Electronic Instrumentation Third Edition PDF

Electronic Instrumentation Third Edition About the Author H S Kalsi obtained a Diploma in Electronics and Radio Engineering (DERE) from St Xavier’s Technical Institute, Mumbai, and a Diploma in Technical Teaching from TTTI, Bhopal. Presently, he is Lecturer (Selection Grade) in the Department of Electronics at St Xavier’s Technical Institute, Mumbai. His area of special interest is Electronic Instrumentation. He is also a member of ISTE. Electronic Instrumentation Third Edition H S Kalsi Lecturer (Selection Grade) St Xavier’s Technical Institute Mumbai Tata McGraw Hill Education Private Limited NEW DELHI McGraw-Hill Ofﬁces New Delhi New York St Louis San Francisco Auckland Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto Tata McGraw-Hill Published by Tata McGraw Hill Education Private Limited, 7 West Patel Nagar, New Delhi 110 008 Electronic Instrumentation, 3e Copyright © 2010, 2004, 1995 by Tata McGraw Hill Education Private Limited 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 Education Private Limited. ISBN (13): 978-0-07-070206-6 ISBN (10): 0-07-070206-3 Managing Director: Ajay Shukla Head—Higher Education Publishing and Marketing: Vibha Mahajan Manager—Sponsoring SEM & Tech Ed: Shalini Jha Assoc. Sponsoring Editor: Suman Sen Development Editor: Manish Choudhary Executive—Editorial Services: Sohini Mukharjee Sr Production Manager: P L Pandita Dy Marketing Manager—SEM & Tech Ed: Biju Ganesan General Manager—Production: Rajender P Ghansela Asst. General Manager—Production: B L Dogra 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. Typeset at Text-o-Graphics, B1/56 Arawali Apartment, Sector 34, Noida 201301 and printed at Gopal Jee Enterprises, 190/5, Main Road, Maujpur, Delhi 110 053 Cover Printer: SDR Printers DZXLCRAZRQCLY In the everloving and fond memory of My Elder Brother Contents Preface xix List of Abbreviations xxiii List of Important Formulae xxvi 1. Qualities of Measurements 1 1.1 Introduction 1 1.2 Performance Characteristics 1 1.3 Static Characteristics 2 1.4 Error in Measurement 2 1.5 Types of Static Error 5 1.6 Sources of Error 8 1.7 Dynamic Characteristics 8 1.8 Statistical Analysis 11 1.9 Standard 15 1.10 Electrical Standards 16 1.11 Atomic Frequency and Time Standards 19 1.12 Graphical Representation of Measurements as a Distribution 20 Review Questions 22 Multiple Choice Questions 23 Practice Problems 24 Further Reading 24 2. Indicators and Display Devices 25 2.1 Introduction 25 2.2 Basic Meter Movement 26 2.3 Taut Band Instrument 31 2.4 Electrodynamometer 32 2.5 Moving Iron Types Instrument 35 2.6 Concentric Vane Repulsion Type (Moving Iron Type) Instrument 36 2.7 Digital Display System and Indicators 38 2.8 Classiﬁcation of Displays 38 2.9 Display Devices 39 2.10 Light Emitting Diodes (LED) 39 2.11 Liquid Crystal Display (LCD) 41 viii Contents 2.12 Other Displays 43 2.13 Printers 54 2.14 Classiﬁcation of Printers 54 2.15 Printer Character Set 55 2.16 Character at a Time Impact Printers for Fully Formed Characters (Drum Wheel) 55 2.17 Line at a Time Impact Printers for Fully Formed Characters (Line Printers) 57 2.18 Drum Printer 58 2.19 Dot-Matrix Printers 59 2.20 Character at a Time Dot-Matrix Impact Printer 59 2.21 Non-Impact Dot-Matrix (NIDM) Printers 61 Review Questions 61 Multiple Choice Questions 63 Further Reading 63 3. Ammeters 64 3.1 DC Ammeter 64 3.2 Multirange Ammeters 66 3.3 The Aryton Shunt or Universal Shunt 67 3.4 Requirements of a Shunt 71 3.5 Extending of Ammeter Ranges 71 3.6 RF Ammeter (Thermocouple) 72 3.7 Limitations of Thermocouples 73 3.8 Effect of Frequency on Calibration 74 3.9 Measurements of Very Large Currents by Thermocouples 75 Review Questions 76 Multiple Choice Questions 77 Practice Problems 77 Further Reading 78 4. Voltmeters and Multimeters 79 4.1 Introduction 79 4.2 Basic Meter as a DC Voltmeter 79 4.3 DC Voltmeter 80 4.4 Multirange Voltmeter 81 4.5 Extending Voltmeter Ranges 84 4.6 Loading 87 4.7 Transistor Voltmeter (TVM) 91 4.8 Chopper Type DC Ampliﬁer Voltmeter (Microvoltmeter) 92 4.9 Solid State Voltmeter 95 4.10 Differential Voltmeter 96 4.11 DC Standard/Difference Voltmeter 96 4.12 AC Voltmeter Using Rectiﬁers 99 Contents ix 4.13 AC Voltmeter Using Half Wave Rectiﬁer 100 4.14 AC Voltmeter Using Full Wave Rectiﬁer 101 4.15 Multirange AC Voltmeter 104 4.16 Average Responding Voltmeter 105 4.17 Peak Responding Voltmeter 106 4.18 True RMS Voltmeter 107 4.19 True RMS Meter 107 4.20 Considerations in Choosing an Analog Voltmeter 109 4.21 Ohmmeter (Series Type Ohmmeter) 110 4.22 Shunt Type Ohmmeter 117 4.23 Calibration of DC Instrument 120 4.24 Calibration of Ohmmeter 120 4.25 Multimeter 121 4.26 Multimeter Operating Instructions 123 Review Questions 124 Multiple Choice Questions 125 Practice Problems 126 Further Reading 127 5. Digital Voltmeters 128 5.1 Introduction 128 5.2 RAMP Technique 129 5.3 Dual Slope Integrating Type DVM (Voltage to Time Conversion) 130 5.4 Integrating Type DVM (Voltage to Frequency Conversion) 132 5.5 Most Commonly Used Principles of ADC (Analog to Digital Conversion) 135 5.6 Successive Approximations 136 5.7 Continuous Balance DVM or Servo Balancing Potentiometer Type DVM 140 5.8 3½-Digit 140 5.9 Resolution and Sensitivity of Digital Meters 141 5.10 General Speciﬁcations of a DVM 142 5.11 Microprocessor-Based Ramp Type DVM 142 Review Questions 145 Multiple Choice Questions 145 Practice Problems 146 Further Reading 146 6. Digital Instruments 147 6.1 Introduction 147 6.2 Digital Multimeters 148 6.3 Digital Frequency Meter 152 6.4 Digital Measurement of Time 155 6.5 Universal Counter 158 x Contents 6.6 Decade Counter 159 6.7 Electronic Counter 160 6.8 Digital Measurement of Frequency (Mains) 162 6.9 Digital Tachometer 165 6.10 Digital pH Meter 165 6.11 Automation in Digital Instruments 166 6.12 Digital Phase Meter 171 6.13 Digital Capacitance Meter 172 6.14 Microprocessor-Based Instruments 173 6.15 The IEEE 488 Bus 173 Review Questions 174 Multiple Choice Questions 175 Further Reading 175 7. Oscilloscope 176 7.1 Introduction 176 7.2 Basic Principle 176 7.3 CRT Features 180 7.4 Block Diagram of Oscilloscope 184 7.5 Simple CRO 185 7.6 Vertical Ampliﬁer 186 7.7 Horizontal Deﬂecting System 187 7.8 Triggered Sweep CRO 188 7.9 Trigger Pulse Circuit 189 7.10 Delay Line in Triggered Sweep 190 7.11 Sync Selector for Continuous Sweep CRO 191 7.12 Typical CRT Connections 191 7.13 High