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L13_Engineering Measurements Part 2

# L13_Engineering Measurements Part 2 - Lecture 13...

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Slide #1 ECE 4001 L13 © 2008 Lecture 13 Engineering Measurements – Part 2

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Slide #2 ECE 4001 L13 © 2008 Outline Calculating Experimental Errors Calibration Issues Experimental Test Plan Summary
Slide #3 ECE 4001 L13 © 2008 Combinations of Errors Consider additive errors; i.e. Usually all of the errors do not assume their “worst case” values at the same time It is overly conservative to estimate the uncertainty as the sum of the worst case values It is more accurate to take the square root of the sum of the squares total repeatability zero sensitivity linearity hysteresis resolution other e e e e e e e e = + + + + + + 1 2 2 2 2 1 2 1 max error from source number of error sources ; too conservative! .... i N i i N i N i e i N w e w e e e e = = = = = = + + +

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Slide #4 ECE 4001 L13 © 2008 Combination of Errors Example 8 Bit A/D Converter 8-bit A/D Converter for measuring voltage with an input range of -5 to +5 volts (10 Vpp) 8 bits corresponds to 2 8 = 256 levels Digital values range from 0 to 255 One bit (1 LSB) corresponds to 10V/256 = 0.0391 V Value of 0 corresponds to -5 V Value of 1 corresponds to -5+0.0391 = -4.9609 V Value of 128 corresponds to 0 V Value of 255 corresponds to +5-0.0391 = +4.9609 V 5 10 volts 256 value V = - +
Slide #5 ECE 4001 L13 © 2008 Combination of Errors Example 8 Bit A/D Converter Specifications: 8-bits of resolution Input range of -5 to 5 volts Relative accuracy: ± 0.9 LSB typical Sensitivity error: 0.1% of reading (max) Offset error: ± 5mV (max) Assume “typical” means ± 1σ Multiply by 2 to get 95% confidence level Assume “max” means ± 3σ Multiply by 2/3 to get 95% confidence level

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Slide #6 ECE 4001 L13 © 2008 Combination of Errors Example 8 Bit A/D Converter Individual uncertainties (1 bit = 0.0391 V) Resolution: ± ½(0.0391) = ± 0.0195 V Accuracy: ± 0.9 LSB = ± (2)(0.9)(0.0391) = ± 0.0704 V Sensitivity: 0.1% (max) = ± (0.00067)(Voltage) Offset: ± 5mV (max) = ± 0.0033 V Calculate overall uncertainty for measured value of 187 Voltage is 2.305 V 5 10 volts 256 value V = - + 2 2 2 2 2 2 2 2 0.0195 0.0704 0.0015 0.0033 0.0731 volts total resolution accuracy sensitivity offset w w w w w = + + + = + + + = Voltage = 2.31 ± 0.07 volts
Slide #7 ECE 4001 L13 © 2008 Temperature Measurement Example Thermocouple Meter with Analog Output Thermocouple Instrument with analog output Range of -75 °C to +125 °C, voltage out of 0 to 5V A/D card in PC, 12 bits, input range of 0 to 10 V Assume instrument and A/D card are calibrated What is the uncertainty of a reading?

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L13_Engineering Measurements Part 2 - Lecture 13...

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