Analysis of Digital PCM-Controlled Boost Converter With Trailing-Edge Modulation Based on z-Domain and Describing-Function Model

Digital trailing-edge modulated peak-current-mode (PCM) control scheme is commonly used in power converters, due to the similar excellent characteristics with its peer analog controller and being achieved easily in practice. However, the additional issues, such as time delays, quantization error, and resolution of the digital pulsewidth modulator (DPWM), in the digital controller, not only reduce the stability of the converter but also make the modeling and analysis more complicated. Taking the digital controlled boost converter as an example, this article presents a z-domain model of the whole converter system on the basis of a describing-function method by considering the effects of the abovementioned problems. The influences of time delays from analog-to-digital conversion (ADC) and DPWM and resolution from the DPWM module can be analyzed clearly according to the proposed model. And more importantly, the critical resolution between stable and unstable operations of the converter can be determined by checking the eigenvalues. Furthermore, the stability analysis based on the presented z-domain model is verified by the simulations and experiments.