Asynchronous-Switching Map-Based Stability Effects of Circuit Parameters in Fixed Off-Time Controlled Buck Converter

Both constant on-time (COT) and fixed off-time (FOT) control techniques are suitable for various applications requiring fast transient response. However, the discrete-time model of COT controlled buck converter only has two switched borderlines, whereas that of FOT controlled buck converter has four switched borderlines. Based on the derivations of these borderlines, an asynchronous-switching map of FOT controlled buck converter is established. With the decrease of equivalent series resistance (ESR) of output capacitor, instability and mode shifting from continuous conduction mode (CCM) to discontinuous conduction mode (DCM) are discussed. Furthermore, with small ESR of output capacitor, stability effects of load resistance and inductance on dynamical behaviors are investigated, and the approximate stability criteria and the corresponding normalized critical conditions are obtained. The theoretical analyses and experimental results show that the converter operates in DCM chaos via period-doubling and border-collision bifurcation routes, and its instability caused by small ESR can be removed by choosing appropriate load resistance, inductance, and voltage transfer ratio, which are very suitable for the circuit design of FOT controlled buck converter.