Frequency CRT or Travelling Wave Type CRT 192 7.14 Dual Beam CRO 193 7.15 Dual Trace Oscilloscope 194 7.16 Electronic Switch 200 7.17 (VHF) Sampling Oscilloscope 201 7.18 Storage Oscilloscope (For VLF Signal) 202 7.19 Digital Readout Oscilloscope 204 7.20 Measurement of Frequency by Lissajous Method 206 7.21 Spot Wheel Method 208 7.22 Gear Wheel Method 209 7.23 Checking of Diodes 211 7.24 Basic Measurement of Capacitance and Inductance 211 7.25 Oscilloscope as a Bridge Null Detector 213 7.26 Use of Lissajous Figures for Phase Measurement 214 7.27 Standard Speciﬁcations of a Single Beam CRO 216 7.28 Probes for CRO 217 7.29 Attenuators 220 Contents xi 7.30 Applications of Oscilloscope 222 7.31 Delayed Sweep 223 7.32 Digital Storage Oscilloscope (DSO) 224 7.33 Fibre Optic CRT Recording Oscilloscope 226 7.34 Oscilloscope Operating Precautions 228 7.35 Placing an Oscilloscope in Operation 229 Review Questions 230 Multiple Choice Questions 231 Practice Problems 232 Further Reading 232 8. Signal Generators 233 8.1 Introduction 233 8.2 Fixed Frequency AF Oscillator 234 8.3 Variable AF Oscillator 234 8.4 Basic Standard Signal Generator (Sine Wave) 235 8.5 Standard Signal Generator 235 8.6 Modern Laboratory Signal Generator 236 8.7 AF Sine and Square Wave Generator 238 8.8 Function Generator 239 8.9 Square and Pulse Generator (Laboratory Type) 240 8.10 Random Noise Generator 242 8.11 Sweep Generator 243 8.12 TV Sweep Generator 244 8.13 Marker Generator 245 8.14 Sweep-Marker Generator 247 8.15 Wobbluscope 247 8.16 Video Pattern Generator 247 8.17 Colour Bar Generator 249 8.18 Vectroscope 253 8.19 Beat Frequency Oscillator (BFO) 255 8.20 Standard Speciﬁcations of a Signal Generator 256 Review Questions 257 Multiple Choice Questions 258 Further Reading 259 9. Wave Analyzers and Harmonic Distortion 260 9.1 Introduction 260 9.2 Basic Wave Analyzer 261 9.3 Frequency Selective Wave Analyzer 262 9.4 Heterodyne Wave Analyzer 263 9.5 Harmonic Distortion Analyzer 265 9.6 Spectrum Analyzer 267 9.7 Digital Fourier Analyzer 269 xii Contents 9.8 Practical FFT Spectrum Analysis Using a Waveform Processing Software (Ss-36) 273 Review Questions 276 Multiple Choice Questions 277 Further Reading 277 10. Measuring Instruments 278 10.1 Introduction 278 10.2 Output Power Meters 278 10.3 Field Strength Meter 279 10.4 Stroboscope 280 10.5 Phase Meter 281 10.6 Vector Impedance Meter (Direct Reading) 283 10.7 Q Meter 286 10.8 LCR Bridge 295 10.9 RX Meters 303 10.10 Automatic Bridges 304 10.11 Transistor Tester 305 10.12 Megger 310 10.13 Analog pH Meter 311 10.14 Telemetry 315 Review Questions 319 Multiple Choice Questions 320 Practice Problems 321 Further Reading 321 11. Bridges 322 11.1 Introduction 322 11.2 Wheatstone’s Bridge (Measurement of Resistance) 322 11.3 Kelvin’s Bridge 328 11.4 Practical Kelvin’s Double Bridge 331 11.5 Bridge Controlled Circuits 332 11.6 Digital Readout Bridges 334 11.7 Microprocessor Controlled Bridges 335 11.8 AC Bridges 336 11.9 Capacitance Comparison Bridge 337 11.10 Inductance Comparison Bridge 339 11.11 Maxwell’s Bridge 340 11.12 Hay’s Bridge 342 11.13 Schering’s Bridge 345 11.14 Wien’s Bridge 351 11.15 Wagner’s Earth (Ground) Connection 354 11.16 Resonance Bridge 355 11.17 Maxwell–Wien Bridge 356 Contents xiii 11.18 Anderson Bridge 358 11.19 The Owen Bridge 359 11.20 De Sauty Bridge 360 11.21 Carey Foster / Heydweiller Bridge 361 11.22 Types of Detectors 363 11.23 Precautions to be Taken when Using a Bridge 363 Review Questions 364 Multiple Choice Questions 365 Practice Problems 366 Further Reading 369 12. Recorders 370 12.1 Introduction 370 12.2 Strip Chart Recorder 371 12.3 Galvanometer Type Recorder 374 12.4 Null Type Recorder (Potentiometric Recorders) 376 12.5 Circular Chart Recorder 381 12.6 X–Y Recorder 382 12.7 Magnetic Recorders 385 12.8 Frequency Modulation (FM) Recording 388 12.9 Digital Data Recording 390 12.10 Objectives and Requirements of Recording Data 392 12.11 Recorder Selections for Particular Applications 393 12.12 Recorder Speciﬁcations 393 12.13 Potentiometric Recorder (Multipoint) 394 12.14 Digital Memory Waveform Recorder (DWR) 399 12.15 Applications of a Strip Chart Recorder 401 Review Questions 403 Multiple Choice Questions 404 Practice Problems 405 Further Reading 405 13. Transducers 406 13.1 Introduction 406 13.2 Electrical Transducer 406 13.3 Selecting a Transducer 408 13.4 Resistive Transducer 408 13.5 Resistive Position Transducer 411 13.6 Strain Gauges 413 13.7 Resistance Thermometer 423 13.8 Thermistor 425 13.9 Inductive Transducer 428 13.10 Differential Output Transducers 432 13.11 Linear Variable Differential Transducer (LVDT) 433 xiv Contents 13.12 Pressure Inductive Transducer 440 13.13 Capacitive Transducer (Pressure) 446 13.14 Load Cell (Pressure Cell) 448 13.15 Piezo Electrical Transducer 449 13.16 Photo Electric Transducer 451 13.17 Photo-Voltaic Cell 454 13.18 Semiconductor Photo Diode 454 13.19 The Photo-Transistor 455 13.20 Temperature Transducers 456 13.21 Frequency Generating Transducer 479 13.22 Reluctance Pulse Pick-Ups 479 13.23 Flow Measurement (Mechanical Transducers) 479 13.24 Mechanical Flow Meter 480 13.25 Magnetic Flow Meters 480 13.26 Turbine Flowmeter 483 13.27 Measurements of Thickness Using Beta Gauge 484 Review Questions 488 Multiple Choice Questions 491 Further Reading 492 14. Signal Conditioning 493 14.1 Introduction 493 14.2 Operational Ampliﬁer (OPAMP) 497 14.3 Basic Instrumentation Ampliﬁer 511 14.4 Applications of Instrumentation Ampliﬁers (Speciﬁc Bridge) 518 14.5 Chopped and Modulated DC Ampliﬁer 521 14.6 Modulators 522 Review Questions 530 Further Reading 531 15. Filters 532 15.1 Introduction 532 15.2 Fundamental Theorem of Filters 532 15.3 Passive Filters 536 15.4 Active Filters 540 15.5 Butterworth Filter 544 15.6 Band Pass Filter 554 15.7 Band Reject (Stop) Filter 562 15.8 All Pass Filter 564 15.9 Universal Active Filters 566 15.10 Designing Procedures for FLT-U2 568 15.11 Types of Active Filters 572 15.12 Digital Filters 574 15.13 Discrete Functions 575 Contents xv 15.14 The 1-D Sampling Theorem 576 15.15 The 2-D Sampling Theorem 576 15.16 The 1-D Z-Transform 576 15.17 Fundamental Properties of 1-D Digital Systems 577 15.18 Fundamental Property of 2-D Digital Systems 578 15.19 Frequency Domain Representation 578 15.20 FIR 1-D Digital Filter Design (The Window Method) 583 15.21 Design Methods for IIR Digital Filters 585 15.22 1-D IIR Filter Design 