Microcomputer Controlled Systems for A/D Converter Testing and Musical Instrument Analysis, Exams of Microcomputers

Information about two microcomputer-controlled systems designed for testing 12-bit a/d converters and analyzing the harmonic content of musical instruments. Problem statements, instructions, and equations for designing and implementing these systems. Students enrolled in the electrical engineering and computer sciences department at the university of california, berkeley, may find this document useful for studying for the eecs 145m midterm #2 exam.

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Name (Last, First)
UNIVERSITY OF CALIFORNIA
College of Engineering
Electrical Engineering and Computer Sciences Department
EECS 145M: Microcomputer Interfacing Laboratory
Spring Midterm #2
Monday, April 21, 1997
Closed book- calculators OK
Many equations are listed at the back of the exam
You must show your work to get full credit
PROBLEM 1 (50 points)
Design a computer controlled system for the automatic testing of 12-bit A/D converters.
You are provided with the following:
A microcomputer equipped with a 16-bit parallel input port, and a 16-bit parallel output port.
A 16-bit D/A converter with ±1 LSB absolute accuracy.
You may assume the following:
The 16-bit parallel output port is in “transparent” mode. A 16-bit word A written to the output
port using the command outport(1, A) immediately appears on the output lines.
The 16-bit parallel input port requires a low-to-high edge on a “strobe” input line for external
data to be latched onto the 16 bit registers. The program can read these registers using the
command B = inport(1).
The parallel input port has an “input data available” line that can be asserted high or low by an
external device and read by the program using the command C = inport(2).
The parallel input port has an external “ready for input data” line that can be set high using the
program command outport(2,1), and set low using outport(2,0).
The A/D converter requires a “start conversion” low-to-high signal and after conversion
provides a “data ready” low-to-high signal that goes low when “start conversion” goes low.
The A/D reference voltages are Vref = 0.0000 V and Vref+ = 4.095 V
The D/A reference voltages are Vref = 0.0000 V and Vref+ = 4.096 V
EECS145M 1997 Midterm #2 Page 1 Derenzo
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UNIVERSITY OF CALIFORNIA

College of Engineering Electrical Engineering and Computer Sciences Department

EECS 145M: Microcomputer Interfacing Laboratory

Spring Midterm # Monday, April 21, 1997

  • Closed book- calculators OK
  • Many equations are listed at the back of the exam
  • You must show your work to get full credit

PROBLEM 1 (50 points)

Design a computer controlled system for the automatic testing of 12-bit A/D converters.

Y ou are provided with the following:

  • A microcomputer equipped with a 16-bit parallel input port, and a 16-bit parallel output port.
  • A 16-bit D/A converter with ±1 LSB absolute accuracy.

You may assume the following:

  • The 16-bit parallel output port is in “transparent” mode. A 16-bit word A written to the output port using the command outport(1, A ) immediately appears on the output lines.
  • The 16-bit parallel input port requires a low-to-high edge on a “strobe” input line for external data to be latched onto the 16 bit registers. The program can read these registers using the command B = inport(1).
  • The parallel input port has an “input data available” line that can be asserted high or low by an external device and read by the program using the command C = inport(2).
  • The parallel input port has an external “ready for input data” line that can be set high using the program command outport(2,1), and set low using outport(2,0).
  • The A/D converter requires a “start conversion” low-to-high signal and after conversion provides a “data ready” low-to-high signal that goes low when “start conversion” goes low.
  • The A/D reference voltages are Vref–^ = 0.0000 V and Vref+^ = 4.095 V
  • The D/A reference voltages are Vref–^ = 0.0000 V and Vref+^ = 4.096 V

1a. [25 points] Draw a block diagram of the major components, including the A/D circuit being tested. Show and label all essential components, data lines, and control lines.

1b. [10 points] How would you measure the maximum absolute accuracy error of the A/D? (Explain the procedure in steps or with a flow diagram.)

2a. [10 points] How does your design avoid aliasing? Give details.

2b. [10 points] What is the minimum sampling frequency required?

2 c. [5 points] What is the minimum time needed to take all the required samples?

2d. [5 points] What is the minimum number of samples required?

2 e. [5 points] Would a Hanning window be useful in your design? Explain your reasoning.

2 f. [5 points] To what frequency does the first FFT coefficient H 1 correspond?

2 g. (10 points] For a musical instrument with a first harmonic frequency of 500 Hz, which FFT magnitudes would you expect to be non zero?

Equations, some of which you might find useful:

G ( a ) =

2 πσ^2

exp −

a −μ σ

^2

 μ ≈^ a^ =^ m^1 ai i = 1

m

σ a^2 = Var( a ) =

m − 1

 (^) Ri^2 i = 1

m

∑ =^

m − 1

 ( a i − a )^2

i = 1

m

∑ Var( a^ )^ =^ Var( a )/^ m

t =

σ∆

ab

σ^2 a^ + σ^2 b^

ab

σ a^2 / ma + σ b^2 / mb

σ (^2) f^ =

fa 1

2 σ a^21 +

fa 2

2 σ a^2 2 + +

fan

2 σ an^2

f = k a ( + b ) σ^2 f^ = k^2 (σ a^2 + σ b^2 ) f = kab σ 2 f^ f^2 = σ^2 a^ a^2 +σ b^2 b^2