aS US Electronic Pee tee rad Second Edition es 40 © » =A-C VOL H S Kalsi aInformation contained in this work has been obtained by Tata McGraw-Hill, from sources believed to be reliable. However, neither Tata McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw- Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information, This work is published with the understanding that Tata McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. NZ NY, i=) Tata McGraw-Hill Copyright © 2004, 1995, by Tata McGraw-Hill Publishing Company Limited. Sixthreprint 2006 RQLZRRYKRADZQ No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not.be reproduced for publication. This edition can be exported from India only by the publishers, Tata McGraw-Hill Publishing Company Limited. ISBN0-07-058370-6 Published by Tata McGraw-Hill Publishing Company Limited, 7 West Patel Nagar, New Delhi 110 008, typeset in Times at Script Makers, 19, Al-B, DDA Market, Paschim Vihar, New Delhi 110 063 and Printed at Gopaljee Enterprises, 190/5 Main Road, Maujpur, Delhi 110053 Cover: MeenakshiPreface to the Second Edition vii Preface to the First Edition xix Acknowledgements xxi 1. Qualities of Measurements 1 I nil L3 tatic acteristics L4___Error in Measurement 2 1.5 Types of Static Error 5 L6 Sources of Error _& 1.7 Dynamic Characteristics 9 1.8 Statistical Analysis J/ L9___Standard 16 1.10 Atomic Frequency and Time Standards 17 L11__Electrical Standards 18 1.12 Graphical Representation of Measurements as a Distribution /9 Review Questions 20 Practive-Probleme. 21 Further Reading 21 2.__ Indicators and Display Devices 22 2.1___Introduction 22 2.3 Taut Band Instrument _28 2.4 Electrodynamometer 29 2.5 Moving Iron Types Instrument 32 2.6 Concentric Vane Repulsion Type (Moving Iron Type) Instrument _34 2.7__ Digital Display System and Indicators _35 2.8 Classification of Displays 35 2.9 Display Devices 36 - 2.10__Light Emitting Diodes (LED) 37 2.11 Liquid Crystal Display(LCD) 38 2.12 Other Displays 4] 2.13 Pri 2.14 Classification of Printers 52 2.15 Printer Character Set 53 Copyrighted material‘Vili mm Contents 2.16 Character at a Time Impact Printers for Fully Formed - Characters (Drum Wheel) 53 2.17__Line at a Time Impact Printers for Fully Formed Characters Line Printers) 55 i i 5; 2 = ix Pri 5 2.20 Character at a Time Dot-Matrix Impact Printer 58 2.21 _Non-Impact Dot-Matrix (NIDM) Printers 60 Review Questions 60 a.__Ammeters 62 3.1 DC Ammeter 62 Multirange Ammeters 63 _The Aryton Shunt or Universal Shunt _ 64 4 Requirements of a Shunt _67 Extending of Ammeter Ranges 67 3.6 RF Ammeter (Thermocouple) 68 3.7 Limitations of Thermocouples 70 3.8 Effect of Frequency on Calibration 70 3.9 Measurements of Very Large Currents by Thermocouples _7/ Further Reading 73 4.2 Basic Meter as aDC Voluneter 75 4.3 DC Volimeter 75 44 Multirange Voltmeter _76 4.5 Extending Voltmeter Ranges 78 4.6 Loading 80 47 Transistor Voltmeter (TVM) 84 4.8 Chopper Type DC Amplifier Voiumeter (Microvolimeter) _ 85 49 i vi 87 10_Differential Vol 5 4.11 DC Siandard/Difference Volimeter 89 4.12 AC Voluneter using Rectifiers 92 4.13 AC Voltmeter using Half Wave Rectifier 93 4.14 AC Volumeter using Full Wave Rectifier 94 415 Multirange AC Voltmeter 96 4.16 Average Responding Voltmeter _96 4.17 Peak Responding Voltmeter 97 i Volimeter 98 Copyrighted maContents mam Ix 4.19 True RMS Meter 99 4.20 Considerations in Choosing an Analog Voltmeter__/0/ 4.21__Ohmmeter (Series Type Ohmmeter) 102 4.22 Shunt Type Ohmmeter _/05 3 erat aces 4.25 Multimeter 107 4.26 Multimeter Operating Instructions 1/0 Review Questions I] Practice Problems 111 Further Reading 113 ‘ Digital Voltmeters 114 5.2 Ramp Technique 7/5 5.3 Dual Slope Integrating Type DVM (Voltage to Time Conversion) 1/6 5.4 Integrating Type DVM (Voltage to Frequency Conversion) 179 5.5 Most Commonly used Principles of ADC — (Analog to Digital Conversion) /2/ 5.6 Successive Approximations /22 5.7___ Continuous Balance DVM or Servo Balancing Potentiometer Type DVM 126 5.8 34-Digit 127 5.9 Resolution and Sensitivity of Digital Meters 127 5.10 General Specifications of aDVM 129 5.11 _Microprocessor-Based Ramp Type DVM_129 Review Questions 132 Further Reading 132 Digital_Instruments 133 611 : ; 6.2 Digital Multimeters _/34 6.3 Digital Frequency Meter 138 6.4 Digital Measurement of Time _/47 ‘vera 1 6.6 Decade Counter 145 6.7 Electronic Counter [47 6.8 Digital Measurement of Frequency (Mains) 149 6.9 Digital Tachometer_152 : 6.10 Digital pH Meter_/52 6.11 Automation in Digital instruments 153 6.12 Digital Phase Meter _/58 6.13 Digital Capacitance Meter_159 Copyrighted materialXam Contents Review Questions 161 Further Reading 162 7.__ Oscilloscope 163 2.1 Introduction _163 7.2 BasicPrinciple 164 7.3 CRT Features 168 7.4 Block Diagram of Oscilloscope 172 75 SimpleCRO 173 7.6 Vertical Amplifier 175 7.1 Horizontal Deflecting System 176 7.8 Triggered Sweep CRO_177 ‘79 Trigger Pulse Circuit 177 7.10 Delay Line in Triggered Sweep 178 7.11 Syne Selector for Continuous Sweep CRO_179 7.12 Typical CRT Connections 179 7.13 High Frequency CRT or Travelling Wave Type CRT_181 714 Dual Beam CRO 182 7.15 Dual Trace Oscilloscope _ 182 AY nic Swit 188 7.17__ (VHF) Sampling Oscilloscope, 189 7.18 Storage Oscilloscope (for VLF Signal) 190 7.19 Digital Readout Oscilloscope 193 7.20 Measurement of Frequency by Lissajous Method 194 7.21 Spot Wheel Method 196 L.22__Gear Wheel Method 198 7.23 Checking of Diodes 199 7 7.24 Basic Measurement of Capacitance and Inductance 200 7.25 Oscilloscope as a Bridge Null Detector 201 7.26 Use of Lissajous Figures for Phase Measurement 203 7.27 Standard Specifications of a Single Beam CRO 203° '1.28__Probes for CRO 205° 129 Attenuators 208 7.30__Applications of Oscilloscope _ 2/0 31 Delayed Swi 212 7.32__ Digital Storage Oscilloscope (DSO) 212 7.33 Fibre Optic CRT Recording Oscilloscope 215 7.34 Oscilloscope Operating Precautions 2/6 7.35. Placing an Oscilloscope in Operation 217 Review Questions 218 Further Reading 219 Copyrighted material8. 10. 8.20 Standard Specifications of a Contents mum xt Signal Generators 8.1 Introduction _220 8.2 Fixed Frequency AF Oscillator _22/ 8.4 Basic Standard Signal Generator (Sine Wave) 222 8.5 Standard Signal Generator 222 8.6 Moder Laboratory Signal Generator 223 8.7__AF Sine and Square Wave Generator 225 Function G : 8.9 Square and Pulse Generator (Laboratory Type) 228 8.10 ndom Noise ral 0 8.11 Sweep Generator 237 : 8.12__TV Sweep Generator 232 8.13 Marker Generator 233 8.14 Sweep-Marker Generator 234 8.15 Wobbluscope 235 Ni 8.17 Colour Bar Generator_237 8.18 Vectroscope 24] 8.19 Beat Frequency Oscillator (BFO) 243 ignal Generator _ 245 Review Questions 245 Further Reading 245 Wave Analyzers and Harmonic Distortion 91 Introduction 247 9.2 Basic Wave Analyzer_248 9.3 Frequency Selective Wave Analyzer 249 9.4 Heterodyne Wave Analyzer 250 ‘955: a Distortion Analyzer 252 9.6 ectrum. Analyzer 254 9.7 alFourier Analyzer 258 9.8 Practical FFT Spectrum Analysis using a Waveform Processing Software (SS-36) 261 Review Questions 264 Further Reading 265 Measuring Instruments 10.2 Output Power Meters 266 10.3 Field Strength Meter 267 10.4 Stroboscope 269 10.5 Phase Meter 270 10.6 Vector Impedance Meter (Direct Reading) 271 247 Copyrighted materialxi mam Contents 11. 