587 15.23 Program for the Design of Butterworth and Chebyschev IIR Digital Filters by Means of the Bilinear Transformation 591 15.24 Microprocessor Based Digital Filter 595 15.25 Applications of Digital Filters 596 Review Questions 600 Multiple Choice Questions 603 Practice Problems 604 Further Reading 604 16. Measurement Set-up 605 16.1 Introduction 605 16.2 Measurements of Microwave Frequencies 605 16.3 Resonant Co-Axial Lines 606 16.4 Cavity Wavemeters 607 16.5 RF/UHF Field Strength Meter (Methods for Measuring the Strength of Radio Waves) 607 16.6 Measurement of Sensitivity 608 16.7 Measurement of Selectivity 609 16.8 Intermodulation Method of Measuring Non-Linear Distortion 610 16.9 Measuring Frequency Response in Audio Ampliﬁers 614 16.10 Modulation 615 16.11 Measuring Frequency Modulation 618 16.12 Measuring Frequency Deviation with a Radio Receiver 618 16.13 Measuring Amplitude Modulation Using CRO 619 Review Questions 623 Multiple Choice Questions 624 Further Reading 625 17. Data Acquisition System (DAS) 626 17.1 Introduction 626 17.2 Objective of a DAS 628 17.3 Signal Conditioning of the Inputs 628 17.4 Single Channel Data Acquisition System 630 17.5 Multi-Channel DAS 632 17.6 Computer Based DAS 636 xvi Contents 17.7 Digital to Analog (D/A) and Analog to Digital (A/D) Converters 637 17.8 Data Loggers 653 17.9 Sensors Based Computer Data Systems 663 17.10 Electromechanical A/D Converter 671 17.11 Digital Transducer 673 Review Questions 675 Multiple Choice Questions 677 Practice Problems 678 Further Reading 679 18. Data Transmission 680 18.1 Introduction 680 18.2 Data Transmission Systems 682 18.3 Advantages and Disadvantages of Digital Transmission Over Analog 682 18.4 Time Division Multiplexing (TDM) 684 18.5 Pulse Modulation 686 18.6 Digital Modulation 695 18.7 Pulse Code Format 704 18.8 Modems 706 Review Questions 710 Multiple Choice Questions 711 Further Reading 712 19. Frequency Standards 713 19.1 Introduction 713 19.2 Primary Standards 713 19.3 Secondary Standards of Frequency 714 19.4 Practical Frequency Standards 714 19.5 Radio Signals as Frequency Standards 715 19.6 Precision Frequency Standards 715 19.7 The Atomic Clock 716 Review Questions 717 Multiple Choice Questions 717 Further Reading 717 20. Measurement of Power 718 20.1 Introduction 718 20.2 Requirements of a Dummy Load 718 20.3 Bolometer 718 20.4 Bolometer Method of Power Measurement 719 20.5 Bolometer Element 719 20.6 Bolometer Mount 720 20.7 Measurement of Power by Means of a Bolometer Bridge 720 Contents xvii 20.8 Unbalanced Bolometer Bridge 722 20.9 Self Balancing Bolometer Bridge 723 20.10 Measurement of Large Amount of RF Power (Calorimetric Method) 724 20.11 Measurement of Power on a Transmission Line 726 20.12 Standing Wave Ratio Measurements 727 20.13 Measurement of Standing Wave Ratio Using Directional Couplers 728 Review Questions 731 Multiple Choice Questions 732 Practice Problems 732 Further Reading 732 21. Control Systems 733 21.1 Basic Control Action 733 21.2 Deﬁnition (Terminology) 734 21.3 On–Off Control Action 736 21.4 Proportional Control Action 738 21.5 Offset 739 21.6 Basic Controller Conﬁguration 739 21.7 Classiﬁcation of Controllers 740 21.8 Electronic Controllers (EC) 740 21.9 Analog Electronic Process Controllers 741 21.10 Temperature Control using an Analog Electronic Controller 745 21.11 Choice of Electronic Transmission Signal 747 21.12 Digital Controllers 748 21.13 Digital Process Controller 750 21.14 Cascade Process Controller with Digital Controllers 751 21.15 Programmable Logic Controller 753 21.16 Distributed Control Systems 796 Review Questions 815 Further Reading 816 Answers to Objective Type Questions 817 Index 820 Preface The tremendous and overwhelming response received by the second edition of this book inspired me to bring out the third edition. This new edition has been revised and updated based on the suggestions received from the students and teachers using this book. The book is written in a simple and lucid manner with systematically arranged chapters which enable the reader to get thorough knowledge, starting from the basic concepts to the sophisticated advancements 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 with in detail in a 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 different applications. New to this Edition v Inclusion of new topics on Telemetry, Electric and Voltage Standards and Rotational Variable Differential Transducers (RVDT) v Expanded coverage of Bridges which now includes Maxwell–Wien Bridge, Anderson Bridge, Carey–Foster Bridge, De Sauty Bridge and Owen Bridge v Thoroughly revised pedagogy including + 300 Review questions + 200 Objective type questions + 125 Solved examples and practice questions, with easy steps introduced for solved examples Chapter Organisation Chapter 1 covers the basic characteristics and the errors associated with instruments. Different types of indicating and display devices are dealt with in detail in Chapter 2. This chapter discusses different types of printers and printer heads used with computers. The basic analog-type ammeters for both dc and RF frequencies and different types of voltmeters, ohmmeters and multimeters are discussed in Chapters 3 and 4. xx Preface Digital instruments ranging from a simple digital voltmeter to a microprocessor- based instrument and their measurement techniques are presented in a comprehensible manner for easy understanding in Chapters 5 and 6. Chapter 7 on oscilloscopes has been dealt with 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. In industry, it is required to transmit signals or the changes in parameters from the measurement site location to the control room. Hence in Chapter 10, telemetry systems have been covered to get a brief insight of the various transmission methods used in industry. Most instruments used in process control plants measure various parameters such as resistance, inductance, capacitance, dissipation factor, temperature, etc. To obtain accurate measurement of the changes in parameters, bridges are used. Hence, Chapter 11 covers most of the types of bridges used for measurement of different parameters, for example, Wheatstone’s bridge, Maxwell’s Bridge, Hay’s Bridge, Schering Bridge, etc. Instruments and the instrumentation systems also use bridges as the input stage. 