Switch-Mode Power Converters: Design and Analysis

1.8: Voltage-Mode CCM Small-Signal Stability

1.8 Voltage-Mode CCM Small-Signal Stability

By nature, switch-mode power converters with feedback control are nonlinear control systems. Nonlinear control systems certainly are not easily subjected to the conventional linear system analysis, in which the superposition principle applies and the classical system stability theory is also applicable. Stated differently, switch-mode converters without the support of a grand vision cannot enjoy the vast amount of analytical benefits maturely developed in 1950 1980 for linear systems. Fortunately, that grand vision came in the mid-1970s. Dr. R. Middlebrook and his then graduate student Slobodan Cuk at the California Institute of Technology conceived the concept of state-space averaging. Based on the concept, nonlinear power converters, power stages in particular, are given equivalent linear models. Once that hurdle was surmounted, switch-mode power converters have been well investigated, employing those tools originally developed for linear systems. Since then, streams of in-depth studies and insightful results have been generated and reported. We utilize many models developed by those two visionary figures without proof but with great appreciation. Readers interested in the topics should refer to [1] for details.

Based on the state-space averaging technique, the nonisolated buck converter power stage in the CCM can be represented by Figure 1.12 for small-signal studies. To fit our application in which isolation transformer and line filter are included, the model must be modified as Figure 1.13.


Figure 1.12: Small-signal model for a nonisolated converter in the CCM

Figure 1.13: Small-signal model for an isolated converter in the CCM

Figure 1.13 with transfer...

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