Small-Signal Transfer Function Model of Multi-Cycle Controller for High-Frequency SMPSs

Increasing the switching frequency of SMPSs (Switched-Mode Power Supplies) can reduce their size and weight; However, developing high-frequency SMPSs with digital controllers is challenging. In conventional digital controllers, control outputs are updated every switching cycle, and therefore, if the switching period is shorter than the calculation time of the controller, the control cannot be achieved. Recently, multi-cycle control has been proposed to address this issue, where control outputs are periodically updated every multiple switching cycles. Despite its potential, the dynamic characteristics of multi-cycle controllers have not been thoroughly investigated. This study employs a multi-cycle voltage-mode PID controller in a trailing-edge modulated buck converter and investigates its small-signal transfer functions. The derived transfer functions are compared with the transfer characteristics obtained from circuit simulations and real circuit experiments in the form of Bode diagrams and time-domain waveforms, which validate the proposed model. The feedback gain is designed using the proposed model, and the results of the real circuit experiments indicate that this feedback gain achieves the design goal. The obtained results confirm that the proposed model is effective for controller design.