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 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. Chapter 21 discusses control systems, electronic control systems in particular. This chapter covers the basic control systems, electronic control systems, electronic controllers, PLC and advanced control systems such as DCS used in process control plants. Web Supplements The Web supplements can be accessed at http://www.mhhe.com/kalsi/ei3, which contains the following: For Instructors Solution Manual, PowerPoint Lecture Slides For Students Additional Review Questions and Web links for useful reference materials. Acknowledgements First of all, I express my deepest thanks and gratitude to my younger brother who gave me all his support, without which it would have been difﬁcult to complete Preface xxi this project. Secondly, I thank all the reviewers for their important suggestions which helped me a lot while revising this book. Their names are given below. Nilesh Chaurasia Sri Vaishnav Institute of Technology and Science Indore, Madhya Pradesh Praveen Tiwari IIMT Engineering College Meerut, Uttar Pradesh S B L Seksena National Institute of Technology (NIT) Jamshedpur, Jharkhand Sunit Kumar Sen University College of Science and Technology Kolkata, West Bengal Samir Ekbote Datta Meghe College of Engineering Navi Mumbai, Maharashtra V G Sarode Xavier Institute of Engineering Mumbai, Maharashtra Sreeprabha P K Indian Institute of Space Science and Technology (IIST), Thiruvanathpuram, Kerala P Thirumurthy Kumaraguru College of Technology Coimbatore, Tamil Nadu K E Srinivas Murthy Sri Venkateswara Institute of Technology Anantpur, Andhra Pradesh Signet Electronics Ltd, who made available the photographs of instruments, deserves a special note of appreciation. I am deeply indebted to my wife and other family members for their never- ending encouragement, moral support and patience during the preparation of this book. I appreciate the efforts of all members of the Tata McGraw-Hill family, especially Shalini Jha, Suman Sen, Manish Choudhary, Sohini Mukherjee and P L Pandita, whose help and cooperation shaped the book in all its stages. Last, but not the least, I would like to thank my friends and colleagues who helped me in the writing of this book. I hope 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. You can send your feedback to my email id: [email protected] H S KALSI Publisher’s Note Tata McGraw Hill invites comments, views and suggestions from readers, all of which can be sent to [email protected]. Piracy-related issues may also be reported. List of Abbreviations μA Micro Amperes ADC Analog to Digital Converter AF Audio Frequency ALU Arithmetic Logic Unit AM Amplitude Modulation ASCII American Standard Code for Information Interchange B.W Bandwidth BCD Binary Coded Decimal BFO Beat Frequency Oscillator BJT Bipolar Junction Transistor CCIR Committee Counsultatif International Radio telecommunique CDRX Critically Damping External Resistance CL Control Language CMRR Common Mode Rejection Ratio cps Character per second CRO Cathode Ray Oscilloscope CRT Cathode Ray Tube CSC Computer Supervisory Control CVSD Continuous Variable Slope DM DAC Digital to Analog Converter DAS Data Acquisition System dB deci-Bel DCE Data Circuit terminating Equipment DCS Distributed Control System DDA Decade Divider Assemblies DDC Direct Digital Control DFT Discrete Fourier Transform DM Delta Modulation DMM Digital Multimeter DPDT Double Pole Double Throw DPM Digital Panel Meter xxiv List of Abbreviations DPST Double Pole Single Throw DSO Digital Storage Oscilloscope DTE Data Terminal Equipment DVM Digital Voltmeter DWR Digital Waveform Recorder EDM Electrodynometer EHT Extra High Tension EL Electro- Luminescent EM Electro Magnetic EPID ElectroPhoretic Image Display EPROM Erasable Programmable Read Only Memory EXT External F/F Flip-Flop FDM Frequency Division Multiplexing FET Field Effect Transistor FFT Fast Fourier Transform FIR Finite Impulse Response FM Frequency Modulation FSK Frequency Shift Keying GaAsP Gallium Arsenide Phosphide GaP Gallium Phosphide GHz Giga Hertz HDP Horizontal Deﬂection Plates HF High Frequency HV High Voltage Ifsd Full scale deﬂection Current IIR Inﬁnite Impulse Response INT Internal Ku Kilo unit LCD Liquid Crystal Display LED Light Emitting Diode lpm line per minute LSB Least Signiﬁcant Bit LV Low voltage LVD Liquid Vapour Display LVDT Linear Variable Differential Transformer mA/mV milli-Amperes/milli-Volts MCR Master Control Reset MHz Mega Hertz MOS Metallic Oxide Semiconductor MSB Most Signiﬁcant Bit NIDM Non-Impact Dot Matrix NLC Nematic Liquid Crystal NO/NC Normal Open/Norma Close List of Abbreviations xxv NRZ Non Return to Zero NTC Negative Temperature Co-efﬁcient PCB Printed Circuit Board PCM Pulse Code Modulation PDM Pulse Duration Modulation PGA Programmable Gain Ampliﬁer PLC Programmable Logic Controller PMMC Permanent Magnet Moving Coil p-p peak to peak PPM Pulse Position Modulation PSK Phase Shift Keying PTC Positive Temperature Co-efﬁcient PWM Pulse Width Modulation RAM Random Access Memory RF Radio Frequency RMS Root Mean Square ROM Read Only Memory RTD Resistance Temperature Detector RVDT Rotary Variable Differential Transformer RZ Return to Zero S/H Sample and Hold SAR Successive Approximation Register SMPTE Society of Motion Pictures and Television Engineers TC Thermocouple TDM Time Division Multiplexing TRP Total Radiation Pyrometer TTL Transistor Transistor logic TV Television TVM Transistor Voltmeter UART Universal Asynchronous Receiver Transmitter UDC Up-Down Counter UHF Ultra High Frequency UJT Unijunction Transistor VDP Vertical Deﬂection Plates VHF Very High Frequency VLF Very Low Frequency VTVM Vacuum Tube Voltmeter List of Important Formulae 1. Absolute Error E = Yn – Xn (Where E = Absolute Error Yn = Expected Value Xn = Measured Value) Yn - X n 2. Accuracy A =1- Xn 3. Deﬂecting torque td = B ¥ A ¥ N ¥ I Shunt resistance for I m Rm 4. Rsh = Ammeter I - Im V 5. Multiplier for dc Voltmeter Rs = - Rm Im Multiplier Resistor for ac 0.45 ¥ Erms 6. Rs = - Rm Range I dc If sd Rm Rh R1 = Rh - V 7. R1 and R2 for an Ohmmeter If sd Rm Rh R2 = V - If sd Rh 8. Sensitivity of Digital S = (fs)min ¥ R Meters (Where (fs)min = lowest full scale on meter R = 1/10n n = number of full digits) 9. Resistance Value for R2 R3 Wheatstone’s Bridge Rx = R1 List of Important Formulae xxvii 10. Maxwell’s Bridge R2 R3 Rx = and Lx = C1R2R3 R1 Q = w C1R1 R2 R3C1 Lx = 1 + w2C12 R12 11. Hay’s Bridge wC1 R2 R3 Rx = 1 + w2 C12 R12 R2C1 Rx = C3 12. Schering Bridge R1C3 Cx = R2 1 13. Wien’s Bridge R2/R4 = 2 and f = 2p RC s xl 14. Resistance R= A DR /R 15. Gage Factor GF ( K ) = Dl /l 16. Resistance of Conductor Rt = Rref (1 + a Dt) n2 xer 17. For a Dual Slope DVM ei = n1 Input Capacitance of a Rin (Cin + C2 ) 18. C1 = CRO Probe R1 C1 - 4C2 19. Distributed Capacitance Cs = 3 Closed-loop Voltage Ê RF ˆ 20. gain for Non-Inverting AF = Á1 + Ampliﬁer Ë R1 ˜¯ xxviii List of Important Formulae Closed-loop Voltage gain Ê RF ˆ 21. AF = Á - for Inverting Ampliﬁer Ë R1 ˜¯ Output Voltage of an Ê 2R ˆ 22. AF = Á1 + 2 ˜ (e2 - e1 ) Instrumentation Ampliﬁer Ë R1 ¯ Chapter Qualities of Measurements 1 INTRODUCTION 1.1 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. PERFORMANCE CHARACTERISTICS 1.2 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. 