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351 Midterm Exam solutions - Midterm Exam SOLUTIONS ENME...

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1 Midterm Exam SOLUTIONS ENME 351, Spring 2010 1. Short Answers (a) The full-scale output range (FSR) of a particular sensor systemis 0-10 V . The system includes analog-to-digital conversion with a 12-bit quantizer. How many states can the quantizer produce? # states = 2 12 = 4096 (b) What is the resolution of the sensor system in (a) due to quantization? Resolution due to quantization: Q = (full-scale range)/(#states) = 10 V / 4096 = 2.44 mV Resolution limit due to noise: 1 mV (given) Quantization dominates, and the resolution is 2.44 mV (c) What is the dynamic range of the sensor system in (a) due to quantization (express in dB)? DR = 20 log(Q) = 20 log(4096) = 72.2 dB (d) Now consider a particular measurement system that is entirely analog, i.e. no A/D converter. In this system, due to random noise, an output voltage noise signal up to 1 mV is observed when no input is applied. A given measurement with the sensor in (a) yields an output of 2 V . What is the signal-to-noise ratio (SNR) for the sensor, expressed as signal (not power) in dB? SNR = 20 log(signal/noise) = 20 log(2/.001) = 20 log(2000) = 66.0 (e) In one sentence, state the reason for using inductors (instead of resistors) between adjacent stages of a Butterworth filter. To avoid significant changes to the phase of the signal. (f) Consider the following 4th order system. What is the steady-state value of y(t)?
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