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Semi-analytical recursive algorithms of convolution calculations for digitally controlled buck converter design

Modern power systems have to ensure the quality of power supply in spite of the rapid changes of power consumption. Choosing the appropriate parameters of the transfer function of the digital control circuit of the converter main block is especially important. The most common method of obtaining the discrete transfer function of control circuit is an analog prototype. An important problem is the accurate conversion of the analog transfer function in the discrete transfer function. Inaccurate transformation of the analog transfer function causes significant deterioration of the dynamic parameters of the converter controlled digitally in comparison to the converter controlled by an analog control system prototype. The paper shows how to use semi-analytical recursive algorithms of convolution calculations (SARA) to convert analog transfer function in discrete form. With SARA algorithms it is possible to reduce twice the frequency of the digital circuit of the converter in comparison to the frequency of the converter power stage.