A Comparative Study on Experimental Loop Gain Measurement Techniques Applied to Digitally Controlled Buck-Type Power Converters

This paper presents a study on experimental loop gain measurement techniques in the context of digitally controlled buck-type converters. The work limits itself to the popular digital design choice in which the ADC sampling frequency equals the converter switching frequency. It is known that Middlebrook's continuous-time perturbation injection approach for experimental loop gain measurements presents limitations when assessing digital control loops. Nevertheless, this work aims to analyse the approximations obtained by using this popular and practical technique in comparison to the actual discrete-time control loop dynamics. Cases considered are the single current loop, the multiloop (voltage loop embedding a current loop) and the single voltage loop. It is concluded that the continuous-time injection approach remains especially problematic in the digital current loop, typically being a strong violation of the small-aliasing assumption, whereas it is useful in voltage loops (with and without embedded current loop) at frequencies well-below the Nyquist frequency thanks to the output voltage typically being a well-filtered state variable.