UNIVERSITY OF CALIFORNIA
College of Engineering
Electrical Engineering and Computer Sciences Department
145M Microcomputer Interfacing Lab
Final Exam Solutions May 20, 1994
1a Comparator circuit: Circuit with two analog inputs and one digital input. The output state is
determined from the relative value of the two inputs. Usually consists of a differential amplifier
with very high gain and voltage limited outputs.
1b Harmonic (of a periodic signal): Component of the signal that has an exact whole number
multiple of the fundamental frequency of the signal itself. The complex amplitudes of the
harmonic components can be determined from the Fourier transform of the signal.
1c Data bus (for connecting 2 or more parallel outputs): Hardware circuit where a number of
parallel outputs can be selectively connected to a common set of parallel signal lines called a
bus. Only one parallel output can be asserted on the bus at any one time.
1d Differential Linearity Error (of an A/D converter): The difference between the step sizes and
the average step size. Each step is the difference between neighboring transition voltages.
1e Fourier Convolution Theorem: The Fouler transform of the convolution of two functions is
the simple product of the Fourier transforms of the two functions.
1f Spectral Leakage (as seen in the FFT of a periodic signal): When a frequency component of a
signal does not have a whole number of cycles in the sampling window, the discontinuity at the
edges of the window generates frequency components not present in the original signal. This
appears as leakage into the adjoining Fourier coefficients and can be described by convolving
the true Fourier transform with the Fourier transform of a the rectangular sampling window.
2a 1Set i1 =0.
2Output the number i1 on the parallel output port
3The D/A produces an analog voltage that appears on all 8 A/D inputs
4Using parallel output port #1, output a start pulse
5All eight A/D converters convert the D/A output
6When each A/D finishes, its “done” pulse latches the 12 bits of data onto its 12-bit register
7The program waits a bit more than 11 µs for all A/Ds to finish converting
8Set i2 = 1
9The program selects tri-state buffer #i2 and de-selects the other 7 tri-state buffers by
outputting a number on parallel output port #2 which has a 1 in bit position #i2 and a 0 in
the other 7 positions.
10 The program reads the input port to obtain the output of A/D #i2 and saves it in a
temporary memory location
11 If the result of step 10 has changed from the last value of the D/A input i1, save the D/A
voltage value that corresponds to i1 as a transition voltage for A/D #i2.
12 Set i2 = i2 +1 and loop back to step 9 until i2 = 8
13 Set i1 = i1 + 1 and loop back to step 2 until i1 = 65,535 (i.e. 216 – 1)
14 Set i2 = 1
15 For A/D converter #i2, compute the difference between each transition voltage and its ideal
value (the absolute error). Determine the maximum value (the maximum absolute error).
16 Subtract neighboring transition voltages to produce a table of step sizes and determine
minimum and maximum values of step sizes for A/D converter #i2
17 Set i2 = i2 + 1 and loop back to step 15 until i2 = 8
(another way to find step sizes is to count the number of D/A inputs that produce the same A/D
output.)
[10 points off if only 12 D/A bits are used, since this approach cannot accurately measure
transition voltages]
145M Final Exam Solutions page 1 May 20, 1994 S. Derenzo/T. Tokuyasu
