Limits of the frequency response for the analysis of ripple-based controllers

Advanced control techniques like V
²
, V
_out
hysteresis or V
²
I
_c
can strongly reduce the required output capacitance in PowerSoC converters. Techniques to analyze power converters based on the analysis of the frequency response are not suitable for ripple-based controllers that use fast-scale dynamics to control the power stage. This paper proves that the use of discrete modeling together with Floquet theory is a very powerful tool to model the system and derive stable region diagrams for sensitivity analysis. It is applied to V
²
I
_c
control, validating experimentally that Floquet theory predicts accurately sub-harmonic oscillations. This method is applied to several ripple-based controllers, providing higher accuracy when it is compared with other techniques based on the frequency response. The paper experimentally validates the usefulness of the discrete modeling and the Floquet theory on a 5 MHz Buck converter with a V
²
I
_c
control.