Energy-based approach for predicting limit cycle oscillations in voltage-mode digitally-controlled dc-dc converters

This paper investigates an energy-based approach for the prediction of limit-cycle oscillations (LCOs) in digitally controlled dc-dc converters due to quantization effects on the A/D converters and digital pulse-width modulator (DPWM). Existing static and dynamic models predict the existence of only a part of limit cycle oscillations, so that extensive time-domain simulations are usually needed in order to verify the presence of limit-cycle oscillations under different load and input voltage conditions. This paper proposes an alternative approach based on the incremental energy of converter state variables, which is suited for voltage-mode digitally controlled dc-dc converters. By predicting the variation of the incremental energy due to impulse response of the voltage loop, it is possible to establish when the incremental energy becomes small enough to avoid limit-cycle oscillations. This relation, which is expressed as a function of control and converter parameters, represents a necessary condition for the elimination of limit-cycle oscillations. Extensive time-domain simulations have shown that this relation is also close to the effective limit which ensures the absence of LCOs. Simulation and experimental results confirm the validity of the proposed method.