Small-signal model analysis and design of constant-on-time V2 control for low-ESR caps with external ramp compensation

Constant-on-time V² control is widely used in DC-DC buck converters. However, sub-harmonic oscillations occur in constant-on-time V² control employing low-ESR caps. For digital constant-on-time V² control, the instability issue is worse due to the sampling effect. In both cases, external ramp compensation is one simple solution to solve the instability issue, although the characteristic of constant-on-time V² with external ramp is not fully understood. This paper provides design guidelines for external ramp by factorizing the previous small-signal model of analog constant-on-time V² control. Then the design strategy of the external ramp is extended to digital constant-on-time V² control. Moreover, the small-signal models between analog and digital constant-on-time V² control are compared to reveal the sampling effect. The small-signal analysis is verified with simulation and experimental results.