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F07 314 HW 11 all

# F07 314 HW 11 all - EECS 314 Fall 2007 HW 11 For extra...

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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 vibration-caused signal at 1.5 kHz will contaminate your data: it will be undersampled and – due to aliasing – might be seen as a lower-frequency signal. To avoid the trouble, you decided to build a simple Low-Pass RC filter, using a 5 k Ω resistor, so that the cutoff (half-power) 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 signal-to-noise, 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 Low-Pass filter with the cutoff (half-power) 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 so-called positive logic HIGH voltage ~ 5 V means “1” and LOW voltage ~ 0 V means “0”, while in the so-called 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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