Measurement and instrumentation , Lecture notes of Electrical Engineering

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EE-336: Electrical Measurement &

Instrumentation (3-3-4)

 Dr. Amjad Ullah, Professor,

 Engr. Numan Khurshid, Lecturer,

 Grading:

 50 % Final  25 % Mid Term  25 % Sessionals

 Recommended Books:

 Modern Electronic Instrumentation and Measurements Techniques by A.D.Helfrick, W.D. Cooper  Electrical Instrumentation and Measurement techniques ,By A.K.Sawhney

Course Out lines

 Please note them now

 You will not be provided with any soft copy of

syllabus or lectures; you have to read the book

thoroughly

 Definitions and classification of errors,

 instrument errors,  environmental errors, temperature effect,

 Method of avoiding and correction errors.

 Engineering units and Standards,

Course Out lines…….

 Principle, Operation, working and Construction of

Different Analog and Digital Meters,

 Oscilloscope and its Measurements,  Recording Instruments and signal generators.  Transducers,

 Different types of Bridges for Measurements of

 Resistance,  Inductance,  Capacitance. High Voltage Measurements,

Course Out lines…….

 Precision Measurements Terminologies Including

 Resolution,  Sensitivity,  Accuracy,  Uncertainty.

 Mechanical Measurements:

 Length,  Force,  Displacement,  Stress and Strain.

Course Out lines…….

 Thermodynamic Measurements

 temp and  pressure,

 Measurements in fluid Flows:

 velocity,  Flow rate,

 Data Manipulation and presentation

 Basic data Manipulation skills using personal

Computers.

 Spread sheets and graphs,

 Static and Dynamic Measurements:

 Time Series and Sampling Requirements.

 Data Acquisition System. Software Simulation.

5

 Electronics

 deals with motion of electrons

 Measurement :

man uses his imaginative skills

 to identify a physical

phenomena

 Developed & utilized a means to

understand this.

 To measure = to determine the

magnitude or extent or degree of the condition of system in terms of some standard.

 All measuring systems- based on laws

of nature.

 E.g. Venturimeter- flow measurement –

Bernoulli's theorem

 Meter :

 instrument used to indicate or record

measured value

 Measurand :

 variable under measurement

 Metrology :

 science dealing with precise and accurate

measurements

Instrument : A device for determining the value or

magnitude of or variable.

 The instrument serves as an extension of human faculties

 and in many cases enables a person to determine the value of an unknown quantity which his unaided human faculties could not measure

 The electronic instrument, as its name implies, is based on electrical or electronic principles for its measurement function

 A device of simple construction such as a basic dc current meter

 Instrument :

tool or equipment for

 Sensing

 Detecting

 Measuring

 Recording

 Controlling

 Communicating

 Measurand Can be manual or automatic

 Definitions & Terms

 Instrument: a device for determining the value or magnitude of a quantity or variable.

 Accuracy: closeness with which an instrument reading approaches the true value of the variable being measured.

 Precision: a measure of the reproducibility of the measurements; i.e., given a fixed value of a variable, precision is a measure of the degree to which successive measurements differ from another.

 Sensitivity: the ratio of output signal or response of the instrument to a change of input or measured variable.

 Resolution: the smallest change in measured value to which the instrument will respond.

 Error: deviation from the true value of the measured variable.

 Error Minimization Techniques

 Several techniques may be used to minimize the effects of errors

 For example, in making precision measurements, it is advisable to record a series of observations rather than rely on one observation.

 Alternate methods of measurement, as well as the use of different instruments to perform the same experiment, provide a good technique for increasing accuracy.

 These techniques tend to increase the precision of measurement by reducing error, they cannot account for instrumental error

 Accuracy And Precision

 Accuracy refers to the degree of closeness or conformity to the true value of the quantity under measurement.

 Precision refers to the degree of agreement within a group of measurements or instruments.

 But what is the difference?

 Lets have two voltmeters of the same make and model may be compared.

 Both meters have knife-edged pointers and mirror-backed scales to avoid parallax and they have carefully calibrated scales.

 They may therefore be read to the same precision.

 But If the value of the series resistance in one meter changes considerably,  its readings may be in error by a fairly large amount.

 Therefore the accuracy of the two meters may be quite different. 14

 Precision

 Precision is composed of two characteristics:  Conformity and  the number of significant figures to which a measurement maybe made

 Example

 A resistor, whose true resistance is 1,384,572 Ω, is measured by an ohmmeter which consistently and repeatedly indicates 1. MΩ.

 estimates from the scale reading consistently yield a value of 1.4 MΩ i.e. close to the true value

 But the “ error” created by the limitation of the scale reading is a precision error

 Precision is a necessary, but not sufficient, condition for accuracy.

 the accuracy of a reading is not necessarily guaranteed by its precision.

 Significant Figures

 An indication of the precision of the measurement is obtained from the number of significant figures in which the result is expressed

 Significant figures convey actual information regarding the magnitude and the measurement precision of a quantity the more significant figures,  the greater the precision of measurement.

 For example,

 if a resistor is specified as having a resistance of 68Ω, its resistance should be closer to 68Ω than to 67Ω or 69Ω.