2 Electronic Instrumentation STATIC CHARACTERISTICS 1.3 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. Accuracy 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, i.e. 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. ERROR IN MEASUREMENT 1.4 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-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 = Yn – Xn Qualities of Measurements 3 where e = absolute error Yn = expected value Xn = measured value Absolute value e Therefore % Error = ¥ 100 = ¥ 100 Expected value Yn Ê Yn - X n ˆ Therefore % Error = Á ¥ 100 Ë Yn ˜¯ It is more frequently expressed as a accuracy rather than error. Y - Xn Therefore A=1– n Yn where A is the relative accuracy. Accuracy is expressed as % accuracy a = 100% – % error a = A ¥ 100 % where a is the % accuracy. Example 1.1 (a) 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. Solution (i) Absolute error e = Yn – Xn = 80 – 79 = 1 V Yn - X n 80 - 79 (ii) % Error = ¥ 100 = ¥ 100 = 1.25% Yn 80 (iii) Relative Accuracy Yn - X n 80 - 79 A = 1- =1- Yn 80 \ A = 1 – 1/80 = 79/80 = 0.9875 (iv) % of Accuracy a = 100 ¥ A = 100 ¥ 0.9875 = 98.75% or a = 100% – % of error = 100% – 1.25% = 98.75% Example 1.1 (b) The expected value of the current through a resistor is 20 mA. However the measurement yields a current value of 18 mA. Calculate (i) absolute error (ii) % error (iii) relative accuracy (iv) % accuracy Solution Step 1: Absolute error e = Yn – Xn where e = error, Yn = expected value, Xn = measured value 4 Electronic Instrumentation Given Yn = 20 mA and Xn = 18 mA Therefore e = Yn – Xn = 20 mA – 18 mA = 2 mA Step 2: % error Y - Xn 20 mA - 18 mA 2 mA % error = n ¥ 100 = ¥ 100 = ¥ 100 = 10 % Yn 20 mA 20 mA Step 3: Relative accuracy Yn - X n 20 mA - 18 mA 2 A =1- =1- =1- = 1 - 0.1 = 0.90 Yn 20 mA 20 Step 4: % accuracy a = 100% – %error = 100% – 10% = 90% and a = A ¥ 100% = 0.90 ¥ 100% = 90% 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 Xn - Xn P =1- Xn where Xn = value of the nth measurement – X n = average set of measurement Example 1.2 Table 1.1 gives the set of 10 measurement that were recorded in the laboratory. Calculate the precision of the 6th measurement. Table 1.1 Measurement Measurement value number Xn 1 98 2 101 3 102 4 97 5 101 6 100 7 103 8 98 9 106 10 99 Qualities of Measurements 5 Solution The average value for the set of measurements is given by Sum of the 10 measurement values Xn = 10 1005 = = 100.5 10 Xn - Xn Precision = 1 - Xn For the 6th reading 100 - 100.5 0.5 100 Precision = 1 - =1- = = 0.995 100.5 100.5 100.5 The accuracy and precision of measurements depend not only on the quality of the measuring instrument but also on the person using it. However, whatever the quality of the instrument and the case exercised by the user, there is always some error present in the measurement of physical quantities. TYPES OF STATIC ERROR 1.5 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, i.e. 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 elimination 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 recording 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)). (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 Errors These errors occur due to shortcomings of the instrument, such as defective or worn parts, or ageing or effects of the environment on the instrument. 6 Electronic Instrumentation 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) Observational. (i) 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)). (b) applying correction factors after determining the amount of instrumental error. (c) calibrating the instrument against a standard. (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. (iii) 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. 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. Example 1.3 (a) A voltmeter having a sensitivity of 1 kW/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. Qualities of Measurements 7 Solution VT 80 (i) The total circuit resistance RT = = = 8 kW I T 10 mA (Neglecting the resistance of the milliammeter.) (ii) The voltmeter resistance equals Rv = 1000 W/V ¥ 150 = 150 kW RT ¥ Rv 8 k ¥ 150 k \ actual value of unknown resistance Rx = = Rv - RT 150 k - 8 k 1200 k 2 = = 8.45 W 142 k Actual value - Apparent value 8.45 k - 8 k (iii) % error = = ¥ 100 Actual value 8.45 k = 0.053 ¥ 100 = 5.3% Example 1.3 (b) Referring to Ex. 1.3 (a), if the milliammeter reads 600 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 unknown 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 W/V.) Solution 1. The total circuit resistance is given by VT 30 RT = = = 50 W I T 0.6 2. The voltmeter resistance Rv equals Rv = 1000 W/V ¥ 150 = 150 kW Neglecting the resistance of the milliammeter, the value of unknown resistance = 50 W R ¥ Rv 50 ¥ 150 k 7500 k Rx = T = = = 50.167 W Rv - RT 150 k - 50 149.5 k 50.167 - 50 0.167 % Error = ¥ 100 = ¥ 100 = 0.33% 50.167 50.167 In Example 1.3 (a), a well calibrated voltmeter may give a misleading resistance 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. 8 Electronic Instrumentation 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. SOURCES OF ERROR 1.6 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 DYNAMIC CHARACTERISTICS 1.7 Instruments rarely respond instantaneously to changes in the measured variables. 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 primary element (sensing element) to some unknown and predetermined variations in the measured quantity. The three most common variations in the measured quantity are as follows: 1. Step change, in which the primary element is subjected to an instantaneous and ﬁnite change in measured variable. 