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# Equivalent Circuit Model and Design of Constant On-time Current Mode Control With External Ramp Compensation

This nugget proposes a three-terminal equivalent circuit model of Constant on-time current mode control with external ramp compensation. A multi-phase constant on-time current mode control based on pulse distribution structure is widely used in the Voltage Regulator application for a microprocessor. To minimize the ripple cancellation effect, an external ramp compensation is used in current solution as shown in Fig.1(a). However, an external ramp will introduce a dynamic to the system and the AVP requirement will be violated without considering the effect of the external ramp. For small D, The simplified control-to-output current transfer function with external ramp is shown as follows:

The external ramp will make the circuit behave as a non-ideal current source, as it will bring one moving pole, which is related to the magnitude of the external ramp, and one static zero, which is located at f

_{sw}/π. The proposed equivalent circuit to represent this non-ideal current source is shown in Fig. 1(b). Where the R

_{e2}-L

_{e2}branch is utilized to resemble the non-idealness of this current source. R

_{e2}and L

_{e2}form a static zero while R

_{e2}, L

_{e2}and L

_{s}form the moving pole. For a large duty cycle application, there is an additional double pole, which is shown by a R

_{e}-C

_{e}branch resonating with the power stage inductor. The three-terminal switch equivalent circuit model is shown in Fig. 2, where all the transfer functions (control-to-output, output impedance, input impedance and audio susceptibility) can be examined and extended very easily to multi-phase case. This equivalent circuit model is an extension of the original three-terminal current mode control by adding a R

_{e2}-L

_{e2}branch that resembles the effect of the external ramp in constant on time control.

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