Small-signal modeling of uniformly sampled phase shift modulators

Phase shift modulation (PSM) is a commonly used technique for controlling the active power flow in resonant dc-ac and dc-dc converters. Although traditionally developed as an analog modulation scheme, digital PSM is being increasingly used in conjunction with advanced multi-variable digital controllers and online efficiency optimization algorithms. While analog PSM is known not to introduce additional dynamics from a small-signal standpoint, the analysis disclosed in this work indicates that discrete-time, or uniformly sampled, PSM introduces a transport delay of small-signal nature. Furthermore, and in close analogy with the theory of uniformly sampled pulse width modulators, such delay depends on the modulator carrier type as well as on the converter operating point. The paper first clarifies the modeling procedure for describing the small-signal dynamics of uniformly sampled phase shift modulators. Secondly, it provides an extension of traditional phasor modeling to digital phase-controlled converters, allowing to account for the additional modulator dynamics in the design of the closed-loop compensation. Theoretical findings are validated via simulation and experimental results.