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ecen5797hw1

# ecen5797hw1 - Points are indicated in square brackets Show...

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Points are indicated in square brackets. Show all work, partial credit will be given, except for extra-credit questions. ECEN4007/ECEN5797 Power Electronics 1 Fall 2001 Homework #1 4007 students do problems 1, 2 and 3 (problem 4 is extra credit); 5797 students do all 5 problems. 1. [50pts] (all students) The switches in the converter shown below operate synchronously: each is in position 1 for 0 t DT s , and in position 2 for DT s < t < T s . The switching is periodic with period T s . + 1 2 2 1 V g + _ v i 1 ( t ) L i 2 ( t ) i ( t ) C R (a) Find the dependence of the equilibrium (i.e. steady-state) output voltage V and inductor current I on the duty ratio D , input voltage V g , and load resistance R . You may assume that the inductor current ripple and capacitor voltage ripple are small. Sketch your results over the range 0 D < 1. (b) The converter is used to generate DC output voltage V = 1 . 8V from a battery with V g = 1 . 5V. The load resistance is R = 1 , and the switching frequency is f s = 500kHz.

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