2. Linear change, in which the primary element is following a measured variable, changing linearly with time. Qualities of Measurements 9 3. Sinusoidal change, in which the primary element follows a measured variable, the magnitude of which changes in accordance with a sinusoidal function of constant amplitude. The dynamic characteristics of an instrument are (i) speed of response, (ii) ﬁdelity, (iii) lag, and (iv) dynamic error. (i) Speed of Response It is the rapidity with which an instrument responds 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). (iii) 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 d n xo d n -1 xo d xo an n + an - 1 n -1 + + a1 + a0 xo dt dt dt m d xi d m -1 xi d xi = bm m + + bm - 1 m -1 + + b1 + b0 xi (1.1) dt dt dt where xo = output quantity xi = input quantity t = time a’s and b’s are combinations of systems physical parameters, assumed constant. When all the a’s and b’s, other than a0 and b0 are assumed to be zero, the differential equation degenerates into the simple equation given as a0xo = b0xi (1.2) Any instrument that closely obeys Eq. (1.2) over its intended range of operating 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 b0 xo = xi = K.xi a0 where K = b0/a0 = static sensitivity 10 Electronic Instrumentation Since the equation xo = K xi is an algebraic equation, it is clear that no matter how xi might vary with time, the instrument output (reading) follows it perfectly 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 b’s other than a1, a0, b0 are taken as zero, we get d xo + a0xo = b0 xi a1 dt Any instrument that follows this equation is called a ﬁrst order instrument. By dividing by a0, the equation can be written as a1 d xo b + xo = 0 xi a0 d t a0 or (t ◊ D + 1) ◊ xo = K xi where t = a1/a0 = time constant K = b0/a0 = static sensitivity The time constant t always has the dimensions of time while the static sensitivity K has the dimensions of output/input. The operational transfer function of any ﬁrst order instrument is xo K = xi t D + 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 d 2 xo d xo a2 2 + a1 + a0 xo = b0 xi dt dt The above equations can be reduced as Ê D2 2 x D ˆ Á 2 + w + 1˜ ◊ xo = Kxi Ë wn n ¯ a0 where wn = = undamped natural frequency in radians/time a2 2x = a1 / a0 a2 = damping ratio K = b0/a0 = static sensitivity Qualities of Measurements 11 Any instrument following this equation is a second order instrument. A practical example of this type is the spring balance. Linear devices range from mass spring arrangements, transducers, ampliﬁers and ﬁlters to indicators and recorders. Most devices have ﬁrst or second order responses, i.e. the equations of motion 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. STATISTICAL ANALYSIS 1.8 The statistical analysis of measurement data is important because it allows an analytical determination of the uncertainty of the ﬁnal test result. To make statis- tical analysis meaningful, a large number of measurements is usually required. Systematic errors should be small compared to random errors, because statistical analysis of data cannot remove a ﬁxed bias contained in all measurements. 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 measurements at a speciﬁc count of the variable x is given by the expression n x1 + x2 + x3 + + xn Â xn n =1 x= = n n where x̄ = Arithmetic mean xn = 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, x1, is called d1 and that of the second reading x2 is called d2, and so on, The deviations from the mean can be expressed as d1 = x1 – x̄, d2 = x2 – x̄..., similarly dn = xn – x̄ The deviation may be positive or negative. The algebraic sum of all the deviations must be zero. 12 Electronic Instrumentation Example 1.4 For the following given data, calculate (i) Arithmetic mean; (ii) Deviation of each value; (iii) Algebraic sum of the deviations Given x1 = 49.7; x2 = 50.1; x3 = 50.2; x4 = 49.6; x5 = 49.7 Solution (i) The arithmetic mean is calculated as follows x1 + x2 + x3 + x4 + x5 x= 5 49.7 + 50.1 + 50.2 + 49.6 + 49.7 = = 49.86 5 (ii) The deviations from each value are given by d1 = x1 – x̄ = 49.7 – 49.86 = – 0.16 d2 = x2 – x̄ = 50.1 – 49.86 = + 0.24 d3 = x3 – x̄ = 50.2 – 49.86 = + 0.34 d4 = x4 – x̄ = 49.6 – 49.86 = – 0.26 d5 = x5 – x̄ = 49.7 – 49.86 = – 0.16 (iii) The algebraic sum of the deviation is dtotal = – 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 |d1 | + |d 2 | + |d3 | + + |d n | Dav = n or Dav = Â | dn | n where Dav = average deviation |d1|, |d2|, …, |dn| = Absolute value of deviations and n = total number of readings Highly precise instruments yield a low average deviation between readings. Qualities of Measurements 13 Example 1.5 Calculate the average deviation for the data given in Example 1.4. Solution The average deviation is calculated as follows |d1 | + |d 2 | + |d3 | + + |d n | Dav = n | - 0.16 | + | 0.24 | + | 0.34 | + | - 0.26 | + | - 0.16 | = 5 1.16 = = 0.232 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 d12 + d 22 + d32 + + d n2 d n2 s= = n n where s = 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. Example 1.6 Calculate the standard deviation for the data given in Example 1.4. Solution d12 + d 22 + d32 + + d n2 Standard deviation = n -1 (- 0.16) 2 + (0.24) 2 + (0.34) 2 + (- 0.26) 2 + (- 0.16) 2 s= 5 -1 0.0256 + 0.0576 + 0.1156 + 0.0676 + 0.0256 s= 4 0.292 s= = 0.073 = 0.27 4 Therefore, the standard deviation is 0.27. 14 Electronic Instrumentation 1.8.5 Limiting Errors Most manufacturers of measuring instruments specify accuracy within a certain % 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. Example 1.7 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. Solution The magnitude of the limiting error is 0.02 ¥ 600 = 12 V. Therefore, the limiting error for 250 V is 12/250 ¥ 100 = 4.8% Example 1.8 (a) A 500 mA voltmeter is speciﬁed to be accurate with ±2%. Calculate the limiting error when instrument is used to measure 300 mA. Solution Given accuracy of 0.02 = ±2% Step 1: The magnitude of limiting error is = 500 mA ¥ 0.02 = 10 mA 10 mA Step 2: Therefore the limiting error at 300 mA = ¥ 100% = 3.33% 300 mA Example 1.8 (b) 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 ¥ 100 = 1.5 V The limiting error at 70 V is 1.5 ¥ 100 = 2.143 % 70 The magnitude of limiting error of the ammeter is 0.015 ¥ 150 mA = 2.25 mA The limiting error at 80 mA is 2.25 mA ¥ 100 = 2.813 % 80 mA Therefore, the limiting error for the power calculation is the sum of the individual limiting errors involved. Therefore, limiting error = 2.143 % + 2.813 % = 4.956 % Qualities of Measurements 15 STANDARD 1.9 A standard is a physical representation of a unit of measurement. A known accurate 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 Sèvres, 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 gm/s. 