Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters
For power electronics engineers designing buck converters, this provides a unified theoretical framework to predict subharmonic oscillations, though it is an incremental extension of known results.
The paper derives a general closed-form critical condition for subharmonic oscillations in buck converters in terms of loop gain, unifying and extending previous results for various control schemes. It also provides a systematic procedure to derive conditions for arbitrary control schemes and explains a peculiar oscillation window in average current mode control.
A general critical condition of subharmonic oscillation in terms of the loop gain is derived. Many closed-form critical conditions for various control schemes in terms of converter parameters are also 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 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.