10.7 QMeter 274 10.8 LCRBridge 283 10.9 RXMeters 29] 10.10 Automatic Bridges 292 10.11 Transistor Tester 293 10.12 Megger 298 10.13 Analog pH Meter 299 Review Questions 303 Practice Problems 304 Further Reading 304 Bridges 305 11.2__Wheatstone’s Bridge (Measurement of Resistance) 305 11.3 Kelvin’s Bridge 3/2 11.4 Practical Kelvin’sDouble Bridge 315 11.5 Bridge ControlledCircuits 316 11.6 Digital Readout Bridges 3/8 11.7 Microprocessor Controlled Bridges 319 11.8 ACBridges 320 11.9 Capacitance Comparison Bridge 321 11.10 Inductance Comparison Bridge 322 11.11 Maxwell's Bridge 323 11.12 Hay'’sBridge 324 11.13 Schering's Bridge 327 11.14 Wien’s Bridge 329 11.15 Wagner’s Earth (Ground) Connection 331 11.16 Resonance Bridge 333 11.17 Types of Detectors 334 11.18 Precautions to be Taken When Using a Bridge 335 Review Questions 335 Practice Problems 336 Further Reading 339 Recorders 340 2 Introduction 340 12.2 Strip Chart Recorder _ 341 12.3 Galvanometer Type Recorder 344 12.4 Null Type Recorder (Potentiometric Recorders) 347 12.5 Circular Chart Recorder 357 12.6 X-Y Recorder 352 12.7__ Magnetic Recorders 355 12.8 Frequency Modulation (FM) Recording 358 12.9 Digital DataRecording 360 12.10 Objectives and Requirements of Recording Data 36214. Contents mam xill 12.11 Recorder Selections for Particular Applications 363 12.12 Recorder Specifications 363 12.13 Potentiometric Recorder (Multipoint) 364 12.14 Digital Memory Waveform Recorder(DWR) 369 12.15 Applications of a Strip Chart Recorder 371 Review Questions 373 Further Reading 374 375 13.3 Selecting a Transducer 377 3.4 Resistive Transducer 378 13.6 Strain Gauges 383 13:7 Resisnnce Thermometel®’ 397 3.8 hermistor 396 13.9 Inductive Transducer 398 13.10 Differential Output Transducers 402 13.11 Linear Variable Differential Transducer (LVDT) 404 13.12 Pressure Inductive Transducer 408 13.13 Capacitive Transducer (Pressure) 4/5 13.14 Load Cell (Pressure Cell) 417 13.16 Photo Electric Transducer 419 13.17 Photo-VoltaicCell 423 13.18 Semiconductor Photo Diode 423 13.19 The Photo-Transistor 424 13.20 Temperature transducers 425 13.21 Frequency Generating Transducer 447 13.22 Reluctance Pulse Pick-Ups 447 13.23 Flow Measurement (Mechanical Transducers) 448 13.24 Mechanical Flow Meter 449 13.25 Magnetic Flow Meters 449 13.26 Turbine Flowmeter 451 13.27 Measurements of Thickness Using BetaGauge 453 Review Questions 457 Further Reading 459 Signal Conditioning 460 14.1 Introduction 460 14.2 Operational Amplifier (OPAMP) 464 14.3 Basic Instrumentation Amplifier 479 14.4 Applications of Instrumentation Amplifiers (Specific Bridge) 485aly am Contents 16. 14.5.- Chopped and Modulated DC Amplifier 489 14.6 Modulators 490 Filters. 500 15.1 Introduction _500 15.2__Fundamental Theorem of Filters 500 15.3 Passive Filters 504 15.4 ActiveFilters 508 15.5 Butterworth Filter 512 15.6 Band Pass Filter 523 15.7 Band Reject (Stop) Filter 53/ 15.8 AllPass Filter 534 15.9 Universal Active Filters 536 15.10 Designing Procedures for FLT-U2 537 15.11 Types of Active Filters 54] 15.12 Digital Filters 544 15.13 Discrete Functions 546 15.14 1-D Sampling Theorem 546 15.15 The 2-D Sampling Theorem 547 15.16 The 1-D Z-Transform 547 15.17 Fundamental Properties of 1-D Digital Systems 547 15.18 Fundamental Property of 2-D Digital Systems 549 15.19 Frequency Domain Representation 549 15.20 Fir 1-D Digital Filter Design (The Window Method) 554 15.21 Design Methods for IIR Digital Filters 556 15.22 1-D IIR Filter Design 559 15.23 Program for the Design of Butterworth Chebyschev IIR Digital Filters by Means of the Bilinear Transformation 563 15.24 Microprocessor Based Digital Filter 567 15.25 Applications of Digital Filters 568 Review Questions 512 Practice Problems 573 Further Reading 574 Measurement Set-up 575 16.1 Introduction 575 16.2 Measurements of Microwave Frequencies 575 16.3 ResonantCo-Axial Lines 576 16.4 Cavity Wavemeters 577 16.5 RF/UHF Field Strength Meter (Methods for measuring the Strength of Radio Waves) 577 16.6 Measurement of Sensitivity 579 16.7 Measurement of Selectivity 579 16.8 Intermodulation Method of Measuring 580 Non-Linear Distortion 58017. 18. 19. Contents om xv 16.9 Measuring Frequency Response in 585 Audio Amplifiers 16.10 Modulation 586 16.11 Measuring Frequency Modulation 589 16.12 Measuring Frequency Deviation 589 with a Radio Receiver 589 16.13 Measuring Amplitude Modulation Using CRO 590 Review Questions 594 Further Reading 595 Data Acquisition and Conversion 596 17.1 Introduction 596 17.2. ObjectiveofaDAS 598 17.3 Signal Conditioning of the Inputs 598 174 Single Channel Data AcquisitionSystem 600 17.5 Multi-ChannelDAS 602 17.6 ComputerBased DAS 606 17.7 Digital to Analog (D/A) and Analog to Digital (A/D) Converters 607 17.8 Data Loggers 623 17.10 Electromechanical A/D Converter 643 17.11 Digital Transducer 645 Review Questions 647 Practice Problems 648 Further Reading 649 Data Transmission 650 18.1 Introduction 650 18.2 Data Transmission Systems 652 18.3 Advantages and Disadvantages of Digital Transmission overAnalog 653 18.4 Time Division Multiplexing (TDM) 654 18.5 Pulse Modulation 656 18.6 Digital Modulation 666 18.7 Pulse Code Format 675 18.8 Modems 677 Review Questions 681 Further Reading 681 Frequency Standards 682 19.1 Introduction 682 19.2 Primary Standards 682 19.3. Secondary Standards of Frequency 683 19.4 Practical Frequency Standards 683Xvi sua Contents 21. 19.5 Radio Signals as Frequency Standards 684 19.6 Precision Frequency Standards 684 19.7_The Atomic Clock 685 Review Questions 686 Further Reading 686 Measurement of Power 687 20.1 Introduction 687 20.2 Requirements of a Dummy Load 687 20.3 Bolometer 687 20.4 Bolometer Method of Power Measurement 688 20.5 BolometerElement 688 20.6 Bolometer Mount 689 20.7 Measurement of Power by Means of a Bolometer Bridge 690 20.8 Unbalanced Bolometer Bridge 691 20.9 SelfBalancing Bolometer Bridge 692 20.10 Measurement of Large Amount of RF Power (Calorimetric Method) 693 20.11 Measurement of Power on a Transmission Line 695 20.12 Standing Wave Ratio Measurements 696 20.13 Measurement of Standing Wave Ratio using Directional Couplers 698 Review Questions 701 Further Reading 701 Control Systems 702 21.1 Basic Control Action 702 21.2 Definition (Terminology) 703 21.3. ON-OFF Control Action 705 21.4 Proportional Control Action 707 21.5 Offset 708 21.6 Basic Controller Configuration 708 21.7 Classification of Controllers 709 218 Electronic Controllers (EC) 709 21.9 Analog Electronic Process Controllers 7/0 21.10 Temperature Control using an Analog Electronic Controller 7/4 21.11 Choice of Electronic Transmission Signal 7/6 21.12 DigitalControllers 717 21.13 Digital Process Controller 719 21.14 Cascade Process Controller with Digital Controllers 721 21.15 Programmable Logic Controller 723 21.16 Distributed Control Systems 767 Index 790Preface to the Second Edition The tremendous response to the first edition of this book has inspired me to bring out this second edition, which has been revised and updated, based on the suggestions received from the students and teachers using the book. As in the first edition, the book is written in a simple and lucid manner with the chapters arranged systematically to enable the reader to get thorough knowledge of all types of measuring instruments and measurement techniques. With the advancement of technology in integrated circuits, instruments are becoming increasingly compact and accurate. In view of this, sophisticated types of instruments covering digital and microprocessor-based instruments are dealt in detail, in a simple and systematic manner for easy understanding. The basic concepts, working operation, capabilities and limitations of the instruments discussed in the book will also guide the users in selecting the right instrument for certain application. Chapter 1 covers