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# chap11 - 11 AC and DC Equivalent Circuit Modeling of the...

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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. 11.1, the basic dc conversion prop- erty 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 func- tions. 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. What are the basic dc and small-signal ac equivalent circuits of converters operating in the dis- continuous conduction mode (DCM)? It was found in Chapter 5 that, in DCM, the output voltage becomes load-dependent: the conversion ratio M ( D , K ) is a function of the dimensionless parameter which in turn is a function of the load resistance R. So the converter no longer has a voltage- source output characteristic, and hence the dc transformer model is less appropriate. In this chapter, the averaged switch modeling [1-8] approach is employed, to derive equivalent circuits of the DCM switch network. In Section 11.1, it is shown that the loss-free resistor model [9-11] is the averaged switch model of the DCM switch network. This equivalent circuit represents the steady-state and large-signal dynamic characteristics of the DCM switch network, in a clear and simple manner. In the discontinuous conduc- tion mode, the average transistor voltage and current obey Ohm’s law, and hence the transistor is mod- ele d by an effective resistor The average diode voltage and current obey a power source characteristic, with power equal to the power effectively dissipated in Therefore, the diode is modeled with a dependent power source. 11

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410 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode Since most converters operate in discontinuous conduction mode at some operating points, small-signal ac DCM models are needed, to prove that the control systems of such converters are cor- rectly designed. In Section 11.2, a small-signal model of the DCM switch network is derived by linear- ization of the loss-free resistor model. The transfer functions of DCM converters are quite different from their respective CCM transfer functions. The basic DCM buck, boost, and buck-boost converters essen- tially exhibit simple single-pole transfer functions [12, 13], in which the second pole and the RHP zero (in the case of boost and buck-boost converters) are at high frequencies. So the basic converters operating
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chap11 - 11 AC and DC Equivalent Circuit Modeling of the...

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