Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters

TL;DR

This paper derives a comprehensive set of closed-form critical conditions for subharmonic oscillations in buck converters, unifying various control schemes and providing a systematic method to predict oscillations.

Contribution

It introduces a generalized framework for critical conditions, including a systematic procedure applicable to any control scheme, and explains phenomena like oscillation windows in current mode control.

Findings

Unified critical conditions for multiple control schemes.

Systematic procedure for deriving control-specific conditions.

Explanation of subharmonic oscillation windows in current mode control.

Abstract

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.