Boundary Conditions of Subharmonic Oscillations in Fixed-Switching-Frequency DC-DC Converters

Design-oriented boundary conditions for subharmonic oscillations are of great interest recently. Based on a subharmonic oscillation boundary condition reported in a PhD thesis more than a decade ago, extended new boundary conditions are derived in closed forms for general switching DC-DC converters. Sampled-data and harmonic balance analyses are applied and generate equivalent results. It is shown that the equivalent series resistance causes the boundary conditions for voltage/current mode control to have similar forms. Some recently reported boundary conditions become special cases in view of the general boundary conditions derived. New Nyquist-like designoriented plots are proposed to predict or prevent the occurrence of the subharmonic oscillation. The relation between the crossover frequency and the subharmonic oscillation is also analyzed.