Small-Signal Analysis and Optimal Design of Constant Frequency $V^{2}$ Control

Recently, $V^{2}$ control and its variety named ripple-based control has been gaining more and more popularity in academia research and commercial products. However, for constant frequency $V^{2}$ control, design methodology is not clear due to insufficient knowledge about the small-signal model. This paper investigates the small-signal model and optimal design strategy for constant frequency $V^{2}$ control. The factorized small-signal control-to-output voltage transfer function and output impedance are investigated. The stability criterion is obtained and design considerations are analyzed. Moreover, the small-signal model with ramp compensations is presented and optimal design guidelines from dynamic performance point of view are provided. For the first time, it is found the external ramp is good enough to get a well-damped performance when current feedback strength is strong (for example, when employing OSCON capacitors). However, the current ramp is necessary to achieve a good dynamic performance when the current feedback strength is weak (for example, when employing ceramic capacitors). As a result, a new control strategy with the hybrid ramp is proposed for ceramic capacitor applications. The small-signal model and proposed design guidelines are verified with Simplis simulation and experimental results.