Chapter 1 :

Introduction to Instrumentation

KNL 1453 Electrical Instrumentation

Outlines Function and Characteristics of Instruments

Measurement Standards

A Review on Electrical Units

Errors in Measurement

General Categories of Error [gross errors, random errors, systematic errors]

Other Errors [absolute and relative errors]

Accuracy, Precision, Resolution and Significant Figures

Measurement Error Combinations

Basic of Statistical Analysis

KNL 1453 Electrical Instrumentation

Introduction

• No electronic component or instrument is perfectly accurate; all have some error or inaccuracy

• It is important to understand how these errors are specified and how they combine to create even greater errors in measurement systems

• Apart form equipment errors, some operator or observer error is inevitable.

Uncertainty estimation • When measuring physical quantities with an instrument

and obtain a numerical value, it is important to know how close this value is to the true value.

(True value) – (Measured value) = Error

• Unfortunately, the true value is generally unknown. Since this is the case, the exact error is never known. We can only estimate error.

General categories of error

There are three general categories of error:

Erro

r Gross errors

Systematic errors

Random errors or precision errors

a) Gross Errors

• Undetected mistakes that cause a measurement to be very much farther from the mean measurement than other measurements.

• Eg. – Simple misreading of an instrument

– Misuse of equipment

– The proper use of incorrect or inadequate equipment

– Misrepresentation of data obtained

!

• To solve the problem ;

– Trial and error (reading the operation manual and experimenting).

- Since this approach is time

consuming, it is imperative that the

operation manual be read BEFORE

any instrument is used.

– Following through a course or text in conjunction with a lab experience ;

- The more equipment is used, the

more familiar the technician, engineer become

with it, and the more consistently valid

the resulting data will be.

b) Systematic Errors

• Result from mechanical weaknesses of an instrument.

– eg. Worn bearings on meter movements and nonlinear sweeps on oscilloscopes

• Determinate error.

• Have an identifiable cause and affect the accuracy of results.

• Occur because the measurement system affects the measured quantity.

• To solve;

– Diagnose the situation correctly and repair or replace the defective equipment,

– Recalibration or compensation for the error

Systematic errors

c) Random errors/Precision errors

• Are errors that affect the precision of a set of measurements.

• Error whose cannot be directly established because they appear to be random variations in the electrical parameters of the measuring system or device under test.

• Scatters measurements above and below the mean, with small random errors being more likely than large ones.

• The deviation of the measurement from the true value resulting from the finite precision of the measurement method being used.

• Instrument friction or hysteresis

• Errors from calibration drift

• Variation of procedure or interpretation of experimenters

• Test condition variations or environmental effects

• Reduce random errors by conducting more experiments/take more data.

Random errors/ Precision errors

Summarizing the Differences

Systematic & Random Errors

Absolute error is the amount of physical error in a measurement. Exmp: A meter stick is used to measure a given distance. The error is rather hastily made, but it is good to ±1mm. This is the absolute error of the measurement. Absolute error = ±1mm (0.001m).

Absolute Error

Absolute error = Δ x

Relative error gives an indication of how good a measurement is relative to the size of the thing being measured.

Relative Error

Relative Error = Absolute Error

Value of thing measuredx 100%

= Δx

x x 100%

Absolute and relative errors

Absolute errors Relative errors

The uncertainty in a measurement, expressed with

appropriate units. Also used to expressed

inaccuracies.

The uncertainty in a

measurement compared to the size of the measurement.

Example - Absolute Errors

• Given three replicate weights for an object;

1.00 g, 1.05 g, 0.95 g

• The absolute error ± 0.05 g

• Given true value is 1.00 g, and the measured is 1.11 g

– The absolute error

• 1.00 g – 1.11 g = －0.11 g

Determinate Errors (sign)

Indeterminate Errors (±)

Example - Relative Errors

• Given three replicate weights for an object;

2.00 g, 2.05 g, 1.95 g

absolute error: ± 0.05 g

relative error: =± 0.05 g / 2.00 g

= ± 0.025

= ± 2.5%

More example….

Exercise I

A component manufacturer constructs certain resistances to be anywhere between 1.14 kΩ and 1.26 kΩ and classifies them to be 1.2 kΩ resistors. Determine the Absolute Error and Relative Error.

Accuracy, Precision, Resolution and Significant Figures

• Accuracy and precision

– When a voltmeter with an error of ±1% indicates exactly 100V, the true level of the measured voltage is somewhere between 99V and 101V.

Accuracy - defines how close the measurement is to the actual measured quantity

Precision - with which the measurement is made is not the same as the accuracy of measurement, although accuracy and precision are related.

Differences between precision and accuracy accuracy precision

Inaccurate but precise

Exercise II

More example…

Reading shows 8.135V, if the increase and decrease of reading is 1mV, the reading becomes 8.136V or 8.134V

The precision is 1mV.

Resolution

The smallest observable change of the instrument.

• In the case of 10V analog instrument scale that can be read to a precision of 50mV, 50mV is the smallest voltage change that can be observed.

• Thus the measurement resolution is 50 mV

• Similarly, the digital instrument, the measurement resolution is 1 mV.

Significant Figures

The number of significant figures used in a measured quantity indicate the precision of measurement.

Given 8.135 V how many significant figures?

4 significant figures meaning that measurement precision is 0.001 or 1 mV

Exercise III

What if the readings indicate that the value you are collected is equal to 5.23V ?

i. How many significant figures we have?

ii. What is the measurement precision?

Exercise IV Given the voltage of an electronic circuit is 8.14 V, and the current is 2.33 mA. Calculate the resistance of the circuit in its significant figures.

Notes

– No greater number of a significant figures should be used in a calculation result than those in the original quantities.

– If the quantities in a calculation have different precisions, the precision of the answer should not be greater than the least precise of the original quantities.

Prefixes of Units

Assessment I

i. Determine the mean

ii. Draw the distribution curve for these 2

Given the above two sets of experimental results A and B obtained for a particular measured quantity. i. Which reading is more precise and why? Ii. Which reading is more accurate and why?

A component manufacturer constructs certain resistances to be anywhere between 1.1 kΩ and 0.9kΩ and classifies them to be 1.0 kΩ resistors.

i. Determine the Absolute Error and Relative Error.