L13_ECE4001_Spring_2011

# L13_ECE4001_Spring_2011 - 1 Slide#1 ECE 4001 L13 © 2011...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Slide #1 ECE 4001 L13 © 2011 Lecture 13 Engineering Measurements – Part 2 Slide #2 ECE 4001 L13 © 2011 Outline • Calculating Experimental Errors • Calibration Issues • Experimental Test Plan • Summary Slide #3 ECE 4001 L13 © 2011 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 © 2011 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 = - + ⋅ 2 Slide #5 ECE 4001 L13 © 2011 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 ± 1 σ – Multiply by 2 to get 95% confidence level • Assume “max” means ± 3 σ – Multiply by 2/3 to get 95% confidence level Slide #6 ECE 4001 L13 © 2011 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 © 2011 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?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

L13_ECE4001_Spring_2011 - 1 Slide#1 ECE 4001 L13 © 2011...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online