 If the value of the resistor is described as 68.0Ω,  it means that its resistance is closer to 68.0Ω than it is to 67.9Ω or 68.1Ω.  more significant figures, expresses a measurement of greater precision

 Significant Figures……

 Another example ,

 the population of a city is reported in six figures as 380,000.

 This may imply that the true value of the population lies between 379,999 and 380,

 Means the population is closer to 380,000 than to 370,000 or 390,000.

 A more technically correct notation uses powers of ten, 38 x 10^4 or 3.8 x l0^5.  Means no confusion for a technical person

 Another way of expressing result indicates the range of possible error.

 The voltage may e.g. be expressed 117.1 ± 0.05 V, indicating that the value of the voltage lies between 117.15 V and 117. V.

 EXAMPLE: 1-

A set of independent voltage measurements taken by four observers was recorded as 117.02 V, 117.11 V, 117.08 V, and 117.03 V. Calculate (a) the average voltage; (b) the range of error

 Solution: a.

b. Rang = Emax – Eav = 117.11 – 117.06 = 0.05V But also Eav – Emin = 117.06 – 117.02 = 0.04 V The average range of error therefore equals  When two or more measurements with different degrees of accuracy are added, the result is only as accurate as the least accurate measurement

N E (^) avE^1 E^2 E^3 E^4

117.02^ 117.11 4 117.08117.03117.06V

0.05 2 0.040.0450.05V

 Example: 1-2 (See Examples 1-3,1-4 & 1-5)

 Two resistors, R 1 and R 2 , are connected in series. Individual resistance measurements, using a digital multimeter, give R 1 = 18.7Ω and R 2 3.624Ω. Calculate the total resistance to the appropriate number of significant figures.

 Solution

R 1 = 18.7Ω (three significant figures) R 2 = 3.624Ω (four significant figures) RT = R 1 + R 2 = 22. 324 Ω (five significant figures) = 22.3Ω

 The doubtful figures are written in italics to indicate that in the addition of R 1 and R 2 the last three digits of the sum are doubtful figures.

 There is no value whatsoever in retaining the last two digits (the 2 and the 4) because one of the resistance is accurate only to three significant figures or tenths of an ohm.

 The result should therefore also be reduced to three significant figures or the nearest tenth, i.e., 22.3 Ω.

 Types Of Errors

 No measurement can be made with perfect accuracy,

 but it is important to find out  what the accuracy actually is? and  how different errors have entered into the measurement?

 A study of errors is a first step in finding ways to reduce them

 Such a study also allows us to determine the accuracy of the final test result.

 Sources of Errors

 Errors come from different sources and are usually classified under three main headings

1. Gross errors: largely human errors, among them misreading

of instruments incorrect adjustment and improper application of instruments, and computational mistakes.

2. Systematic errors: shortcomings of the instruments, such

as defective or worn parts, and effects of the environment on the equipment or the user.

3. Random errors: those due to causes that cannot be directly

established because of random variations in the parameter or the system of measurement.

 Gross Errors

 This class mainly covers human mistakes in reading or using instruments and in recording and calculating measurement results.

 Inevitable if human factor is involved

 Although complete elimination of gross errors is probably impossible,  Try to anticipate and  Correct them

 One common gross error, involves the improper use of an instrument

 In general, indicating instruments change conditions when connected into a complete circuit  the measured quantity is altered by the method employed  For example, a well-calibrated voltmeter may give a misleading reading when connected across two points in a high-resistance circuit

 Example: 1-7 (see example 1-8)

 A voltmeter, having a sensitivity of 1,000 Ω/V, reads 100 V on its 150-V scale when connected across an unknown resistor in series with a milliammeter. When the milliammeter reads 5 mA, 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.

 Solution:

a. The total circuit resistance equals Neglecting the resistance of the milliammeter, the value of the unknown resistor is Rx 20 kΩ,

b. The voltmeter equals

Since the voltmeter is in parallel with the unknown resistance, we can write

c. % Error = (^) 100% = 13.23% 23.05 100% 23.05 actual

actual apparent  

R VI 100V 5mA 20kΩ T T  T  

RV  1,000V^ Ω150V150kΩ

RX RR RR^20130150 23.05kΩ V T

T V     

 Gross Errors

 Errors caused by the loading effect of the voltmeter can be avoided by using it intelligently.  For example, a low-resistance voltmeter should not be used to measure voltages in a vacuum tube amplifier. In this particular measurement, a high- input impedance voltmeter (such as a VTVM or TVM) is required.

 A large number of gross errors can be attributed to carelessness or bad habits  improper reading of an instrument,  recording the result differently from actual reading taken,  or adjusting the instrument incorrectly  e.g. multirange voltmeter errors in range selection scale

 Errors like these cannot be treated mathematically.

 They can be avoided only by taking care in reading and recording the measurement data.

Systematic Errors

 This type of error, is usually divided into two different categories:

 1. instrumental error, defined as shortcomings of the instruments;  2. environmental errors, due to extern conditions affecting the measurement.  Instrumental errors are errors inherent in measuring instruments because of their mechanical structure.  For example the d‟Arsonval movement friction in bearings of various moving components may cause incorrect readings  Irregular spring tension, stretching of the spring, or reduction in tension due to improper handling or overloading of the instrument will result in errors.  calibration errors, causing the instrument to read high or low along its entire scale