EECS145M Midterm 2: Microcomputer Interfacing Laboratory, Exams of Microcomputers

The instructions and problems for the midterm 2 exam in the microcomputer interfacing laboratory (eecs145m) course at the university of california, berkeley. The exam covers topics such as fft analysis, anti-aliasing filters, and d/a converter testing.

Typology: Exams

2012/2013

Uploaded on 03/22/2013

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Name (Last, First)
Student ID number
EECS145M 2005 Midterm #2 Page 1 Derenzo
UNIVERSITY OF CALIFORNIA
College of Engineering
Electrical Engineering and Computer Sciences Department
EECS 145M: Microcomputer Interfacing Laboratory
Spring Midterm #2 (Closed book- equation sheet provided- calculators OK)
Full credit can only be given if you show your work.
Wednesday, April 13, 2005
Problem 1 (15 points)
You sample exactly 5 cycles of a 15 Hz symmetric square wave (after anti-alias filtering) and
compute the FFT. The magnitudes of your FFT coefficients are plotted in the figure below.
Explain the non-zero values at n = 5, 15, 20, 25, 35, 45, 55, 73, 83, 93, 103, 108, 113, and 123.
(You do not need to explain the amplitudes, just why they are non-zero.)
Frequency index
16
0
10
20
30
40
50
60
70
80
90
0 32 48 64 80 96 112 128
pf3
pf4
pf5

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UNIVERSITY OF CALIFORNIA

College of Engineering Electrical Engineering and Computer Sciences Department EECS 145M: Microcomputer Interfacing Laboratory Spring Midterm #2 (Closed book- equation sheet provided- calculators OK) Full credit can only be given if you show your work. Wednesday, April 13, 2005 Problem 1 (15 points) You sample exactly 5 cycles of a 15 Hz symmetric square wave (after anti-alias filtering) and compute the FFT. The magnitudes of your FFT coefficients are plotted in the figure below. Explain the non-zero values at n = 5, 15, 20, 25, 35, 45, 55, 73, 83, 93, 103, 108, 113, and 123. (You do not need to explain the amplitudes, just why they are non-zero.) Frequency index 16 0 10 20 30 40 50 60 70 80 90 0 32 48 64 80 96 112 128

PROBLEM 2 (15 points) Design a Butterworth anti-aliasing low pass filter that meets the following requirements:

  • Gain > 0.90 for frequencies below 20 kHz
  • Gain < 0.001 for frequencies that alias below 20 kHz
  • The sampling frequency is 100 kHz
  • The filter has the minimum number of components (lowest order) PROBLEM 3 (35 points) A colleague has taken 16,348 (=2^14 ) samples of a bandwidth-limited nontrivial waveform for one second, takes the fast Fourier transform (FFT), and then deletes the data. After informing you of this, you ask "Did you use a raised cosine window?". Your colleague replies "What is a raised cosine window?", tells you that it is not possible to take the data again, and asks whether you can fix the available FFT. 3a (10 points) Describe in words how your colleague's FFT is related to the true frequency spectrum of the waveform.

PROBLEM 4 (35 points) Design a system for the assembly line testing of D/A converters. The design requirements are as follows:

  • Sixteen 12-bit D/A converters are plugged into the system and the absolute accuracy, relative accuracy, and differential linearity measured completely under computer control The components available are as follows:
  • One 16-bit D/A converter with ±1/2 LSB absolute accuracy
  • Sixteen 12-bit D/A converters (to be tested)
  • All D/A converters need a steady input for a steady output
  • Sixteen comparators
  • A microcomputer with two 16-bit output ports and one 16 bit input port
  • The output and input ports are operated in transparent mode (no handshaking) 4a. (15 points) Draw a block diagram of your system, showing and labeling all essential components, connections, and signals.

4b. (15 points) List the steps necessary to determine the maximum absolute error, the maximum linearity error, and the maximum differential linearity error for each 12-bit D/A converter. 4c. (5 points) With what accuracy (in units of 1 LSB) can this system measure the quantities in part 4b?