Necessary and Sufficient Conditions for the Stability of Buck-Type Switched-Mode Power Supplies

Necessary and sufficient conditions are derived for the small-signal stability of forward (buck-type) switched-mode power supplies with a constant switching frequency in the continuous conduction mode. It is shown that the maximum allowable gain of the error amplifier is a function of the modulation process, the duty cycle of the switch, and the filter elements of the supply. Under certain conditions, the gain can be made infinitely large. This can occur for duty cycles less than 50 percent if the end of the ``on´´ time is modulated and for duty cycles between 50 and 100 percent if the start of the ``on´´ time is modulated. Excellent agreement with computer simulations and laboratory measurements has been observed.