Sampled-data analysis and harmonic balance analysis are applied to analyzeswitching DC-DC converters under constant on-time control. Design-orientedboundary conditions for the period-doubling bifurcation and the saddle-nodebifurcation are derived. The required ramp slope to avoid the bifurcations andthe assigned pole locations associated with the ramp are also derived. Thederived boundary conditions are more general and accurate than those recentlyobtained. Those recently obtained boundary conditions become special casesunder the general modeling approach presented in this paper. Different analysesgive different perspectives on the system dynamics and complement each other.Under the sampled-data analysis, the boundary conditions are expressed in termsof signal slopes and the ramp slope. Under the harmonic balance analysis, theboundary conditions are expressed in terms of signal harmonics. The derivedboundary conditions are useful for a designer to design a converter to avoidthe occurrence of the period-doubling bifurcation and the saddle-nodebifurcation.
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