Electrical Measurements and Instrumentation
Chapter One General Principles of measurement and instrumentation
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Outline • Course objectives, assessment, and rules • Introductions • Significant figures • Types of Error • Types of Measurement • Generalized measuring system • Standard of Measurement System • Characteristics of instruments • Noise and Interference in Instrumentations 3
Course objectives, assessment, Rules • The course aims at introducing you the following topics General Principles of measurement and instrumentation (1) Electronic Instruments for Measuring Basic Parameters (2) Sensors and Applications (3) Signal Conditioning and Processing Elements (4) Output Presentation (5) Frequency Counters and Time Interval Measurements (6) Introduction to data Acquisition and Communication Systems (7) Evaluation Assignments, quizzes, Labs and projects: 35% (five tests, two assignments and one paper based projects) Mid‐term Exam: 30% Final Exam: 35% 4
Cont’d … • Rules Quizzes can be given at any time with no prior knowledge of any student, hence you must attend the lectures. In case you are absent from the quizzes and Mid‐exam which are assumed as a continuous assessment, you must come in the following day with officially accepted documents. Thus you can seat for the quizzes as well as the mid‐exam. Home works, assignments and project must be submitted at a specified time. You must attend the laboratory hours. They are marked.
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Introduction • Measurement is the experimental process of acquiring any quantitative information about physical quantity. • When doing a measurement, we compare the measurable quantity – measurand ‐ with another same type of quantity. This other quantity is called measurement unit • Measurand – a physical quantity, property, or condition which is measured • An Instrumentation a Device used in measurement system 6
Continued Why measurement? •In the case of process industries and industrial manufacturing… •To improve the quality of the product •To improve the efficiency of production •To maintain the proper operation.
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Continued Why instrumentation? • To
acquire
data
or
information
(hence
data
acquisition) about parameters, in terms of: putting the numerical values to the physical quantities making measurements otherwise inaccessible. producing data agreeable to analysis (mostly in electrical form) 8
Continued •The purpose of the measurement system is to link the observer to the process
•The input to the measurement system is the true value of the variable •The system output is the measured value. 9
Continued •Physical quantity: variable such as pressure, temperature, mass, length, etc. •Data:
Information
obtained
from
the
instrumentation /measurement system as a result of the measurements made of the physical quantities 10
Continued • Accuracy is the degree of closeness or conformity to the true value of the quantity under measurement. • Precision is the degree of agreement within a group of measurement or instruments. • Sensitivity is the response of the instrument to a change of the input or measured variable. • Error is the deviation from the true value of the measured variable. 11
Significant figures • Significant numbers convey actual information regarding the magnitude and the measurement precision of a quantity. • The more significant figures, the greater the precision of measurement. • When a zero digit is used to locate the decimal point, it is not significant. For example, the numbers 0.048, 0.0032, and 0.00057 each have two significant digits 12
Continued •When a zero appears between two nonzero digits in a number, it is significant. For example, 2.04 has three significant digits; 8.002 has four significant digits. •The number 5480 can be written for three significant digits 5.48 X 103; for four significant digits 5.480 X 103 13
Continued • As a general rule, the number of significant digits of the product or the division of two or more measurements should be no greater than that of the measurement with the least number of significant digits. • For example: the length of a table is measured with a meter stick as 1.8245 m (5 significant figures) and the width as 0.3672 m (4 significant figures). The area A = 1.8245 m X 0.3672 m = 0.06703213 m2 as shown on a calculator. 14
Continued • The correct value for the area is 0.06703 m2. This value has four significant digits corresponding to the least number of significant digits in the two numbers making up the original data. • Similarly, when two or more measurements with different degrees of accuracy are added, the result is only as accurate as the least accurate
measurement. 15
Continued •Suppose two resistance are added in series, R1=18.7 ohm (three significant numbers), R2=3.624 ohm (four significant numbers) •Then RT=R1 + R2=22.324 ohm (five significant numbers), therefore the result should be accurate only to three significant numbers; 22.3 ohm 16
Continued • Example: In calculating voltage drop, a current of 3.18A is recorded
in a resistance of 35.68 ohm.
