One-Dimensional Discontinuous Map Analysis of Dc–dc Converters Under Voltage Controlled Pulse Skipping Modulation

A pulse skipping modulation (PSM) technique is useful for improving the efficiency of a dc–dc converter under light load conditions. Under such condition, the discrete-time model of the converter could be modeled as a discontinuous map, comprising either 1D functions only or a combination of 1D and 2D functions. Using the PSM mechanism, efficiency and spectral composition could be further improved by incorporating a voltage feedback loop. In this paper we show that, in a converter under voltage controlled PSM, the entire map can be restricted to one dimension for a wide range of parameters, by properly designing the controller. As a parameter is varied, the periodicity of the output waveform may change either monotonically or non-monotonically depending on the character of the voltage mode control loop. Technically it is desirable to operate the converter in such a way that a variation of a parameter can cause only incremental change in the periodicity and hence in the spectral composition. In the nonlinear dynamics literature, such a bifurcation scenario is known as pure period incrementing cascade. Using the theory for 1D discontinuous maps, we obtain the conditions on the converter's parameters such that such a cascade is obtained, and the variation of a parameter does not cause large variation of the periodicity. The results have been experimentally validated.