Mixed-mode simulations to check stability of an adaptive constant on-time DC-DC converter

In this paper we consider performances of a version of a constant on-time (COT) DC/DC converter. There is a renewed interest in COT converters since they offer interesting features such as speed and low cost implementation. The duty cycle of these converters is varied by acting on the working frequency and this introduces problems in modeling, in deriving transfer functions and in studying stability properties. Largely adopted averaging methods, that assume that the control loop bandwidth is much smaller than the converter switching frequency, risk to be no longer applicable since COT converters do not satisfy this hypothesis. Also conventional methods and techniques that exploit Floquet theory and variational model can not be applied since differential algebraic equations modeling switching converters show discontinuities in the vector field (switching). In this paper we use saltation matrices to allow the application of consolidated numerical techniques to the specific case of COT converters and, more in general, to the broad class of switching converters modeled by mixed analog/digital models.