Accurate Analysis of Subharmonic Oscillations of $V^2$ and $V^2I_c$ Controls Applied to Buck Converter

V
²
Ic control provides very fast dynamic performance to the Buck converter both under load steps and under voltage reference steps. However, the design of this control is complex since it is prone to subharmonic oscillations and several parameters affect the stability of the system. This paper derives and validates a very accurate modeling and stability analysis of a closed-loop V
²
Ic control using the Floquet theory. This allows the derivation of sensitivity analysis to design a robust converter. The proposed methodology is validated on a 5-MHz Buck converter. The work is also extended to V
²
control using the same methodology, showing high accuracy and robustness. The paper also demonstrates, on the V
²
control, that even a low bandwidth-linear controller can affect the stability of a ripple-based control.