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, 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. 16 Electronic Instrumentation 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 standard. 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. ELECTRICAL STANDARDS 1.10 All electrical measurements are based on the fundamental quantities I, R and V. A systematic measurement depends upon the deﬁnitions of these quantities. These quantities are related to each other by the Ohm’s law, V = I.R. It is therefore sufﬁcient to deﬁne only two parameters to obtain the deﬁnitions of the third. Hence, in electrical measurements, it is possible to assign values of the remaining standard, by deﬁning units of other two standards. Standards of emf and resistance are, therefore, usually maintained at the National Laboratory. The base values of other standards are deﬁned from these two standards. The electrical standards are (a) Absolute Ampere (b) Voltage Standard (c) Resistance Standard 1.10.1 Absolute Ampere The International System of Units (SI) deﬁnes the Ampere, that is, the fundamental unit of electric current, as the constant current which if maintained in two straight parallel conductors of inﬁnite length placed one metre apart in vacuum, will produce between these conductors a force equal to 2 ¥ 107 newton per metre length. These measurements were not proper and were very crude. Hence, it was required to produce a more practical, accurate and reproducible standard for the National Laboratory. Hence, by international agreement, the value of international ampere as discussed in the previous topic, was then based on the electrolytic deposition of silver from a silver nitrate solution. In this method, difﬁculties were encountered in determining the exact measurement of the deposited silver and slight differences existed between the measurements made independently by various National Standard laboratories. Qualities of Measurements 17 The International Ampere was then replaced by the Absolute Ampere. This Absolute Ampere was determined by means of a current balance, which measures the force exerted between two current-carrying coils. This technique of force measurement was further improved to a value of ampere which is much superior to the early measurement (the relationship between force and the current which produces the force, can be calculated from the fundamental electromagnetic theory concepts). The Absolute Ampere is now the fundamental unit of electric current in the SI system and is universally accepted by international agreements. Voltage (V), current (I) and resistance (R) are related by Ohm’s law V = I.R. If any of the two quantities is deﬁned, the third can be easily known. In order to deﬁne the Ampere with high precision over long periods of time, the standard voltage cell and the standard resistor are used. 1.10.2 Voltage Standards As described before, if two parameters of Ohm’s law are known, the third can be easily derived. Standard voltage cell is used as one of the parameter. The standard voltage called the saturated standard cell or standard cell was based on the principle of electrochemical cell for many years. But the standard cell had a drawback that it suffered from temperature dependence. This voltage was a function of a chemical reaction and was not directly related to any other physical constants. Hence, a new standard for volt was developed. This standard used a thin ﬁlm junction, which is cooled to nearly absolute zero and irradiated with microwave energy, a voltage is developed across the junction. This voltage is related to the irradiating frequency by the relation V = (h.f )/2e where h is the Planck’s constant (6.63 ¥ 10–34 J-s), ‘e’ is the charge of an electron (1.602 ¥ 10–19C) and ‘f ’ is the frequency of the microwave irradiation. Since ‘f ’, the irradiating frequency is the only variable in the equation, hence the standard volt is related to the standard frequency (or time). The accuracy of the standard volt including all system inaccuracies approximately is one part in 109, when the microwave irradiating frequency is locked to an atomic clock or to a broadcast frequency standard. Standard cells are used for transferring the volt from the standard. Based on the thin ﬁlm junction to the secondary standards used for calibration, this device is called the normal or saturated Weston cell. The saturated cell has mercury as the positive electrode and cadium amalgam (10% cadium). The electrolyte used is a solution of cadium sulphate. These electrodes with the electrolyte are placed in a H-shaped glass container as shown in Fig 1.1. There are two types of Weston cells called the saturated cell and the unsatu- rated cell. In a saturated cell, the electrolyte used is saturated at all temperatures by the cadium sulphate crystals covering the electrodes. In the unsaturated cell, the concentration of cadium sulphate is such that it produces saturation at 40°C. The unsaturated cell has a negligible temperature coefﬁcient of voltage at normal room temperature. 