Analytical Determination of Fast-Scale Instability Boundaries for Current Mode Controlled DC–DC Converters With CPL and Closed Voltage Loop

Abstract

In this paper fast-scale instability boundary in power converters loaded by a constant power load is addressed using an analytical approach. From a piecewise linearized model of the converter, the discrete-time steady-state values of the electrical variables are first determined. Based on justified and realistic approximations of the voltage and current ripples, simple and accurate expressions for these steady-state values are derived and validated. Starting from a matrix-based analytical expression representing the fast-scale instability boundary, a simple design-oriented approximate expression is derived showing insight into how the different system parameters influence this boundary. We highlight its dependency on ripple and slope quantities of the electrical variables of the converter and we explore the impact of variation of parameters in different projections of the multi-dimensional parameter space. An important parameter is the outer voltage controller gain which we demonstrate mathematically that it could have an either stabilizing or destabilizing effect depending whether the steady-state duty cycle is smaller or larger than 1/2. Experimental measurements from a laboratory prototype are in correlation with the theoretical predictions.