Small-Signal Model of Multiphase Constant On-Time Control with Phase Overlapping

Multiphase Constant On-Time (COT) controlled buck converters that power modern processors are expected to handle large currents and achieve fast transient response. To meet these requirements, the phase number of these regulators continues to increase. With more phases, these converters operate with phase-overlapping even within practical duty cycle range of interest. This paper finds that, under small-signal perturbation with phase overlapping, the total current waveform exhibits variable on-time and off-time modulation. Therefore, single-phase COT control model cannot be directly applied for compensation design in this region. To address this issue, this work introduces a general small-signal model for multiphase COT control that's applicable for both no-phase overlapping and phase overlapping region based on describing function method. A simplified small-signal model accurate up to half the switching frequency is derived using the describing functions to provide design-oriented interpretation. Proposed model is verified with the SIMPLIS simulation and experimental results using a six-phase COT controlled buck platform.