Small-signal modeling of combined phase shift and pulse width uniformly sampled modulators

Multi-variable digital controllers exploiting a combination of phase shift and pulse width modulation (PSM+PWM) have recently been investigated as methods for simultaneously achieving output voltage regulation and efficiency optimization in dc-dc Series Resonant Converters. This paper discusses the small-signal dynamics of such combined phase shift and pulse width modulators when implemented digitally, and clarifies how the dynamical contributions of PSM+PWM around the generic harmonic of the switching rate can be expressed in the framework of dynamic phasor modeling. The study extends known results for uniformly sampled pulse width and phase shift modulators, illustrating the effects of sampling delays on the modulator output dynamics. Furthermore, results indicate that, in general, PWM and PSM individually induce both amplitude and phase modulation in the converter phasor dynamics. Closed-form results are presented for the generic harmonic of the modulated signal. Theoretical findings are validated via simulation and experimental results.