Equivalent circuit model of constant on-time current mode control with external ramp compensation

Multi-phase constant on-time current mode control based on pulse distribution structure is widely used in Voltage Regulator application for microprocessor. To minimize ripple cancellation effect, external ramp compensation is used in commercial products. However, external ramp will introduce dynamic to the system and AVP requirement will be violated without considering its effect. This paper first studies the effect of external ramp by deriving small-signal transfer function based on describing function method. It is found that external ramp brings additional dynamic, with time constant related with switching period. Then, a simple equivalent circuit model based on three-terminal switch concept is proposed, which considers the effect of external ramp by adding an additional R-L branch. The equivalent circuit model can be reduced to previous unified three-terminal switch model when external ramp is zero and can be reduced to model of constant on-time voltage mode control when external ramp is much larger than inductor current ramp. The proposed three-terminal switch model is a complete model which can be used to examine all transfer functions and is accurate up to half of switching frequency. The model is verified by Simplis simulation.