Poles and Zeros for Sampled-Data Duty-Ratio-to-Output Dynamics of Buck and Boost Converters
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Poles and zeros for sampled-data models of buck and boost converters are derived analytically for the first time (to the author's knowledge). Both continuous conduction mode (CCM) and discontinuous conduction mode (DCM) are considered. Comparisons are made with the corresponding results derived from the averaged model. For poles, the two models give similar results except in the DCM operation. For zeros, however the two models give quite different results. The zero obtained for the sampled-data model differs from that obtained for the averaged model. The zero derived from the sampled-data model depends on the switching frequency and duty ratio, as well as on the modulation scheme. For the buck converter in CCM, a single real zero exists even if the equivalent series resistance (ESR) is not modeled. Inclusion of the ESR in the model results in shifting the zero to the right in the complex plane. The zero can be unstable with or without the ESR being modeled. Undershoot is not observed because the zero is less than 1. For the boost converter in CCM, only one zero exists and this zero can be stable when the duty ratio is small. For the buck or boost converter in DCM, only one pole exists and there is no zero. The phase of the frequency response can go beyond -90 degree.