Small Signal Analysis of Energy Factor and Mathematical Modeling for Power DC–DC Converters

Mathematical modeling for power dc–dc converters is a historical problem accompanying dc–dc conversion technology since the 1940s. The traditional mathematical modeling is not available for complex structure converters since the differential equation order increases very high. We have to search for other ways to establish mathematical modeling for power dc–dc converters. We have defined energy factor (EF) and new mathematical modeling for power dc–dc converters that have attracted much attention in recent years. This paper describes the small signal analysis of EF and mathematical modeling for power dc–dc converters in continuous conduction mode and discontinuous conduction mode. EF and the subsequential parameters can illustrate the unit-step response and interference recovery. This investigation may be helpful for system design and dc–dc converters characteristics. Two dc–dc converters: Buck converter and super-lift Luo-converter as the samples, are analyzed in this paper to demonstrate the applications of EF, pumping energy, stored energy (SE), capacitor/inductor SE ratio, energy losses, time constant $\tau$, and damping time constant $\tau_{d}$.