditions become special cases in the generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme. Different control schemes share similar forms of critical conditions. For example, both V² control and proportional voltage mode control have the same form of critical condition. A peculiar phenomenon in average current mode control where subharmonic oscillation occurs in a window value of pole can be explained by the derived critical condition. A ripple amplitude index to predict subharmonic oscillation proposed in the past research has limited application and is shown invalid for a converter with a large pole comparable to the switching frequency.