Small-signal characteristics of switching regulators using Fourier technique in modified nodal approach

A new method for calculating the input-to-output and control-to-output characteristics of DC-DC converters is formulated. The approach is based on a Fourier analysis technique, relating the input and output spectrums of the converter. For small perturbations in either the input line voltage or the control signal, describing functions are defined. At the frequency of interest, which is given by the frequency of the injected sinusoidal perturbation, the zeroth term of the time-varying transfer function of the circuit is determined and the describing functions are evaluated, giving the required small-signal AC characteristics of the converters. The method is integrated with an original algorithm for calculating the time-domain response of the regulator by monitoring the switches´ position, which allows the simulator to find automatically the transition instants and the switching sequence, assuring the generality of the method. The method is exemplified by the simulation of a traditional boost PWM DC-to-DC converter. The results are favorably compared to those obtained in literature by using other approaches and to the experimental results