Extended wide-load range model for multi-level Dc-Dc converters and a practical dual-mode digital controller

This paper addresses limitations of previous models of multi-level flying capacitor (ML-FC) dc-dc converters, in terms of not being able to predict instability in the regulation of the flying capacitor voltage under non-negligible inductor current ripple conditions, usually existing under light to medium load operating conditions. Assuming small-ripple approximation, linear ac equivalent circuit is derived for a general N-level FC dc-dc buck converter and, through a geometrical analysis, limitations of that model are explained. Also, related stability problems are addressed. Then, an extended mathematical model that takes into account the ripple component of the inductor current is derived and used in the design of a practical dual-mode digital controller, which for non-negligible ripple operating conditions changes its mode of operation. Validity of the model and the functionality of the introduced controller are verified both through simulations and experimental verifications. Performance of this controller is tested with a wide input 15 V/3 A, 250 kHz, 45 W, three-level experimental prototype.