Critical output-capacitor ESR for stability of V2 controlled buck converter in CCM and DCM

It has been reported that subharmonic instability exists in the V² controlled buck converter in continuous conduction mode (CCM) when the duty ratio is above 0.5 (D > 0.5) and no stability issue exists in discontinuous conduction mode (DCM) when 0 <; D <; 1. However, the CCM and DCM instabilities will appear in the safe duty ratio range when the equivalent series resistance (ESR) of the output capacitor is below a critical value. The critical output-capacitor ESR for the stability of a V² controlled buck converter in CCM and DCM is investigated by using the discrete-time model and verified by circuit simulations.