  Period doubling bifurcation leading to subharmonic oscillations are undesired
phenomena in switching converters. In past studies, their prediction has been
mainly tackled by explicitly deriving a discrete time model and then
linearizing it in the vicinity of the operating point. However, the results
obtained from such an approach cannot be applied for design purpose.
Alternatively, in this paper, the subharmonic oscillations in voltage mode
controlled DC-DC buck converters are predicted by using a formal symbolic
approach. This approach is based on expressing the subharmonic oscillation
conditions in the frequency domain and then converting the results to
generalized hypergeometric functions. The obtained expressions depend
explicitly on the system parameters and the operating duty cycle making the
results directly applicable for design purpose. Under certain practical
conditions concerning these parameters, the hypergeometric functions can be
approximated by polylogarithm and standard functions. The new approach is
demonstrated using an example of voltage-mode-controlled buck converters. It is
found that the stability of the converter is strongly dependent upon a
polynomial function of the duty cycle.
