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Unformatted text preview: Slide #1 ECE 4001 L13 © 2008 Lecture 13 Engineering Measurements – Part 2 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 = = = = ≠ = = + + + ∑ ∑ Slide #4 ECE 4001 L13 © 2008 Combination of Errors Example 8 Bit A/D Converter • 8bit 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 +50.0391 = +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: – 8bits 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 ± 1 σ – Multiple by 2 to get 95% confidence level (2 σ ) • Assume “max” means ± 3 σ – Multiple by 2/3 to get 95% confidence level (2 σ ) 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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This note was uploaded on 06/09/2009 for the course ECE 4001 taught by Professor Frazier during the Fall '09 term at Georgia Tech.
 Fall '09
 FRAZIER

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