the basic characteristics and the errors associated with an instrument. Different types of indicating and display devices are dealt in Chapter 2. This chapter discusses different types of printers and printer heads used with the computers. The basic analog-type ammeters for both DC and RF frequencies and different types of voltmeters, ohmmeters to multimeters are discussed in Chapters 3 and 4. Digital instruments ranging from a simple digital voltmeter to a microprocessor-based instrument and their measurement techniques are presented in a comprehensible style for easy understanding. Chapter 7 on oscilloscopes has been dealt in depth to familiarize the students with the working of all types of Cathode Ray Oscilloscopes (CROs) and their measurement techniques. Chapter 8 pertains to signal generation. Chapter 9 analyses the frequency component of a generated wave, and its distortion. Every instrument consists of an input sensing element or transducer, a signal conditioner, and a recording or display unit. Chapters 12, 13 and 14 cover the essential components of industrial instruments used for measurements and their usage. Different types of analog and digital filters are given in Chapter 15. A mathematical approach to explaining digital filters has been adopted to provide the students a clear insight into their working. Chapter 16 is on the measurement of microwave frequencies. A detailed discussion on the dataXvili mam Preface to the Second Edition acquisition system along with the latest data logger is covered in Chapter 17. Instruments from remote places transmit signals over long distances to a master control room where they are displayed. This transmission of signals has been explained in detail in Chapter 18. Frequency standards and measurement of Power at RF and Microwave frequencies are dealt with in Chapters 19 and 20 respectively. The last chapter, newly added to this edition, deals with Control Systems, electronic control systems, in particular. This chapter covers the basic control systems, electronic controllers, PLC and advanced control systems such as DCS, used in process control plants. Thope that this edition of the book will prove useful to all readers, students as well as teachers. All suggestions for further improvement of the book are welcome and will be gratefully acknowledged. HS KatsiPreface to the First Edition This book is written to cater specifically to the needs of the students of electronics engineering. It will also be of use to the electronics students at polytechnics and other technical institutes. It is written in a simple and lucid manner with the chapters arranged syste- matically to enable the reader to get a thorough knowledge of all types of measuring instruments and their measurement techniques. With the advance- ment of technology in integrated circuits, instruments are becoming more and more compact and accurate. In view of this, sophisticated types of instruments covering digital and microprocessor-based instruments are dealt in detail, in a simple, step-by-step manner for easy understanding. The basic concepts, working operation, capabilities and limitations of instruments are discussed in the book which will guide the users in selecting instruments for various applications. Chapter 1 covers the basic characteristics and the errors associated with an instrument. Different types of indicating and display devices are dealt in Chapter 2. Computer technology is a rapidly advancing field; and the hardcopy is of prime importance, for which printers are used. This chapter also dis- cusses different types of printers and printer heads. The basic analog type ammeters both for dc and RF frequency and different types of voltmeters, ohmmeters to multimeters are discussed in Chapter 3 and 4, Digital instruments ranging from a simple digital voltmeter to a microprocessor-based instrument and their measurement techniques are presented in a comprehensible style for easy understanding. Chapter 7 on oscilloscopes has been dealt in depth to familiarise the students with the working of all types of Cathode-Ray Oscilloscopes (CRO) and their measurement techniques. Chapter 8 pertains to signal generation. Chapter 9 analyses the frequency component of a wave generated, and its distortion. Any instrument basically consists of an input sensing element or transducer, signal conditioner, and recording or display unit. Chapters 12, 13 and 14 cover the essential components of industrial instruments and their measurement techniques. Different types of analog and digital filters are given in the next chapter. A mathematical approach to explain digital filters has been adopted to provide the students a clear insight into its working. Chapter 16 is on the measurement of microwave frequencies. A detailed discussion on data acquisition system along0c" Preface to the First Edition with the latest data logger is covered in Chapter 17. Instruments from remote places transmit signals over long distances to a master control room where they are displayed. This transmission of signals has been explained in detail in Chapter 18. The last two chapters pertain to frequency standards and measurement of power, respectively. I hope this book will prove to be useful to all readers. I will appreciate any suggestions which will help in the improvement of the book. HS KasiAcknowledgements First of all, I express my deepest thanks and gratitude to my younger brother who gave me support without which it would have been difficult to complete my project. Secondly, I thank reviewers who read some or all of the manuscript, and gave suggestions for the improvement of my book. I also thank Signet Electronics Ltd, who made available the photographs of instruments. I deeply acknowledge my wife and othér family members for their never- ending encouragement, moral support and patience during the preparation of this book. Last, but not the least, I also thank my friends and colleagues who helped me in the writing of the book.“CHAPTER 1 Qualities of Measurements HE introouction Instrumentation is a technology of measurement which serves not only science but all branches of engineering, medicine, and almost every human endeavour. The knowledge of any parameter largely depends on the measurement. The indepth knowledge of any parameter can be easily understood by the use of measurement, and further modifications can also be obtained. Measuring is basically used to monitor a process or operation, or as well as the controlling process. For example, thermometers, barometers, anemometers are used to indicate the environmental conditions. Similarly, water, gas and electric meters are used to keep track of the quantity of the commodity used, and also special monitoring equipment are used in hospitals. Whatever may be the nature of application, intelligent selection and use of measuring equipment depends on a broad knowledge of what is available and how the performance of the equipment renders itself for the job to be performed. But there are some basic measurement techniques and devices that are useful and will continue to be widely used also. There is always a need for improve- ment and development of new equipment to solve measurement problems. The major problem encountered with any measuring instrument is the error. Therefore, it is obviously necessary to select the appropriate measuring instrument and measurement method which minimises error. To avoid errors in any experimental work, careful planning, execution and evaluation of the experiment are essential. The basic concern of any measurement is that the measuring instrument should not effect the quantity being measured; in practice, this non-interference principle is never strictly obeyed. Null measurements with the use of feedback in an instrument minimise these interference effects.2mm Electronic Instrumentation [@ PERFORMANCE CHARACTERISTICS A knowledge of the performance characteristics of an instrument is essential for selecting the most suitable instrument for specific measuring jobs. It consists of two basic characteristics—static and dynamic. static characteristics The static characteristics of an instrument are, in general, considered for instruments which are used to measure an unvarying process condition. All the static performance characteristics are obtained by one form or another of a process called calibration. There are a number of related definitions (or characteristics), which are described below, such as accuracy, precision, repeatability, resolution, errors, sensitivity, etc. 1. Instrument A device or mechanism used to determine the present value of the quantity under measurement. 