Small-Signal Analysis and Optimal Design of External Ramp for Constant On-Time V $^{\bf 2}$ Control With Multilayer Ceramic Caps

Recently, constant on-time V
²
control, and its variety named constant on-time control, or constant on-time ripple-based control is more and more popular in industry products due to features of high light-load efficiency, simple implementation, and fast transient response. However, subharmonic oscillation occurs when using multilayer ceramic caps due to the lagging phase of the capacitor voltage relative to the inductor current. External ramp compensation is one simple solution to solve the instability issue. However, the characteristics of constant on-time V
²
control with external ramp are not fully understood and no explicit design guidelines for the external ramp are provided. This paper investigates the small-signal characteristics of constant on-time V
²
control with external ramp compensation by providing a factorized, easy-to-use small-signal model. The external ramp is a critical parameter because it directly affects the position and damping of two pairs of double poles. Based on this fact, design guidelines of the external ramp for optimal dynamic performance are provided. Moreover, the effect of duty cycle is investigated. Finally, the small-signal experimental results and load transient performance are presented to verify the small-signal analysis and proposed design guideline.