Calculate the voltage drop across the resistor to the appropriate number of significant figures. E=IR=(35.68)*(3.18)=113.4624=113 V • Since there are three significant figures involved in the multiplication, the answer can be written only to a maximum of three significant figures 17
Types of Error • Error may come form different sources and are usually classified under three main categories: Gross error Systematic error Random error •
Gross errors: largely human errors, among them misreading of instruments, incorrect adjustment and improper application of instruments, computational mistakes. 18
Gross errors • Example: A voltmeter, having a sensitivity of 1000Ω/V, reads 100V on its 150V scale when connected across an unknown resistor in series with a milliammeter, while the milliammeter reads 5mA. Calculate (a) the apparent resistance of the unknown resistor; (b) the actual resistance of the unknown resistor; (c) the error due to the loading effect of the voltmeter. 19
Gross errors • Solution: (a) the total circuit resistance is Rt=Vt/It=100V/5mA=20kΩ Neglecting the resistance of the milliammeter, the resistance of the unknown resistor is Rx= 20kΩ (b)The voltmeter resistance is Rv=1000 Ω/V* 150V=150kΩ Since the voltmeter is in parallel with the unknown resistor, we have Rx=(Rt*Rv)/(Rv‐Rt)=23.05kΩ 20
Gross errors (c) % error =(actual–apparent)/(actual) *100%=13.23% Example: repeat the example 2 if the milliammeter reads 800mA the voltmeter reads 40V on its 150V scale. (a) Rt=Vt/It=40V/0.8A=50Ω (b)Rv=1000 Ω/V* 150V=150kΩ Rx=(Rt*Rv)/(Rv‐Rt)=(50*150)/(149.95)=50.1Ω (c) %Error=[(50.1-50)/50.1]*100%=0.2% • Error caused by the loading effect can be avoided by using a proper meter selection 21
Systematic error • Short comings of the instrument (i.e. instrumental error), such as defective or worn part,
and effect of the
environment on the equipment or the user (i.e. environmental error). • Calibration error is another example of instrumental error. • In general, instrumental error may be avoided by: Selecting a suitable instrument for the particular measurement application. 22
Systematic error Applying correction factor after the determining the amount of instrument error. Calibrating the instrument against a standard. • Environmental
error:
effect
of
temperature,
humidity, pressure, or magnetic or electric fields on the measuring instrument. These effects
may be
reduced by including air conditioning, hermetically sealing certain components in the instrument. 23
Systematic error • Systematic error can be also subdivided into static or dynamic errors. • Static errors are caused by limitations of the measuring device or physical laws governing its behavior. • Dynamic errors are caused by the instrument’s not responding fast enough to follow the changes in a measured variable. 24
Random error • Random errors are caused by erratic or unpredictable fluctuations
either in the composition of a material
quantity under measurement or in the procedures and mechanisms employed in conducting measurement exercises. • Random errors often arise when measurements are taken by human observation of an analogue meter, especially where this involves interpolation between scale points. 25
Random error •Electrical noise can also be a source of random errors. •To a large extent, random errors can be overcome by taking the same measurement a number of times and extracting a value by averaging or other statistical techniques.
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Limiting Errors • Circuit components (such as resistors, capacitors) are guaranteed within a certain percentage of the their rated value. The limits of these deviations from the specified values are called Limiting Errors or guaranteed errors. • Example:
A 0‐150V voltmeter has a guaranteed
accuracy of 1 per cent full‐scale reading. The voltage measured by this instrument is 83V. Calculate limiting error in percent. 27
Limiting Errors • The magnitude of the limiting error is 0.01*150V= 1.5V. This is the full‐scale measurement error of the meter. • The percentage error at a meter indication of 83V is (1.5/83)* 100%=1.81 • If we measure voltages of lower magnitude with this meter we should note that the per cent limiting error will increase as it is a fixed quantity based on the full‐scale reading of the meter. • Hence, taking measurements as close to full scale will reduce the per cent limiting error. 28
Probability of Errors • The table below show 50 voltage readings that was taken at small time intervals and recorded to the nearest 0.1V. The nominal value of the measured voltage is 100.0V. Voltage reading (Volts)
Number of readings
99.7
1
99.8
4
99.9
12
100.0
19
100.1
10
100.2
3
100.3
1 ____ 50 29
Probability of Errors • The measurement result can be plotted graphically as shown below in which the number of observation is plotted against each observed voltage reading.
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Probability of Errors • With more and more data, taken at smaller increments, the graph would become a smooth curve. • This bell‐shaped curve is called as a Gaussian curve or Normal distribution of the obtained data. • The sharper and narrower the curve, the more definitely an observer may state that the most probable value of the true reading is the central value or mean reading. 31
Probability of Errors • Mathematically, the normal or Gaussian distribution function is given by
• where: = mean or expected value (specifies center of distribution) • σ = standard deviation (specifies spread of distribution). 32
Probability of Errors • Suppose that a user buys a batch of similar elements, e.g. a batch of 100 resistance temperature sensors, from a manufacturer. • If he/she then measures the resistance R0 of each sensor at 0°C, he/she finds that the resistance values are not all equal to the manufacturer’s quoted value of 100.0 Ω. • A range of values such as 99.8, 100.1, 99.9, 100.0 and 100.2 Ω, distributed statistically about the quoted value, is obtained. This effect is due to small random variations in manufacture and is often well represented by the normal probability density function.
