Analysis of nonlinear phenomena in digital integral-controlled Buck converters

Nonlinear phenomena in a digital integral-controlled synchronous Buck converter working in continuous conduction mode (CCM) are studied in this paper. Firstly, the closed-loop model of the system in z-domain is established. Next, the stability boundary of the system is calculated according to the Routh stability criterion. Then, the two nonlinear quantizers, namely the analog-to-digital converter (ADC) and the digital pulse width modulator (DPWM), are characterized via describing function method, and the approximate boundary to avoid limit-cycle oscillations of output voltage is obtained. Effectiveness of the calculated boundaries is validated by simulation in Simulink. It is found that the system will experience limit cycle oscillations and Hopf bifurcations successively with the increase of integral gain.