15. AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode

So far, we have derived equivalent circuit models for dc–dc pulse-width modulation (PWM) converters operating in the continuous conduction mode. As illustrated in Fig. 15.1, the basic dc conversion property is modeled by an effective dc transformer, having a turns ratio equal to the conversion ratio M(D). This model predicts that the converter has a voltage-source output characteristic, such that the output voltage is essentially independent of the load current or load resistance R. We have also seen how to refine this model, to predict losses and efficiency, converter dynamics, and small-signal ac transfer functions. We found that the transfer functions of the buck converter contain two low-frequency poles, owing to the converter filter inductor and capacitor. The control-to-output transfer functions of the boost and buck–boost converters additionally contain a right half-plane zero. Finally, we have seen how to utilize these results in the design of converter control systems.

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