Multiphase Constant On-Time Control With Phase Overlapping–Part II: Stability Analysis

Processor core voltage regulators (VRs) widely use pulse distributor-based multiphase current-mode constant on-time (COT) control to improve light-load performance, achieve fast transient response, and simplify phase interleaving. Part I of this article presented a small-signal model of this control for the whole duty cycle range. Part II of this article finds that the total current loop of an
$N$
-phase COT-controlled VR becomes unstable for duty cycle
$D>1/N$
without a sufficient external ramp. Also, the minimum ramp (or critical ramp) required to preserve stability varies with the number of overlapping phases. Hence, this article derives the critical ramp in each phase overlapping region using the model from Part I. The unstable closed-loop poles of the total current loop in phase-overlapping regions cause this issue. Hence, we first identified the characteristic equation that introduces these poles. Then, we rearranged it to formulate a theoretical loop gain and derived a stability condition using the discrete-time Nyquist criterion. Finally, we evaluated this condition to determine the exact critical ramp expressions up to four overlapping phases and an analytical approximation for the same beyond four overlapping phases. The critical stability limits are verified using SIMPLIS simulations and experimental results from a six-phase COT-controlled buck platform.