Unified derivation and analysis of duty-ratio constraints for peak-current-mode control in continuous and discontinuous modes

A unified approach to deriving duty-ratio constraints for the fixed-frequency peak-current-controlled converters in continuous and discontinuous mode is presented. The modeling technique is based on the geometric approximation of the dynamics of duty ratio as a function of the other circuit variables and elements. The mode limit is shown to be a consequence of the parabolic shape of the difference between the control current and average inductor current. Physical discrepancies in this are reflected as infinite duty-ratio gain, and consequently, operation in harmonic mode. The developed constraints may be used also to characterize accurately the steady-state operation of a converter, and provide a proof for the existence of the infinite duty-ratio gain.