The dynamics of PWM current-mode DC/DC converters

Exact analysis of current-mode PWM voltage regulators provides their transfer functions in closed form. This result requires that a convergence criterion be satisfied: the norm of a characteristic matrix ||Q|| has to be less than unity. The same condition ensures open-loop circuit stability. In this way, the well known inner-loop instability of these regulators, when the duty-cycle exceeds 50%, finds a precise explanation. The limit value of the compensating slope versus duty-eyele is also derived.