A New Formal Approach for Predicting Period Doubling Bifurcations in Switching Converters

TL;DR

This paper introduces a formal symbolic method to predict period doubling bifurcations in switching converters, providing explicit, design-oriented expressions based on system parameters and duty cycle, improving upon previous models.

Contribution

The paper presents a novel symbolic approach using hypergeometric functions to predict bifurcations, enabling direct application in converter design.

Findings

Stability depends on a polynomial function of duty cycle.

Hypergeometric functions can be approximated by standard functions under practical conditions.

The method is demonstrated on voltage-mode buck converters.

Abstract

Period doubling bifurcation leading to subharmonic oscillations are undesired phenomena in switching converters. In past studies, their prediction has been mainly tackled by explicitly deriving a discrete time model and then linearizing it in the vicinity of the operating point. However, the results obtained from such an approach cannot be applied for design purpose. Alternatively, in this paper, the subharmonic oscillations in voltage mode controlled DC-DC buck converters are predicted by using a formal symbolic approach. This approach is based on expressing the subharmonic oscillation conditions in the frequency domain and then converting the results to generalized hypergeometric functions. The obtained expressions depend explicitly on the system parameters and the operating duty cycle making the results directly applicable for design purpose. Under certain practical conditions concerning these parameters, the hypergeometric functions can be approximated by polylogarithm and standard functions. The new approach is demonstrated using an example of voltage-mode-controlled buck converters. It is found that the stability of the converter is strongly dependent upon a polynomial function of the duty cycle.