The Sampled-Data Modeling for Current Mode Constant On-Time Control with External Ramp Compensation

This paper investigates the application of the sampled-data modeling method for current mode constant-ontime (COT) control with external ramp compensation. Previous sampled-data models have only considered the case with zero slope compensation, revealing that the ratio of duty cycle perturbation to sensed current perturbation at the sampling instant remains constant. However, this paper found it invalid if non-zero slope compensation is introduced. Utilizing the principle of sampled-data modeling, this paper re-derives the modulator model and loop gain. Then the simplified models are derived, from which, for the first time, reveals a clear relationship between the key parameters (bandwidth and closed-loop gain) and circuit parameters, providing designers with a quick reference for evaluating loop behavior during controller design. Finally, the accuracy of the proposed theoretical models is validated through both simulation and experimental results.