ECE433, Homework 1
Due: February 9, 2011
1)
Given the following waveform:
Express f(t) as a Fourier Series. Then use MATLAB to construct the signal from the Fourier Series you
derived to verify your result.
a)
For the waveform shown, by providing enough justification, circle the following statements
that are true:
i)
f(t) can represent a voltage across an inductor
ii) f(t) can represent a current through an inductor
iii) f(t) can represent a current through a capacitor
iv) f(t) can represent a voltage across a capacitor
2)
In the converter of Fig. 1, the switches operate synchronously, each is in position 1 for
0g3409g1872g3409
g1830g1846
g3046
, and in position 2 for
g1830g1846
g3046
g3409g1872g3409g1846
g3046
. Derive an expression for the voltage conversion ratio
g1839g4666g1830g4667g3404g1848/g1848
g3034
. Sketch
M(D)
vs. D and compare with that of a buck converter.
Fig. 1
3)
The converter of Fig. 2 operates with an input voltage
g1848
g3036g3041
g340410g1848
. The output voltage is
g1848
g3042g3048g3047
g340424g1848
and the switching frequency is
g1858
g3046g3050
g3404250g1863g1834g1878
. All elements are ideal, and the
converter operates in steady state.
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 Spring '08
 Staff
 Fourier Series, Switchedmode power supply, duty cycle, voltage conversion ratio

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