Generic Multifrequency Small-Signal Model For Digitally Controlled Buck Converter

Digitally controlled DC-DC converters have received more and more attentions because of lower cost and higher performance of microprocessors. In order to improve the dynamic response of the digitally controlled DC-DC converters, the bandwidth should be pushed as high as possible by optimizing the design of the controller. This thesis focuses on the digitally controlled buck converter, and a generic multifrequency small-signal model is built and the open-loop gain is analyzed and the influence of modulation schemes on the stability is revealed, which provide theoretical foundation for the choice of modulation schemes and the design of converters with high bandwidth.The causes of the aliasing, computation delay, and modulation delay in digitally controlled buck converters are analyzed in this thesis. It is pointed out that the aliasing in the closed-loop induced by the sampling reduces the accuracy of the model of sampler. The model of the digital pulse-width modulation(DPWM) under different modulation schemes is deduced and the law according to which the modulation delay changed with the modulation scheme is revealed. The generic multifrequency small-signal model for digitally controlled buck converters is obtained.Based on the generic multifrequency small-signal model, the expression of the open-loop gain of the system is derived in this thesis. Then, the discrete models under different modulation schemes for the power stage of buck converters are derived, which indicate that the models with trail-edge modulation and lead-edge modulation are the same, and the models with symmetrical dual-edge modulation are related to the sampling time. The method of simplifying the calculations of the open-loop gain through advanced z-transform is proposed, and hence, the z-domain expression of open-loop gain is obtained. The universal method to analyze the stability of the digitally controlled buck converters by means of the z-domain expression of open-loop gain is given, and the correctness of the proposed model and the analyzing method is verified by the simulation results, and the phenomenon that the stability of digitally controlled buck converters is influenced by modulation schemes is explained with the distribution of zeros and poles.The measurement method for open-loop gain of digitally controlled buck converters is introduced. The prototype of the digitally controlled buck converters is designed and built, and the accuracy of the generic multifrequency small-signal model is verified by the open-loop gain measurement.