Article ID: 2024GCP0003
This paper proposes the continuous-time modeling and analysis methods for a hysteretic buck DC-DC converter to examine its frequency characteristics (f-characteristics) and transient response. Determining the small-signal transfer function to derive the fcharacteristics has been challenging due to the hysteretic behavior of the comparator. In this paper, the hysteretic comparator is modeled as an amplifier with a delay time between the input exceeding the hysteresis window boundary and the output state change, and with a voltage gain defined as the ratio between the comparator's output voltage change and the voltage difference of both input terminals during transition. The delay time is calculated based on the f-characteristics of the designed comparator circuits, and the voltage gain is determined using this delay time and the slew rate of the input signal. Subsequently, the overall small-signal transfer function and frequency characteristics are determined. It is also demonstrated that the proposed model accurately predicts the transient response when the load current changes. To verify the proposed modeling and analysis methods, a hysteretic buck DC-DC converter was designed and circuit-simulated using device parameters from a 0.18μm CMOS process. The simulation results closely matched the calculated frequency characteristics and the transient response.
