A New Way to Model Current-Mode Control

May 1, 2007 12:00 PM
By Robert Sheehan, Principal Applications Engineer, National Semiconductor, Santa Clara, Calif.

General Slope-Compensation Criteria

For any mode of operation (peak, valley or emulated), the optimal slope of the ramp presented to the modulating comparator input is equal to the sum of the absolute values of the inductor up-slope and down-slope scaled by the current-sense gain. This will cause any tendency toward subharmonic oscillation to damp in one switching cycle.

For the buck regulator, this is equivalent to a ramp whose slope is VIN × (RI / L).

Up-slope = (VIN - VO) × (RI / L)

Down-slope = VO (RI / L).

For the boost regulator, this is equivalent to a ramp whose slope is VO × (RI / L).

Up-slope = VIN × (RI / L)

Down-slope = (VO - VIN) × (RI / L).

For the buck-boost regulator, this is equivalent to a ramp whose slope is (VIN + VO) × (RI / L).

Up-slope = VIN × (RI / L)

Down-slope = VO × (RI / L).

To avoid confusion, VIN and VO represent the magnitude of the input and output voltages as a positive quantity. By identifying the appropriate sensed inductor slope, it is easy to find the correct slope-compensating ramp.

Rethinking Assumptions

The basic current-mode buck regulator linear model has been developed with gain terms that can be related directly to the model. The three main considerations for current-mode control can be summarized as follows: First, for current-mode operation, the dc or average value of the inductor current must be sampled. Second, the modulator gain is set by the effective slope of the ramp presented to the modulating comparator input. Third, the requirement for slope compensation is dependent upon the relationship of the sampled current to the average value of the inductor current.

Previous researchers have assumed a fixed ramp for the slope compensation to simplify the analysis. When analyzing the peak current-mode buck with a fixed-slope compensating ramp, the dc-modulator gain and the high-frequency criteria for slope compensation are identical. This result has been used to form conclusions about current-mode operation in general. Since the optimal slope of the compensating ramp for this mode is proportional to the down-slope of the inductor current, the preferred method should be to make the compensating ramp proportional to VO.

Though seemingly trivial, the consequence of doing this is profound. In the second part of this article, general gain parameters and sampling gain terms will be introduced. The effect of proportional ramp terms and new operating modes identify limitations of existing models, which provides direction for further research.

Reference

1. Sheehan, Robert. “Emulated Current Mode Control for Buck Regulators Using Sample and Hold Technique,” 2006 Power Electronics Technology Exhibition and Conference. (An updated version of this paper, including complete appendix material, is available from National Semiconductor.)