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Probability of Errors
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Probability of Errors • A manufacturer may state in his/her specification that R0 lies within ±0.15 Ω of 100 Ω for all sensors, i.e. he is quoting tolerance limits of ±0.15Ω. • Thus, in order to satisfy these limits he must reject for sale all sensors with R0 < 99.85 Ω and R0 > 100.15 Ω, so that the probability density function of the sensors bought by the user now has the form shown in the Figure.
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Probability of Errors •An error distribution curve can be drawn based on the normal law and it usually shows a symmetrical distribution of errors. •This normal curve may be regarded as the limiting form of the histogram of previous figure in which the most probable value of the true voltage is the mean value. 36
Probability of Errors •Normal probability density function
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Probability of Errors •In summary for Gaussian or normal error distributions: Area under the probability curve Deviation (±), σ
Fraction of total area included
Meaning
0.6745
0.5
50% of observations lie within ± 0.6745 std dev of mean
1
0.683
68.3% of observations lie within ± 1 std dev of mean
2
0.955
95.5% of observations lie within ± 2 std dev of mean
3
0.997
99.7% of observations lie within ± 3 std dev of mean
Note that total area underneath curve is 1.00 (100%) 38
Probability of Errors • A probable error of a quantity defines the half‐ range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside. Probable error = ±0.6745σ
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Probability of Errors Exercise: • The accuracy of five digital voltmeters are checked by using each of them to measure a standard 1.0000V from a calibration instrument. The voltmeter readings are as follows: V1 = 1.001 V, V2 = 1.002, V3 = 0.999, V4 = 0.998, and V5 = 1.000. Calculate the average measured voltage, the average deviation, the standard error of the measurements and the probable error. 40
Types of measurements • Direct comparison • Easy to do but… less accurate (measured quantity is registered directly from the instruments display.)
e.g. Measuring voltage vith voltmeter and Measuring length with ruler • Indirect comparison(result is calculated (using formula) from the values obtained from direct measurements) Calibrated system; consists of several devices to convert, process (amplification or filtering) and display the output; e.g. to
measure force from strain gages located in a structure. 41
Generalised measuring system
General Structure of Measuring System Stage 1: A detection‐transducer or sensor‐transducer, stage; e.g. temperature sensor, pressure sensor Stage 2: A signal conditioning stage; e.g. amplifiers, filters, bridges Stage 3: Signal processing: ADC or PC or uC or uP Stage 4: A terminating or readout‐recording stage; 42
Contents •Standard of Measurement System Types of Standard
•Static and Dynamic Characteristics of instruments. • Noise and Interference in Instrumentations
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Standard of Measurement System What does a ‘Standard’ mean? Standard • Unit has to have some relation to physical world, therefore, physical records, called standards, are used to permanently record the size of units. Definition of standard: • A standard is a permanent or readily reproducible physical record of the size of a unit of measurement. A universal standard must be one which is reproducible with such a degree of accuracy that for all industrial and scientific purposes it may be considered as absolute. 44
Types of Standard • Four categories of standard: International Standard Primary Standard Secondary Standard Working Standard • International Standard Defined by International Agreement Represent the closest possible accuracy attainable by the current science and technology
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Contd. • Primary Standard Maintained
at
the
National
Standard
Laboratory (different for every country) Function: the calibration and verification of secondary Standard. Each lab has its own secondary standard which are periodically checked and certified by the National Standard Laboratory. 46
Contd. • Secondary Standard Secondary standards are basic reference standards used by measurement and calibration laboratories in industries. Each industry has its own secondary standard. Each laboratory periodically sends its secondary standard to the National standards laboratory for calibration and comparison against the primary standard. After comparison and calibration, the National Standards Laboratory returns the secondary standards to particular industrial laboratory with a certification of measuring accuracy in terms of a primary standard. 47
Contd. • Working Standard Used to check and calibrate lab instrument for accuracy and performance. For
example,
manufacturers
of
electronic
components such as capacitors, resistors and many more use a standard called a working standard for checking the component values being manufactured. 48
Contd. • Few of us will ever see/use a primary standard. Rather, we will generally deal with a secondary standard (say, laboratory standard) that has been copies from another secondary standard that itself may be many steps removed from the primary standard. • An even lower order standard (reference) is present in every instrument that can perform an absolute measurement. • Such instruments should also be calibrated regularly, since aging, drift, wear, etc., will cause the internal reference to become less accurate.
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Contd. Definition of True value •A true value of a variable is the measured value obtained with a standard of ultimate accuracy.
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Traceability ladder (The hierarchy of standards) • Illustration: International standard
Primary standard Increased accuracy
Relative accuracy
Absolute accuracy Secondary standard
Working standard
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IEEE standard •IEEE: Institute of Electrical and Electronics Engineering
headquartered in
New York
City. •IEEE standard are not physical items that are available for comparison and checking of secondary
standards
but
standard
procedures, nomenclature, definitions, etc. 52
Contents • Characteristics of instruments Static Dynamic Characteristics of instruments; • Noise and Interference in Instrumentations
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