The voltage output from a 0-100 psi pressure transducer will vary from 0-4 mV. T
ID: 1718553 • Letter: T
Question
The voltage output from a 0-100 psi pressure transducer will vary from 0-4 mV. The input/output relationship is linear. The signal will be recorded with a 12-bit A/D converter with a 0-10 V input range. The voltage output needs to be amplified before it is converted to a digital signal. What is the gain required to make the digital resolution Q of the signal that is recorded by the computer equal to a change of 0.5 psi in the transducer? What is the gain required if a 14-bit A/D converter is used? In studying the vibration of a motor mount, it was thought that frequencies of up to 20 kHz will be encountered. State the minimum sampling rate for digitally acquiring all frequencies of interest. State the reason for your answer. For the data from problem 3 above, what frequencies need to be filtered-away using an anti-aliasing filter? Assume an idealized sharp cut-off from the filter. The current passing through a resistor in amperes is expressed by l(t) = 5 + 20 sint. Find the mean and rms values of current over an interval of 0 to t_f for: t_f = pi t_f= 2 piExplanation / Answer
3) a) Minium voltage sampled by A/D converter = 10 / 2^12 = 2.4414 mV
For a 0.5 psi change in pressure, output voltage will be = 4 mV * 0.5 / 100 = 0.02 mV
therefore gain K = 2.4414 / 0.02 = 123
b) Minium voltage sampled by A/D converter = 10 / 2^14 = 0.61 mV
For a 0.5 psi change in pressure, output voltage will be = 4 mV * 0.5 / 100 = 0.02 mV
therefore gain K = 0.61 / 0.02 = 30.5
4) From shannons sampling theorem , we know that for best results the minium sampling rate must be atleast twice the highest frequency present. Therefore the signal should be sampled at 2 * 20 kHz = 40 kHz
5) If the sampling frequency is 40 kHz , then an anti aliasing low pass filter must be used to prevent frequencies of over 20 kHz in the signal.
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