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Hence, and and Eqs. 2 Inclusion of Inductor Copper Loss 43 become For the switch is in position 2 and the circuit reduces to Fig. 7(b). The inductor current and capacitor voltage are then given by We again make the small-ripple approximation. The principle of inductor volt-second balance can now be invoked. 9) are used to construct the inductor voltage waveform in Fig. 8. The dc component, or average value, of the inductor voltage is By setting to zero and collecting terms, one obtains (recall that It can be seen that the inductor winding resistance adds another term to the inductor volt-second balance equation.

6] M. R ASHID , Power Electronics: Circuits, Devices, and Applications, 1993. [7] P. K REIN , Elements of Power Electronics, New York: Oxford University Press, 1998. [8] K. K IT S UM , Switch Mode Power Conversion—Basic Theory and Design, New York: Marcel Dekker, 1984. 1 Analysis and design of a buck-boost converter: A buck-boost converter is illustrated in Fig. 28(a), and a practical implementation using a transistor and diode is shown in Fig. 28(b). (a) (b) Find the dependence of the equilibrium output voltage V and inductor current / on the duty ratio input voltage and load resistance R.

26) is equal to zero. Therefore, in equilibrium the integral of the capacitor current over one switching period (having the dimensions of amp-seconds, or charge) should be zero. There is no net change in capacitor charge in steady state. An equivalent statement is 22 Principles of Steady-State Converter Analysis The average value, or dc component, of the capacitor current must be zero in equilibrium. This should be an intuitive result. If a dc current is applied to a capacitor, then the capacitor will charge continually and its voltage will increase without bound.

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