Reconsideration of loop gain and its measurement in DC-DC converters

Two measurement schemes, namely, the modulation signal perturbation scheme and the pulse perturbation scheme, have been used for evaluating the loop gain of dc-dc converters. However, the two measured loop gains do not give consistent results due to the use of different forms of the injected small perturbation signal, and the difference in the two schemes cannot be distinguished by the usual averaged model. In this paper, the two loop gain measurement schemes are analyzed based on an extended-frequency-range small-signal model. Expressions of the loop gain are derived and their use in stability assessment and derivation of closed loop transfer functions is demonstrated. A sample-and-hold scheme is proposed as a simple alternative implementation of the pulse perturbation scheme. Finally, experimental prototypes of buck, boost, and buck-boost converters are tested for verification of the analytical results and the effectiveness of the sample-and-hold scheme.