2. Measurement The process of determining the amount, degree, or capacity by comparison (direct or indirect) with the accepted standards of the system units being used. 3. Aceuracy The degree of exactness (closeness) of a measurement compared to the expected (desired) value. 4. Resolution The smallest change in a measured variable to which an instrument will respond. 5. Precision A measure of the consistency or repeatability of measure- ments, i.e. successive reading do not differ. (Precision is the consistency of the instrument output for a given value of input). 6. Expected value The design value, ic. the most probable value that calculations indicate one should expect to measure. 7. Error The deviation of the true value from the desired value. 8. Sensitivity The ratio of the change in output (response) of the instrument to a change of input or measured variable. MD Enron In MEASUREMENT Measurement is the process of comparing an unknown quantity with an accepted standard quantity. It involves connecting a measuring instrument into the system under consideration and observing the resulting response on the instrument. The measurement thus obtained is a quantitative measure of the so-Qualities of Measurements aus 3 called “true value” (since it is very difficult to define the true value, the term “expected value” is used). Any measurement is affected by many variables, therefore the results rarely reflect the expected value. For example, connecting a measuring instrument into the circuit under consideration always disturbs (changes) the circuit, causing the measurement to differ from the expected value. Some factors that affect the measurements are related to the measuring instruments themselves. Other factors are related to the person using the instrument. The degree to which a measurement nears the expected value is expressed in terms of the error of measurement. Error may be expressed either as absolute or as percentage of error. Absolute error may be defined as the difference between the expected value of the variable and the measured value of the variable, or e=Y,-X, where e = absolute error Y, = expected value X, = measured value Therefore % Error = Absolute value Expected value == x100 Y, Therefore % Error = ( =) 100 In It is more frequently expressed as a accuracy rather than error. Therefore A=1- where A is the relative accuracy. Accuracy is expressed as % accuracy a= 100% — % ertor a=Ax 100% where a is the % accuracy. The expected value of the voltage across a resistor is 80 V. |However, the measurement gives a value of 79 V. Calculate (i) absolute error, \(ii) % error, (iii) relative accuracy, and (iv) % of accuracy.4mm Electronic Instrumentation (i) Absolute error e = ¥, -X, = 80-79 =1V 80-79 , 100 = 1.25% 20 Gi) % Error = 2 f= = x 100 = he (iii) Relative Accuracy ” A= 1 - 1/80 = 79/80 = 0.9875 (iv) % of Accuracy a= 100 XA = 100 x 0.9875 = 98.75% or a= 100% — % of error = 100% — 1.25% = 98.75% If a measurement is accurate, it must also be precise, i.e. Accuracy means precision. However, a precision measurement may not be accurate. (The precision of a measurement is a quantitative or numerical indication of the closeness with which a repeated set of measurement of the same variable agree with the average set of measurements.) Precision can also be expressed mathematically as where X, = value of the nth measurement X, = average set of measurement Table 1.1 gives the set of 10 measurement that were recorded lin nthe laboratory. Calculate the precision of the 6th measurement. Table 1.1 Measurement number Measurement value X, 98 101 102 9o7 101 100 103 98 106 99 SomyuaAnauneQualities of Measurements mam 5 [The average value for the set of measurements is given by Sum of the 10 measurement values 10 x, = 105 - 1005 10 ~~ X, Precision = 1 — Xx, For the 6th reading Precision = - —— = —— = 0.995 100.5 100.5 100.5 me a =1_- 05. _ 100 The accuracy and precision of measurements depend not only on the quality lof the measuring instrument but also on the person using it. However, whatever Ithe quality of the instrument and the case exercised by the user, there is always some error present in the measurement of physical quantities. x (SS) TYPES OF STATIC ERROR The static error of a measuring instrument is the numerical difference between the true value of a quantity and its value as obtained by measurement, ie. repeated measurement of the same quantity gives different indications. Static errors are categorised as gross errors or human errors, systematic errors, and random errors. 1.5.1 Gross Errors These errors are mainly due to human mistakes in reading or in using instruments or errors in recording observations. Errors may also occur due to incorrect adjustment of instruments and computational mistakes. These errors cannot be treated mathematically. The complete climination of gross errors is not possible, but one can minimise them. Some errors are easily detected while others may be elusive. One of the basic gross errors that occurs frequently is the improper use of an instrument. The error can be minimized by taking proper care in reading and tecording the measurement parameter. In general, indicating instruments change ambient conditions to some extent when connected into a complete circuit. (Refer Examples 1.3(a) and (b)).6 as Electronic Instrumentation (One should therefore not be completely dependent on one reading only; at least three separate readings should be taken, preferably under conditions in which instruments are switched off and on.) 1.5.2 Systematic Error These errors occur due to shortcomings of the instrument, such as defective or wom parts, or ageing or effects of the environment on the instrument. These errors are sometimes referred to as bias, and they influence all measurements of a quantity alike. A constant uniform deviation of the operation of an instrument is known as a systematic error. There are basically three types of systematic errors—(i) Instrumental, (ii) Environmental, and (iii) Observa- tional. () instrumental Errors Instrumental errors are inherent in measuring instruments, because of their mechanical structure. For example, in the D’Arsonval movement, friction in the bearings of various moving components, irregular spring tensions, stretching of the spring, or reduction in tension due to improper handling or overloading of the instrument. Instrumental errors can be avoided by (a) selecting a suitable