Modeling of quantization effects in digitally controlled DC-DC converters

In digitally controlled DC-DC converters with a single voltage feedback loop, the two quantizers, namely the A/D converter and the digital pulse-width modulator (DPWM), can cause undesirable limit-cycle oscillations. In this paper, static and dynamic models that include the quantization effects are derived and used to explain the origins of limit-cycle oscillations. In the static model, existence of DC solution, which is a necessary no-limit-cycle condition, is examined using a graphical method. A concept of amplitude and offset dependent gain is introduced to extend the describing function method and derive the dynamic system model. From the static and dynamic models, no-limit-cycle conditions associated with A/D, DPWM and compensator design criteria are derived. The conclusions are illustrated by simulation and experimental examples.