EELE 461/561 – Digital System Design
Homework #1
Name:
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Grade (EELE461): _______ / 10
Grade (EELE561): _______ / 15
NOTE: Print this sheet and use as a cover for your homework set. Staple your solutions to the back with your name
in the upper right corner of each page. Clearly indicate which problem number you are working. Clearly mark your
solution. Show your work for partial credit.
EELE 461 & EELE 561
A) Risetime Bandwidth Product
(8 POINTS)
Use Microsoft Excel or Matlab to construct the Fourier Reconstruction of an ideal Square wave with F=667
MHz and 50% duty cycle. The square wave has an amplitude of 1v and is centered around 0v. You will need
to create the individual sine waves that create the ODD harmonics of the square wave up to the 11th Harmonic.
You will then continually add each harmonic to the fundamental frequency to create 6 separate square waves,
each with continually more harmonics (i.e., fund, fund+3 rd, fund+3rd+5th, etc…). Each time you create a new
square wave representation, record the measured 10%-90% rise time on your plot, the bandwidth and the rise
time bandwidth product. (Hint: the bandwidth is the frequency of the highest frequency that you’re
considering). Fill in the following table and provide the plot of the resultant square wave for each combination.
Graph all 6 square waves on the same plot.
Signal Composition
Rise time
Bandwidth
trise∙BW Product
Just the Fundamental
Fundamental + 3rd Harmonic
Fundamental + 3rd & 5th Harmonic
Fundamental + 3rd , 5th, & 7th Harmonic
Fundamental + 3rd , 5th, 7th & 9th Harmonic
Fundamental + 3rd , 5th, 7th, 9th, & 11th Harmonic
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B) Composite Risetime
(2 POINTS)
What is the resultant risetime that the receiver will see in this circuit?
trise=100ps
BW=3 GHz
ANS
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EELE 561 Only
C) Read the Picosecond Pulse Labs application note posted to the course website under Information. Write a short
summary (<300 words) describing the key points of this paper.
(5 POINTS)