Describing functions of power electronics circuits using progressive analysis of circuit waveforms

This paper presents a technique for calculating the AC line-to-output and control-to-output transfer characteristics of DC/DC converters, in which the time instants switching from one topology to the next one are a priori unknown and are determined by threshold conditions (i.e., by the time evolution of the converter waveforms). Describing functions are defined for small perturbations in either the input voltage or the control signal. After injecting a sinusoidal perturbation at the frequency of interest into the converter, the fundamental component of the output spectrum is determined. The describing functions are thus evaluated and provide the required AC transfer characteristics. The proposed method is integrated with a previously developed time-domain simulation algorithm, which is based on monitoring the switches positions, allowing the simulator to find automatically the switching instants and topological sequence of operation. Different examples are illustrated, including a classical pulse-width-modulated (PWM) converter, a current-programmed PWM regulator, and a switched-capacitor converter. The simulated results are compared with the experimental measurements and the results in the available literature.