EECS 314 Fall 2007 HW 11 For extra credit
Problem 1
Student's name ___________________________
Discussion section # __________
(Last name, first name,
IN INK)
© 2007 Alexander Ganago
For the Big Picture,
see the file 2007 Analog and Digital posted on the web as part of
lecture notes for November 27, 2007.
The Problem
Suppose you are building a data acquisition circuit for your sensor signals, which are
limited to the frequency range between DC and 100 Hz, and you plan to sample them at
350 Hz.
The trouble is that your setup vibrates at the frequency of 1.5 kHz, and you are concerned
that the vibrationcaused signal at 1.5 kHz will contaminate your data: it will be
undersampled and – due to aliasing – might be seen as a lowerfrequency signal.
To avoid the trouble, you decided to build a simple LowPass RC filter, using a 5 k
Ω
resistor, so that the cutoff (halfpower) frequency of your filter equals 350 Hz.
1.
(5 points) Determine the capacitance for your filter
2.
(5 points) Calculate the transfer function magnitude at 100 Hz (the maximal
frequency at which you expect the signals from your sensor) and at 1.5 kHz (the
noise frequency)
3.
(5 points) Assume that, without filtering, the signaltonoise, or S/N ratio (the
ratio of the peak amplitude of signal at 100 Hz to the peak amplitude of the noise
at 1.5 kHz) was 10:1. Calculate the S/N ratio with the filter described above.
4.
(10 points) In an attempt to improve the S/N ratio even further, you are
considering a LowPass filter with the cutoff (halfpower) frequency equal to 100
Hz. Will it be an improvement? Prove by repeating #2 and 3 for the new filter.
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EECS 314 Fall 2007 HW 11 For extra credit
Problem 2
Student's name ___________________________
Discussion section # __________
(Last name, first name,
IN INK)
© 2007 Alexander Ganago
Page 1 of 2
Logic gates: Diode circuits with NEGATIVE logic
The Big Picture
When we analyze the logic function of a circuit, we have to solve 2 distinct questions:
1.
What output voltage does the circuit produce for each of the possible
combinations of input voltages?
2.
What logic function corresponds to this combination of input and output voltages?
To solve question 1, we have to perform the circuit
analysis. Note that in the circuits below the sources
are not shown explicitly. For example, the first
circuit can be redrawn – with the sources shown –
as follows:
In the circuit analysis, we assume that the input
voltages A and B and the output voltage C can be
either LOW ~ 0 V or HIGH ~ 5 V.
To determine whether each of the diodes conducts,
use the ideal diode model.
To answer question 2, we have to compare the obtained combination of HIGH and LOW
voltages with the known truth tables.
Note that two possibilities exist:
•
in the socalled
positive logic
HIGH voltage ~ 5 V means “1” and
LOW voltage ~ 0 V means “0”,
while
•
in the socalled negative logic, which we use in this problem, the meanings of
voltages are opposite:
HIGH voltage ~ 5 V means “0” and
LOW voltage ~ 0 V means “1”.
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 Fall '07
 Ganago
 Extra Credit Problem, Lowpass filter, Alexander Ganago

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