instrument for the particular measurement applications. (Refer Examples 1.3 (a) and (b)). applying correction factors after determining the amount of instrumental error. calibrating the instrument against a standard. C) « (ii) Environmental Errors Environmental errors are due to conditions external to the measuring device, including conditions in the area surrounding the instrument, such as the effects of change in temperature, humidity, barometric pressure or of magnetic or electrostatic fields. These errors can also be avoided by (i) air conditioning, (ii) hermetically sealing certain components in the instruments, and (iii) using magnetic shields. (ill) Observational Errors Observational errors are errors introduced by the observer. The most common error is the parallax error introduced in reading a meter scale, and the error of estimation when obtaining a reading from a meter scale. These errors are caused by the habits of individual observers. For example, an observer may always introduce an error by consistently holding his head too far to the left while reading a needle and scale reading.Qualities of Measurements mm 7 In general, systematic errors can also be subdivided into static and dynamic errors. Static errors are caused by limitations of the measuring device or the physical laws governing its behaviour. Dynamic errors are caused by the instrument not responding fast enough to follow the changes in a measured variable. Bina: A voltmeter having a sensitivity of 1 kQ/V is connected across an unknown resistance in series with a milliammeter reading 80 V on 150 V scale. When the milliammeter reads 10 mA, calculate the (i) Apparent resistance of the unknown resistance, (ii) Actual resistance of the unknown resistance, and (iii) Error due to the loading effect of the voltmeter. maser: Vv; _ 80 (i) The total circuit resistance Rp = —> = i 10mA (Neglecting the resistance of the milliammeter.) (ii) The voltmeter resistance equals R, = 1000 Q/V x 150 = 150kQ. + actual value of unknown resistance R, = fe x8 = ate ee a =8kQ 2 = 120K" 28.45 kQ 142k Gi) % eror = Actual value Apparent value _ 845k—8k , 99 Actual value = 0.053 x 100 = 5.3% AME Referring to Ex. 1.3 (@), if the milliammeter reads 1600 mA and the voltmeter reads 30 V on a 150 V scale, calculate the following: (i) Apparent, resistance of the unknown resistance. (ii) Actual resistance of the lunknown resistance. (iii) Error due to loading effect of the voltmeter. Comment on the loading effect due to the voltmeter for both Examples 1.3 (a) and (b). (Voltmeter sensitivity given 1000 Q/V.) 1. The total circuit resistance is given by 45k8 mms Electronic Instrumentation 2. The voltmeter resistance R, equals R, = 1000 Q/V x 150 = 150 kQ Neglecting the resistance of the milliammeter, the value of unknown resist- lance = 50.Q _ RpXR, _ 50X150k _ 7500k *" RR, 150k-50 1495k = 50.1670 ~ 50167-50 199 _ 0.167 % Exror = = x 100 = 0.33% 50.167 50.167 In Example 1.3 (a), a well calibrated voltmeter may give a misleading resist- lance when connected across two points in a high resistance circuit. The same voltmeter, when connected in a low resistance circuit (Example 1.3 (b)) may give a more dependable reading. This show that voltmeters have a loading effect in the circuit during measurement. 1.5.3 Random Errors These are errors that remain after gross and systematic errors have been substantially reduced or at least accounted for. Random errors are generally an accumulation of a large number of small effects and may be of real concern only in measurements requiring a high degree of accuracy. Such errors can be analyzed statistically. These errors are due to unknown causes, not determinable in the ordinary process of making measurements. Such errors are normally small and follow the laws of probability. Random errors can thus be treated mathematically. For example, suppose a voltage is being monitored by a voltmeter which is read at 15 minutes intervals. Although the instrument operates under ideal environmental conditions and is accurately calibrated before measurement, it still gives readings that vary slightly over the period of observation. This variation cannot be corrected by any method of calibration or any other known. method of control. HE sources oF ERROR The sources of error, other than the inability of a piece of hardware to provide a true measurement, are as follows: 1. Insufficient knowledge of process parameters and design conditions 2. Poor design 3. Change in process parameters, irregularities, upsets, etc. 4. Poor maintenance 5. Errors caused by person operating the instrument or equipment 6. Certain design limitationsQualities of Measurements sam 9 (BR Dynamic cuaractenistics Instruments rarely respond instantaneously to changes in the measured vari- ables. Instead, they exhibit slowness or sluggishness due to such things as mass, thermal capacitance, fluid capacitance or electric capacitance. In addition to this, pure delay in time is often encountered where the instrument waits for some reaction to take place. Such industrial instruments are nearly always used for measuring quantities that fluctuate with time. Therefore, the dynamic and transient behaviour of the instrument is as important as the static behaviour. The dynamic behaviour of an instrument is determined by subjecting its pri- mary element (sensing element) to some unknown and predetermined varia- tions in the measured quantity. The three most common variations in the meas- ured quantity are as follows: 1. Step change, in which the primary element is subjected to an instantane- ous and finite change in measured variable. 2. Linear change, in which the primary element is following a measured variable, changing linearly with time. 3. Sinusoidal change, in which the primary element follows a measured variable, the magnitude of which changes in accordance with a sinusoi- dal function of constant amplitude. The dynamic characteristics of an instrument are (i) speed of response, (ii) fidelity, (iii) lag, and (iv) dynamic error. (Gi) Speed of Response It is the rapidity with which an instrument re- sponds to changes in the measured quantity. (ii) Fidelity It is the degree to which an instrument indicates the changes in the measured variable without dynamic error (faithful reproduction). @ii) Lag It is the retardation or delay in the response of an instrument to changes in the measured variable. (iv) Dynamic Error It is the difference between the true value of a quantity changing with time and the value indicated by the instrument, if no static error is assumed. ‘When measurement problems are concerned with rapidly varying quantities, the dynamic relations between the instruments input and output are generally defined by the use of differential equations. 1.7.1 Dynamic Response of Zero-order Instruments We would like an equation that describes the performance of the zero order instrument exactly. The relations between any input and output can, by using suitable simplifying assumptions, be written as "x, at “at GT dx, 4, alae + Xo10 mum Electronic Instrumentation m ml =b, aes tet Dy a ae dx; ee by =x; (1.1) where x, = output quantity x; = input quantity ime a’s and b’s are combinations of systems physical parameters, assumed con- stant. When all the a’s and b’s, other than ap and by are assumed to be zero, the differential equation degenerates into the simple equation given as gk, = box; (1.2) Any instrument that closely obeys Eq. (1.2) over its intended range of oper- ating conditions is defined as a zero-order instrument. The static sensitivity (or steady state gain) of a zero-order instrument may be defined as follows = ay x, = K x, X i i ‘0 where K = bo/ag = static sensitivity Since the equation x, = K x; is an algebraic equation, it is clear that no matter how x, might vary with time, the instrument output (reading) follows it per- fectly with no distortion or time lag of any sort. Thus, a zero-order instrument represents ideal or perfect dynamic performance. A practical example of a zero order instrument is the displacement measuring potentiometer. 