# 3.8 A 1.5 V battery is to be used to power a 5 V, 1 A load. It has been decided to use a buck boost

3.8 A 1.5 V battery is to be used to power a 5 V, 1 A load. It has been decided to use a buck boost converter in this application. A suitable transistor is found with an on-resistance of 35 mO, and a Schottky diode is found with a forward drop of 0.5 V. The on-resistance of the Schottky diode may be ignored. The power stage schematic is shown in Fig. 3.35. (a) Derive an equivalent circuit that models the dc properties of this converter. Include the transistor and diode conduction losses, as well as the inductor copper loss, but ignore all other sources of loss. Your model should correctly

3.8 A 1.5 V battery is to be used to power a 5 V, 1 A load. It has been decided to use a buck boost converter in this application. A suitable transistor is found with an on-resistance of 35 mO, and a Schottky diode is found with a forward drop of 0.5 V. The on-resistance of the Schottky diode may be ignored. The power stage schematic is shown in Fig. 3.35. (a) Derive an equivalent circuit that models the dc properties of this converter. Include the transistor and diode conduction losses, as well as the inductor copper loss, but ignore all other sources of loss. Your model should correctly describe the converter dc input port. (b) It is desired that the converter operates with at least 70% efficiency under nominal conditions (i.e., when the input voltage is 1.5 V and the output is 5 V at 1 A). How large can the inductor winding resistance be? At what duty cycle will the converter then operate? Note: there is an easy way and a not-so-easy way to analytically solve this part. (c) For your design of part (b), compute the power loss in each element. (d) Plot the converter output voltage and efficiency over the range 0 = D = 1, using the value of inductor winding resistance which you selected in part (b). (e) Discuss your plot of part (d). Does it behave as you expect? Explain. For Problems 3.9 and 3.10, a transistor having an on-resistance of 0.5 O is used. To simplify the problems, you may neglect all losses other than the transistor conduction loss. You may also neglect the dependence of MOSFET on-resistance on rated blocking voltage. These simplifying assumptions reduce the differences between converters, but do not change the conclusions regarding which converter performs best in the given situations.

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