  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 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 design-oriented 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.