1.7.2 Dynamic Response of a First Order Instrument If in Eq. (1.1) all a’s and 8s other than a,, dg, by are taken as zero, we get 4 A + ag, = boX; dt Any instrument that follows this equation is called a first order instrument. By dividing by ao, the equation can be written as K = bo/ay = static sensitivity The time constant t always has the dimensions of time while the static sensi- tivity K has the dimensions of output/input. The operational transfer function of any first order instrument isQualities of Measurements mam 11 K x, tTD+1 A very common example of a first-order instrument is a mercury-in-glass thermometer. 1.7.3 Dynamic Response of Second Order Instrument A second order instrument is defined as one that follows the equation dx, dx, OP +a, F gx, = bok; ‘The above equations can be reduced as 2 a o, where @,= ft a, 2€= a,/,fa,a, = damping ratio K = bo/ay = static sensitivity = undamped natural frequency in radiaris/time Any instrument following this equation is a second order instrument. A prac- tical example of this type is the spring balance. Linear devices range from mass- spring arrangements, transducers, amplifiers and filters to indicators and re- corders. Most devices have first or second order responses, i.e. the equations of mo- tion describing the devices are either first or second order linear differentials. For example, a search coil and mercury-in-glass thermometer have a first order response. Filters used at the output of a phase sensitive detector and amplifiers used in feedback measuring systems essentially have response due to a single time constant. First order systems involve only one kind of energy, e.g. thermal energy in the case of a thermometer, while a characteristic feature of second order system is an exchange between two types of energy, e.g. electrostatic and electromagnetic energy in electrical LC circuits, moving coil indicators and electromechanical recorders. BEE STATISTICAL ANALYSIS The statistical analysis of measurement data is important because it allows an analytical determination of the uncertainty of the final test result. To make sta-12 mam Electronic Instrumentation tistical analysis meaningful, a large number of measurements is usually re- quired. Systematic errors should be small compared to random errors, because statistical analysis of data cannot remove a fixed bias contained in all measure- ments. 1.8.1 Arithmetic Mean The most probable value of a measured variable is the arithmetic mean of the number of readings taken. The best approximation is possible when the number of readings of the same quantity is very large. The arithmetic mean of n meas- urements at a specific count of the variable x is given by the expression Rta taytectx, i where ¥ = Arithmetic mean %, = nth reading taken n= total number of readings 1.8.2 Deviation from the Mean This is the departure of a given reading from the arithmetic mean of the group of readings. If the deviation of the first reading, x,, is called d, and that of the second reading x, is called d,, and so on, The deviations from the mean can be expressed as d, =x,—-X,d,=x,—-X ..., similarly d, =x, ~X The deviation may be positive or negative. The algebraic sum of all the de- viations must be zero. For the following given data, calculate (i) Arithmetic mean (ii) Deviation of each value (iii) Algebraic sum of the deviations Given =x, = 49.7 x, = 50.1 = 50.2 xq = 49.6 X5= 49.7Qualities of Measurements mmm 13 (i) The arithmetic mean is calculated as follows Xy+Xy ty tXy +5 5 y= _ 49.7 + 50.1 + 50.2 + 49.6 + 49.7 - 5 = 49.86 (ii) The deviations from each value are given by d, =x, — ¥ = 49.7 - 49.86 =- 0.16 dy = xy — ¥ =50,1—49.86= + 0.24 d, =x,— ¥ =50.2-49.86= + 0.34 dy = x4— ¥ = 49.6 - 49.86 = - 0.26 ds = x5— ¥ = 49.7- 49.86 = - 0.16 (iii) The algebraic sum of the deviation is Groat = — 0.16 + 0.24 + 0.34 - 0.26 - 0.16 = + 0.58 -0.58=0 1.8.3 Average Deviations The average deviation is an indication of the precision of the instrument used in measurement. Average deviation is defined as the sum of the absolute values of the deviation divided by the number of readings. The absolute value of the deviation is the value without respect to the sign. Average deviation may be expressed as p,, = Melt Malt byl le av n die! or Dy = n where D,, = average deviation |ldj|, Id3l, ..., Id, = Absolute value of deviations and n = total number of readings Highly precise instruments yield a low average deviation between readings.14 mm Electronic Instrumentation Calculate the average deviation for the data given in Example 1.4. The average deviation is calculated as follows ddl + ldgl + ldgl + ---+1d,1 ay n 161 + 10.241 + 10.341 + |-0.261 + |-0.161 5 = MG _ 9232 5 'Therefore, the average deviation = 0.232. 1.8.4 Standard Deviation The standard deviation of an infinite number of data is the Square root of the sum of all the individual deviations squared, divided by the number of readings. It may be expressed as o- | n where o= standard deviation The standard deviation is also known as root mean square deviation, and is the most important factor in the statistical analysis of measurement data. Reduction in this quantity effectively means improvement in measurement. For small readings (n < 30), the denominator is frequently expressed as (n— 1) to obtain a more accurate value for the standard deviation. Calculate the standard deviation for the data given in Example 1.4. dt+de+de+--+d? n Standard deviation = (-0.16)? + (0.24)" + (0.34)? + (-0.26)" + (-0.16)" 5-1Qualities of Measurements mums 15 ga, [9.0256 0.0576 + 0.1156 + 0.0676 + 0.0256 - 4 o= 0292 0.073 = 0.27 Therefore, the standard deviation is 0.27. 1.8.5 Limiting Errors Most manufacturers of measuring instruments specify accuracy within a certain 9% of a full scale reading. For example, the manufacturer of a certain voltmeter may specify the instrument to be accurate within + 2% with full scale deflection. This specification is called the limiting error. This means that a full scale deflection reading is guaranteed to be within the limits of 2% of a perfectly accurate reading; however, with a reading less than full scale, the limiting error increases. A 600 V voltmeter is specified to be accurate within + 2% at full scale. Calculate the limiting error when the instrument is used to measure a voltage of 250 V. The magnitude of the limiting error is 0.02 x 600 = 12 V. Therefore, the limiting error is 250 V is 12/250 x 100 = 4.8% A voltmeter reading 70 V on its 100 V range and an ammeter reading 80 mA on its 150 mA range are used to determine the power dissipated in a resistor. Both these instruments are guaranteed to be accurate within + 1.5% at full scale deflection. Determine the limiting error of the power. | Solution The magnitude of the limiting error for the voltmeter is 0.015 x 100=15V The limiting error at 70 V is BS. x 100 = 2.143 % 70 The magnitude of limiting error of the ammeter is 0.015 x 150 mA = 2.25 mA The limiting error at 80 mA is 2.25 mA 80 mA x 100 = 2.813 %16 ema Electronic Instrumentation Therefore, the limiting error for the power calculation is the sum of the indi- vidual limiting errors involved. Therefore, limiting error = 2.143 % + 2.813 % = 4.956 % Gis) STANDARD A standard is physical representation of a unit of measurement. A known accu- rate measure of physical quantity is termed as a standard. These standards are used to determine the values of other physical quantities by the comparison method. In fact, a unit is realized by reference to a material standard or to natural phenomena, including physical and atomic constants. For example, the fundamental unit of length in the International system (SI) is the metre, defined as the distance between two fine lines engraved on gold plugs near the ends of a platinum-iridium alloy at 0°C and mechanically supported in a prescribed manner. Similarly, different standards have been developed for other units of measurement (including fundamental units as well as derived mechanical and electrical units). All these standards are preserved at the International Bureau of Weight and Measures at Sévres, Paris. Also, depending on the functions and applications, different types of “standards of measurement” are classified in categories (i) international, (ii) primary, (iii) secondary, and (iv) working standards. 1.9.1 International Standards International standards are defined by International agreement. They are periodically evaluated and checked by absolute measurements in terms of fundamental units of Physics. They represent certain units of measurement to the closest possible accuracy attainable by the science and technology of measurement. These International standards are not available to ordinary users for measurements and calibrations. International ohms It is defined as the resistance offered by a column of mercury having a mass of 14.4521 gms, uniform cross-sectional area and length of 106.300 cm, to the flow of constant current at the melting point of ice. International amperes It is an unvarying current, which when passed through a solution of silver nitrate in water (prepared in accordance with stipulated specifications) deposits silver at the rate of 0.00111800 gms. Absolute units International units were replaced in 1948 by absolute units. These units are more accurate than International units, and differ slightly from them, For example,Qualities of Measurements mma 17 1 International ohm = 1.00049 Absolute ohm 1 International ampere = 0.99985 Absolute ampere 1.9.2 Primary Standards The principle function of primary standards is the calibration and verification of secondary standards. Primary standards are maintained at the National Standards Laboratories in different countries. The primary standards are not available for use outside the National Laboratory. These primary standards are absolute standards of high accuracy that can be used as ultimate reference standards. 1.9.3 Secondary Standards Secondary standards are basic reference standards used by measurement and calibration laboratories in industries. These secondary standards are maintained by the particular industry to which they belong. 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 the particular industrial laboratory with a certification of measuring accuracy in terms of a primary stan- dard. 1.9.4 Working Standards Working standards are the principal tools of a measurement laboratory. These standards are used to check and calibrate laboratory instrument for accuracy and performance. For example, manufacturers of electronic components such as capacitors, resistors, etc. use a standard called a working standard for checking the component values being manufactured, e.g. a standard resistor for checking of resistance value manufactured. (BB Atomic FREQUENCY AND TIME STANDARDS The measurement of time has two different aspects, civil and scientific. In most scientific work, it is desired to know how long an event lasts, or if dealing with an oscillator, it is desired to know its frequency of oscillation. Thus any time standard must be able to answer both the question “what time is it” and the two related questions “how long does it last” or “what is its frequency”. ‘Any phenomena that repeats itself can be used as a measure of time, the measurement consisting of counting the repetitions. Of the many repetitive phenomena occurring in nature, the rotation of the earth on its axis which deter- mines the length of the day, has been long used as a time standard. Time de- fined in terms of rotation of the earth is called Universal time (UT).18 wm Electronic Instrumentation Time defined in terms of the earth’s orbital motion is called Ephemersis time (ET). Both UT and ET are determined by astronomical observation. Since these astronomical observations extend over several weeks for UT and several years for ET, a good secondary terrestrial clock calibrated by astronomical observation is needed. A quartz crystal clock based on electrically sustained natural periodic vibrations of a quartz wafer serves as a secondary time standard. These clocks have a maximum error of 0.02 sec per year. One of the most common of time standards is the determination of frequency. In the RF range, frequency comparisons to a quartz clock can be made electronically to a precision of atleast | part in 10'°, To meet a better time standard, atomic clocks have been developed using periodic atomic vibrations as a standard. The transition between two energy levels, E, and E, of an atom is accompanied by the emission (or absorption) of radiation given by the following equation -£-4 h where v= frequency of emission and depends on the internal structure of an atom h = Planck’s constant = 6.636 x 10” J-sec. Provided that the energy levels are not affected by the external conditions such as magnetic field etc. Since frequency is the inverse of the time interval, time can be calibrated in terms of frequency. The atomic clock is constructed on the above principle. The first atomic clock was based on the Cesium atom. The International Committee of Weights and Measures defines the second in terms of the frequency of Cesium transitions, assigning a value of 9,192, 631,770 Hz to the hyperfine transitions of the Cesium atom unperturbed by external fields. If two Cesium clocks are operated at one precision and if there are no other sources of error, the clocks will differ by only 1s in 5000 years. Sa] ELECTRICAL STANDARDS Allelectrical measurements are based on the fundamental quantities, /, R and V_ A systematic measurement depends upon the definition of these quantities. These quantities are related to each other through Ohm's law, V = JR. It is sufficient to define two parameters to obtain the definition of the third. Hence, in electrical measurements, it is possible to assign values to the remaining standard, by defining units of the other two standards. Standards of emf and resistance are therefore usually maintained at the National laboratory. The base values of the other standards are defined from these two standards.Qualities of Measurements am 19 BB GRAPHICAL REPRESENTATION OF MEASUREMENTS AS A DISTRIBUTION Suppose that a certain voltage is measured 51 times. The result which might be obtained are shown in Table 1.2. Table 1.2 x Numberof xd, Voltage Occurrences (v) (a, n(d, (v) (n) 1.01 1 1.01 — 0.04 0.04 «116x104 16x 104 1,02 3 3.06 —0.03 0.09 9x104 27x10 1.03 6 6.18 — 0.02 0.12 4x104 24x 104 1.04 8 8.32 -0.01 0.08 1x1o4 8x10 1,05 10 10.50 0.00 0.00 =0x10* 00x 10% 1.06 7 7A2 +0.01 0.07 =«1x1o* 7x 104 1.07 8 