A Closed Form Expression for Predicting Fast Scale Instability in Switching Buck Converters

Abstract

Fast scale instability is an undesired phenomenon in switching converters. In past studies, its prediction has been mainly carried out by deriving discrete time models and then linearizing the system in the vicinity of a fixed point. However, the results obtained from such an approach cannot be applied for design purpose except for simple cases of current mode control. Alternatively, in this paper, this phenomenon is analyzed by using a unified formal symbolic approach which can be applied for different control strategies. This approach is based on expressing the condition for fast scale instability occurrence using Fourier series and then converting the result into a matrix form expression which depends explicitly on the system parameters making the results directly applicable for design purpose. Under certain practical conditions concerning these parameters, the matrix form expression can be approximated by standard polynomial functions depending on the operating duty cycle. The approximating polynomial functions are widely related to the well known Clausen polynomial functions. The results presented in this work clearly generalize the well known stability condition of current mode control.