18 Electronic Instrumentation The saturated cell has a voltage variation of approximately 40 mV/°C ,but is better reproducible and more stable than the unsaturated cell. Fig 1.1 Voltage Standard More rugged portable secondary and working standards are made of unsaturated Weston cells. These cells are very similar to the normal cell, but they do not require exact temperature control. The emf of an unsaturated cell lies in the range of 1.0180 V to 1.0200 V and the variation is less than 0.01%. The internal resistance of Weston cells range from 500 to 800 ohms. The current drawn from these cells should therefore not exceed 100 mA. Laboratory working standards have been developed based on the operation of Zener diodes as the voltage reference element, having accuracy of the same order as that of the standard cell. This instrument basically consists of Zener controlled voltage placed in a temperature controlled environment to improve it’s long-term stability and having a precision output voltage. The temperature controlled oven is held within + 0.03°C over an ambient temperature range of 0 to 50°C giving an output stability in the order of 10 ppm/month. Zener controlled voltage sources are available in different ranges such as (a) 0–1000 mV source with 1 mV resolution (b) A 1.000 V reference for volt box potentiometric measurements (c) A 1.018 V reference for saturated cell comparison 1.10.3 Resistance Standards The absolute value of resistance is deﬁned as ohms in the SI system of units. We know that the resistance R is given by R = r◊l/A in terms of the length of wire (l), area of cross-section (A) of the wire and the resistivity of the wire (r). Standard resistors are made of high resistivity conducting material with low temperature coefﬁcient of resistance. Manganin, an alloy of copper, having a resistivity and whose temperature resistance relationship is almost constant, is used as the resistance wire. The construction of a resistance standard is as shown in Fig 1.2. Qualities of Measurements 19 A coil of manganin wire as shown in Fig 1.2. is mounted on a double-walled sealed container to prevent the change in resistance due to humidity. The unit of resistance can be represented with precision values of a few parts in 107 over several years, with a set of four or ﬁve resistors of this type. Fig 1.2 Resistance Standard The secondary standard resistors are made of alloy of resistance wire such as manganin or Evan Ohm. The secondary standard or working standard are available in multiple of 10. These laboratory standards can also be referred to as transfer resistors. The resistance coil of the transfer resistance is supported between polyester ﬁlm, in order to reduce stress on the wire and to improve it’s stability. The coil is immersed in moisture-free oil and placed in a sealed container. The connections to the coils are silver soldered and terminals hooks are made of nickel-plated oxygen-free copper. These are checked for stability and temperature characteristics at it’s rated power and operating. Transfer resistors are used in industrial research and calibration laboratory. It is used in determining the value of the unknown resistance and ratio value. These resistors are also used as linear decade dividers resistors. These dividers are used in calibrating universal ratio sets and volt boxes. ATOMIC FREQUENCY AND TIME STANDARDS 1.11 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 20 Electronic Instrumentation 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 determines the length of the day, has been long used as a time standard. Time deﬁned in terms of rotation of the earth is called Universal time (UT). 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 1 part in 1010. To meet a better time standard, atomic clocks have been developed using periodic atomic vibrations as a standard. The transition between two energy levels, E1 and E2 of an atom is accompanied by the emission (or absorption) of radiation given by the following equation E2 - E1 v= h where v = frequency of emission and depends on the internal structure of an atom h = Planck’s constant = 6.636 ¥ 10–34 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. GRAPHICAL REPRESENTATION OF MEASUREMENTS AS A DISTRIBUTION 1.12 Suppose that a certain voltage is measured 51 times. The result which might be obtained are shown in Table 1.2. Qualities of Measurements 21 Table 1.2 x Voltage Number of xn (v) dn = xn – x̄ n |dn| (dn)2 n (dn)2 (V) Occurrences (n) 1.01 1 1.01 – 0.04 0.04 16 ¥ 10–4 16 ¥ 10–4 1.02 3 3.06 – 0.03 0.09 9 ¥ 10–4 27 ¥ 10–4 1.03 6 6.18 – 0.02 0.12 4 ¥ 10–4 24 ¥ 10–4 1.04 8 8.32 – 0.01 0.08 1 ¥ 10–4 8 ¥ 10–4 –4 1.05 10 10.50 0.00 0.00 0 ¥ 10 00 ¥ 10–4 1.06 7 7.42 + 0.01 0.07 1 ¥ 10–4 7 ¥ 10–4 1.07 8 8.56 + 0.02 0.16 4 ¥ 10–4 32 ¥ 10–4 1.08 4 4.32 + 0.03 0.12 9 ¥ 10–4 36 ¥ 10–4 –4 1.09 3 3.27 + 0.04 0.12 16 ¥ 10 48 ¥ 10–4 1.10 0 0.00 + 0.05 0.00 25 ¥ 10–4 00 ¥ 10–4 1.11 1 1.11 + 0.06 0.06 36 ¥ 10–4 36 ¥ 10–4 51 53.75 0.86 234 ¥ 10–4 51 51 51 = Sn = Â xn = Â | dn | Â (d n )2 n =1 n =1 n =1 51 Â xn n =1 53.75 Average x = = = 1.054 V n 51 51 Â |d n | n =1 0.86 Average deviation Dav = = = 0.0168 V n 51 51 Â (d n )2 n =1 234 ¥ 10- 4 Standard deviation s = = = 4.588 ¥ 10-4 V n 51 = 2.142 ¥ 10–2 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. The data given in Table 1.2 may be represented graphically as shown in Fig. 1.3. 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 22 Electronic Instrumentation 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. 1.3. 10 Number of Occurence Values 8 6 Ideal Curve 4 Actual Curve 2 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 x = 1.054 V x (V) Fig. 1.3 Gaussian graph Review Questions 1. What do you understand by static 11. What are the causes of environment characteristics? errors? 2. List different static characteristics. 12. How are instrumental errors different 3. Deﬁne the terms: instrument, accu- from gross errors? Explain. racy, precision and errors. 13. Deﬁne absolute errors. 4. Deﬁne the terms: resolution, sensi- 14. How is accuracy expressed? tivity and expected value. 15. What are the different types of errors 5. Discuss the difference between accu- that occur during measurement? Ex- racy and precision of a measurement plain each. 6. List different types of errors. 16. What do you understand by dynamic 7. Explain gross error in details. How characteristics of an instrument? can it be minimized? 17. Deﬁne speed of response and ﬁdel- 8. Explain systematic error in detail. ity. How can it be minimized? 18. Differentiate between lag and dy- 9. Explain random error in detail. namic error. 10. A person using an ohmmeter reads 19. What are limiting errors? What is the the measured value as 470 Ω , when signiﬁcance of limiting errors? the actual value is 47 Ω. What kind 20. Deﬁne the following terms: of error does this represent? Qualities of Measurements 23 (i) Average value (ii) Arithmetic 26. What do you understand by a work- mean (iii) Deviation (iv) Standard ing standard? deviation 27. State the difference between second- 21. What do you mean by a standard? ary and working standards. What is the signiﬁcance of standard? 28. Explain in brief atomic frequency 22. What are international standards? and time standards. List various international standards. 29. How is time deