ECE472 HOMEWORK #1 DUE: WEDNESDAY, SEPTEMBER 2, 2015

Problem 1.1

m

2V

V

0

−V

−2Vm

m

m

T T

24

T

t (s)

v(t) (V)

3T

4

Show that Vrms = Vm

√2 for the above periodic waveform.

Problem 1.2

(a) Explain why the Fourier series for the waveform in Problem 1.1 is of the form:

v(t) = b1 sinωt+ b3 sin 3ωt+ b5 sin 5ωt+ . . .

(b) Show that bn = (4Vm/nπ)(1 + cos(nπ/3)) analytically for n odd.(c) Find the rms magnitude V1,rms of the fundamental component of v(t).

Problem 1.3

The total harmonic distortion THD of a periodic waveform is defined as

THD =

√√√√V 2rms − V 2

1,rms

V 21,rms

=

√√√√( Vrms

V1,rms

)2

− 1

Find the THD of the waveform in Problem 1.1.

Problem 1.4

The distortion factor DF of a periodic waveform is defined as

DF =V1,rms

Vrms

Compute the DF of the waveform in Problem 1.1 and show in general that

DF =1√

1 + THD2