Extended describing function method for small-signal modeling of resonant and multi-resonant converters

Abstract

The extended describing function method is proposed as a systematic small-signal modeling approach to nonlinear switching circuits. This method offers significant simplification upon the previous work on using the multi-variable describing functions to treat the circuit nonlinearities. As an extension to the statespace averaging method, this modeling technique can incorporate any Fourier components for good model accuracy and provides continuous-time small-signal models for PWM topologies and various soft-switching resonant topologies.

The proposed method is demonstrated using four resonant topologies and two multi-resonant topologies. These circuits are strongly oscillatory, and thus they cannot be modeled by means of traditional averaging techniques. By employing the proposed modeling method, the dynamics of the resonant converters are analyzed with emphasis on the nonlinear interaction between the switching frequency and the circuit natural resonant frequency. Equivalent circuit models are provided for more convenience of practical designs. Small-signal analysis is also performed for two challenging multi-resonant topologies with complex structure and operation. All of the theoretical models are verified experimentally and the predictions are well supported by the measurement data up to the Nyquist frequency.