8.56 +0.02 016 4x1o4 32x10 1.08 4 4.32 + 0.03 0.12 9x104 36x 10+ 1.09 3 3.27 +0.04 0.12 16x10% 48x 104 1.10 0 0.00 +0.05 0.00 625x104 00x 10% 1 1 Lil +0.06 0.06 36x10 36x 104 51 53.75 0.86 234 x 107 = 2375 - 1054 jt 51 Xia, Average x = Average deviation Dyy = = o86 = 0.0168 V Standard deviation o= = 4.588 x 104 V The first column shows the various measured values and the second column, the number of times each reading has occurred. For example, in the fourth row, the measured value is 1.04 V and the next column indicates that this reading is obtained 8 times.20 mm Electronic Instrumentation The data given in Table 1.2 may be represented graphically as shown in Fig. 1.1. We imagine the range of values of x to be divided into equal intervals dx, and plot the number of values of x lying in the interval versus the average value of x within that interval. Hence the eight measurements of 1.04 V might be thought of lying in an 0.01 V interval centred upon 1.04 V, i.e. between 1.035 V to 1.045 V on the horizontal scale. Since with a small number (such as 51), these points do not lie on a smooth curve, it is conventional to represent such a plot by a histogram consisting of series of horizontal lines of length dx centred upon the individual points. The ends of adjacent horizontal lines being connected by vertical lines of appropriate length. If another 51 measurements are taken and plotted we would, in general get a graph which does not coincide with the previous one. The graph plotted is called a Gauss error or Gaussian graph, shown in Fig. 1.1. Ideal Curve Actual Curve Number of Occurence Values a 1,00 101 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 %=1.054V ——» x(v) Fig. 1.1 mm Gaussian graph sess Resting . Define the terms accuracy, error, precision, resolution, expected value, and sensitivity. 2. State the three major categories of error. A person using an ohmmeter reads the measured value as 470 Q, when the actual value is 47 82. What kind of error does this represent? State the three types of systematic errors, giving examples of each. State the difference between accuracy and precision of a measurement. . Define the following terms: (i) Average value (i) Arithmetic mean (ii) Deviation (iv) Standard deviation What are the differences between International and Absolute standards? . State the classifications of standards. e r gas anQualities of Measurements wum 21 9, What are primary standards? Where are they used? 10. What is the difference between secondary standards and working standards? a _ 1. The current through a resistor is 2.5 A, but the measurement yields a value of 2.45 A. Calculate the absolute error and the percentage error of the measurement. 2. The value of a resistance is 4.7 kQ, while measurements yield a value of 4.63 kQ calculate (i) the relative accuracy of measurement, and Gi) % accuracy. 3. The output voltage of an amplifier was measured at eight different intervals using the same digital voltmeter with the following results: 20.00, 19.80, 19.85, 20.05, 20.10, 19.90, 20.25, 19.95 V Which is the most precise measurement? 4. A 270 Q + 10% resistance is connected to a power supply source operating at 300 V de. What range of current would flow if the resistor varied over the range of + 10% of its expected value? What is the range of error in the current? 5. A voltmeter is accurate to 98% of its full scale reading. (i) Ifa voltmeter read 200 V on 500 V range, what is the absolute error? (ii) What is the percentage error reading of part (i)? j A Further Reading j 1. Barry Jones, Instrumentation Measurements and Feedback. 2. Larry D. Jones and A. Foster Chin, Electronic Instruments and Measurement, John Wiley and Sons, 1987. 3. Yardley Beers, Theory of Errors, 1967. 4, Resnick and Halliday, Physics, Wiley Eastern, 1987.» CHAPTER 2 Indicators and Display Devices ay ntrobuction Analogue ammeters and voltmeters are classified together, since there is no basic difference in their operating principles. The action of all ammeters and voltmeters, except those of the electrostatic variety, depends upon a deflecting torque produced by an electric current. In an ammeter this torque is produced by the current to be measured, or by a definite fraction of it. In a voltmeter it is produced by a current that is proportional to the voltage to be measured. Hence both voltmeters and ammeters are essentially current measuring devices. The essential requirements of a measuring instrument are (a) that its intro- duction into the circuit where measurements are to be made, should not alter the circuit conditions, and (b) the power consumed by it be small. 2.1.1. Types of Instrument The following types of instrument are mainly used as ammeters and voltmeters. 1. PMMC .. Moving Iron . Electrodynamometer }. Hot wire . Thermocouple . Induction type . Electrostatic . Rectifier Of these, the PMMC type can be used for dc measurements only, and the induction type for ac measurements only. The other types can be used for both. The moving coil and moving iron types depend upon the magnitude effect of current. The latter is the most commonly used form of indicating instrument, as SNIAANWAKWNIndicators and Display Devices sue 23 well as the cheapest. It can be used for both ac and de measurements and is very accurate, if properly designed. The PMMC instrument is the most accurate type for dc measurement. Instru- ment of this type are frequently constructed to have substandard accuracy. The calibration of the electrodynamometer type of instrument is the same for ac and de. The same situation prevails for thermal instruments. These are particularly suitable for ac measurements, since their deflection depends di- rectly upon the heating effect of the ac, ie. upon the rms value of the current. Their readings are therefore independent of the frequency. Electrostatic instruments used as voltmeters have the advantage that their power consumption is exceedingly small. They can be made to cover a large range of voltage and can be constructed to have sub-standard accuracy. The induction principle is most generally used for Watt-hour meters. This principle is not preferred for use in ammeters and voltmeters because of the comparatively high cost and inaccuracy of the instrument. IEE basic meter MOVEMENT The action of the most commonly de meter is based on the fundamental princi- ple of the motor. The motor action is produced by the flow of a small current through a moving coil, which is positioned in the field of a permanent magnet. This basic moving coil system is often called the D’Arsonval galvanometer. The D’Arsonval movement shown in Fig. 2.1 employs a spring-loaded coil through which the measured current flows. The coil (rotor) is in a nearly homogeneous field of a permanent magnet and moves in a rotary fashion. The amount of rotation is proportional to the amount of s current flowing through the coil. A to pointer attached to the coil indicates Fig. 2.1 mm D'Arsonval Principle the position of the coil on a scale calibrated in terms of current or voltage. It responds to de current only, and has an almost linear calibration. The magnetic shunt that varies the field strength is used for calibration. 2.2.1 Permanent Magnetic Moving Coil Movement In this instrument, we have a coil suspended in the magnetic field of a permanent magnet in the shape of a horse-shoe. The coil is suspended so that it can rotate freely in the magnetic field. When current flows in the coil, the de- veloped (electromagnetic) torque causes the coil to rotate. The electromagnetic