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Problem 4.10 A 16-bit A/D converter has an input range of 0 to 5 V. Estimate the
quantization error (as a percentage of reading) for an input of 1.36 V.
i +40.0000763 V. x 2:5
g.ooze %
This quantization error expressed as a percentage of the 1.36 V reading is + Os6@564%.
error = 40.5
Problem 4.14 A 3.29-V signal is input to a 12-bit successive approximations converter
with an input range of 0 to 10 V and simple binary output. Simulate the successive
approximations process to determine the simple binary output.
o = 0.002441
Pass/Fail Actual Digital Output
Fail (000000000000 (0000)
(010000000000 (1024)
(010000000000 (1024) |
Trial Digital Output (Do)
100000000000 (2048)
‘010000000000 (1024)
‘011000000000 (1536)
(010100000000 (1280) 3.12500 010100000000 (1280)
010110000000 (1408) 3.43750 _ 010100000000 (1280)
(010101000000 (1344) _ 3.28125 ‘010101000000 (1344)
(010101100000 (1376) 3.35938 _ (010101000000 (1344)
010101010000 (1360) 3.32031 (010101000000 (1344)
(010101001000 (1352) 3.30078 (010101000000 (1344)
[—otororo00100 (1348) ~ 3.29102 (010101000000 (1344)
010101000010 (1346) 3.28613 (010101000010 (1346) |
‘010101000011 (1347) | _3.28857_ ‘010101000011 (1347) | ~
‘The simple binary output for the 3.29 V signal would be 010101000011 which has a
decimal equivalent of 1347. Problem 5.11 A function has the form /(t)=Ssin 10#¢ +3cos40z¢ and is sampled at a
rate of 30 samples per second. What alias frequency(ies) would you expect in the
discrete data?
Saas = fof, = 40H2 -30Hz = 10He
I would expect an alias frequency of 10 Hz in the discrete data.
Problem 5.13 What would be the minimum sampling rate to avoid aliasing for the
function in Problem 5.11.
Soar = Fe- fi
O=f-S
f= f.= 40H
‘The minimum sampling rate to avoid aliasing would be 40 Hz.
Problem 5.19 What is the dynamic range of a 16-bit bipolar A/D converter?
dynamic range = 20log,,(2" ) = 201og,.(2'*) = 90.309 dB
‘The dynamic range of a 16-bit bipolar A/D converter is 90.3 4B. = wn a0y
Mareh 10, 200.
Homework #4
Problem 5,
‘A function has the form fd) = 5 sin 101 +3 cos 40t and is sampled at a rate of 30 samples per second.
What alias frequency(ies) would you expect in the discrete data?
Solution —
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