EECS 314
Winter 2013
HW #6
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Discussion section # _____
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© 2013 Alexander Ganago
Page 1 of 4
Last printed 3/8/2013 9:59:00 PM
File: 2013 W 314 HW 6 p1_parts1+2
Problem 1 (100 points)
Build a square wave as a sum of its sinusoidal components;
determine the Rise/Fall Time of the partial sums
Before starting to solve this problem, make sure that you have reviewed the
very end of recording of Lecture #10 (February 18, 2013) and read the
following:
1.
Lab 5 pages 3 – 12, and 25 – 29 in your Lab book
2.
Appendix pages A110 and A111 in your Lab book
3.
“Example for 2013 W 314 HW 6 p1” on CTools in HW 6 folder
Instructors in Discussion sections and office hours will assume that every
student is already familiar with the materials listed above.
In this Problem you will start building the
square wave at 20 kHz and 12 Vppk
(50% duty cycle) as a sum of its sinusoidal components – the fundamental and
harmonics up to the 9
th
, and determine the Rise Time of the waveforms obtained as
the partial sums.
Part 1 (20 points)
The sinusoidal components of the square wave
For square wave with the parameters listed above, calculate the frequency and peak
amplitude of its fundamental and harmonic sinusoidal components up to the 9
th
.
Write your results (with the units of measure) in the table below.
The
fundamental
3
rd
harmonic
5
th
harmonic
7
th
harmonic
9
th
harmonic
Frequency
20 kHz
60 kHz
100 kHz
140 kHz
180 kHz
Peak
amplitude
7.64 V
2.55 V
1.53 V
1.09 V
0.85 V
Show your work for the 5
th
harmonic.
peak amplitude =
peaktopeak amplitude
2
and thus amplitude
𝐴
= 6 V
Amplitude of n
th
harmonic is given as
𝐴
𝑛
=
4𝐴
𝜋𝑛
and so
𝐴
5
=
24
5𝜋
V
(continued on the next page)
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EECS 314
Winter 2013
HW #6 Problem 1
Student’s name _______________________________
Discussion section # _____
© 2013 Alexander Ganago
Page 2 of 4
Last printed 3/8/2013 9:59:00 PM
File: 2013 W 314 HW 6 p1_parts1+2
Using your numerical results for the 5
th
harmonic, write the equation in the form
, where time
t
is in
µ
s and voltage in volts:
Note that
100 kHz
∙
1
µ
s = 0.1
The 5
th
harmonic waveform is
𝑉
5
(
𝑡
) =
24
5𝜋
sin(0.2
∙ 𝜋𝑡
) V = (1.53 V) sin(0.2
∙ 𝜋𝑡
)
Problem 1 Part 2 (40 points)
Plots of the fundamental and partial sums
Use MATLAB to make a computergenerated plot to show the following
four
waveforms
(
1,000 points per period
of the square wave
):
1.
The fundamental alone
2.
The fundamental plus the 3
rd
harmonic
3.
The fundamental plus the harmonics up to the 5
th
4.
The fundamental plus the harmonics up to the 9
th
Do not delete your files until you finish the last part of this Problem!
On your plot:
Label the horizontal axis in microseconds and the vertical axis in volts
Show two periods of the fundamental
Clearly indicate which curve shows what (handwritten, OK)
Make sure that the peaktopeak amplitude of the fundamental is
between ½ and ¾ of the height of the plot
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 Winter '07
 Ganago
 Square wave, Highpass filter, Lowpass filter

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