Sampled-Data Modeling for V-COT Control with External Ramp Compensation

Voltage-mode constant-on-time (V-COT) buck converters are widely adopted for powering high-performance XPUs due to their superior transient performance. Small-signal modeling is essential for evaluating their stability and dynamic behavior. While the conventional describing-function (DF) method is commonly used, it involves a cumbersome derivation and fails to provide an explicit expression for the loop gain. Luckily, emerging sampled-data modeling features a simpler derivation. However, existing work focuses on V-COT without external slope compensation, a feature indispensable in practical applications to suppress subharmonic oscillations. To address this gap, this paper establishes a comprehensive small-signal model for V-COT control with external slope compensation using the sampled-data modeling method. Based on the proposed model, an explicit expression for the crossover frequency is derived, providing a direct theoretical foundation for bandwidth design and ramp-slope optimization. Simulation and experimental results validate the accuracy of the developed models.