Closed-Form Operational Boundaries for Buck Converters With Constant On-Time Control

In this brief, we provide three operational boundaries in closed analytical form for a Constant ON-Time buck converter working in continuous current mode. Two of these boundaries are related to the sudden appearance of pulse-bursting induced by either (i) the hysteresis of the comparator that drives the input of the block implementing the circuit control algorithm (hysteresis condition), or (ii) by a period doubling bifurcation (bouncing condition). The third operational boundary corresponds to the saturation condition of the circuit controller which does no longer guarantee an OFF-time larger than the minimum allowed one. These stability boundaries are provided both for the adaptive and the fixed ON-time working modes.