You are designing a digital bathroom scale for Taylor corporation. You are using

Question

You are designing a digital bathroom scale for Taylor corporation. You are using a force sensor that generates a voltage V = Scale * Weight + Offset, where the scale factor is 1mV/lb, the Weight is in pounds, and the Offset is 0 5 Volts. The uncertainty in the offset is 3mV. Your scale must read weights between 0 and 300 lbs. assume that you are using a 10 bit ADC that has a range of 0 to 5 volts. What is the voltage resolution of your ADC? What is the uncertainty in weight measurement due to your ADC resolution? What is the uncertainty in weight measurement due to the offset uncertainty? If these are the only two sources of uncertainty, and they are worst case estimates, what is the worst case uncertainty of a measurement? If these are the only two sources of uncertainty, and they are standard deviations, what is the expected standard deviation uncertainty of measurements? If you take 100 measurements, what is the estimated standard uncertainty u? Explain your answer. If during initialization you take a single reading from the sensor with 0 weight to measure the offset voltage and use this to correct your weight measurements, what is the expected standard deviation of your measurements and why? If during initialization you take the average of 100 readings from the sensor with 0 weight to measure the offset voltage and use this to correct your weight measurements, what is the expected standard deviation of your measurements and why? By what factor could you amplify the sensor voltage and still keep it in the range of your ADC? How do your answers to 3 and 4 change if you do so? If you zero the voltage offset from the sensor electronically, by what factor could you amplify the sensor voltage and still keep it in the range of your ADC? How do your answers to 3 and 4 change if you do so?

Explanation / Answer

1) voltage resolution = 210 = 1024

2) uncertainty =   9.76 * 10-4 lb

3)   uncertainty =   0.9 lb

4) Worst Case Analysis yields the best value of the result and a range of uncertainty in the form best value ± uncertainty .

5) Uncertainties corresponding to different sources and to different distribution functions are converted to standard uncertainties when uncertainty calculations are performed.

6)   Estimated standard uncertainty becomes 0.01 times .

7) expected standard deviation = 0.03 times offset voltage .

8)   expected standard deviation =    3 times offset voltage .

9) Factor we could amplify = 10 times .

10)    Factor we could amplify = 10/3 = 3.33 times .

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