Power Electronics and Motor Drive Systems

7.8. Simplified Circuits and Approximate Transfer Functions of Boost and Buck Converters

If the semiconductor devices of a boost or a buck converter are removed, then the power circuit with an input dc voltage

{\bar{V}}_{o}

is as shown in Fig. 7.29.

From Fig. 7.29, the following equations are obtained:

$\begin{matrix} {\bar{V}}_{o} - v_{L} - v_{C} = 0 or {\bar{V}}_{o} - L_{o} \frac{di}{dt} - v_{C} = 0 \\ or {\bar{V}}_{o} - L_{o} {\overset{\cdot}{x}}_{2} - x_{1} = 0 or {\overset{\cdot}{x}}_{2} = - \frac{x_{1}}{L_{o}} + \frac{{\bar{V}}_{o}}{L_{o}} \end{matrix}$

and

Figure 7.29 Boost and buck converter without semiconductor devices.

$\begin{matrix} i_{L} - i_{C} - i_{o} = 0 or i_{L} - C_{o} \frac{{dv}_{C}}{dt} - \frac{v_{C}}{R_{o}} = \end{matrix}$

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Power Electronics and Motor Drive Systems by Stefanos Manias

7.8. Simplified Circuits and Approximate Transfer Functions of Boost and Buck Converters

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