  Modeling power electronic converters at frequencies close to or above half
the switching frequency has been difficult due to the time-variant and
discontinuous switching actions. This paper uses the properties of moving
Fourier coefficients to develop the generalized averaging method, breaking
though the limit of half the switching frequency. The paper also proposes the
generalized average model for various switching signals, including pulse-width
modulation (PWM), phase-shift modulation, pulse-frequency modulation (PFM), and
state-dependent switching signals, so that circuits and modulators/controllers
can be modeled separately and combined flexibly. Using the Laplace transform of
moving Fourier coefficients, the coupling of signals and their sidebands at
different frequencies is clearly described as the coupling of moving Fourier
coefficients at the same frequency in a linear time-invariant system framework.
The modeling method is applied to a PWM controlled boost converter, a V2
constant on-time controlled buck converter, and a PFM controlled LLC converter,
for demonstration and validation. Experimental results of the converters in
different operating modes show that the proposed models have higher accuracy
than exiting models, especially in the frequency range close to or above half
the switching frequency. The developed method can be applied to almost all
types of power electronic converters.
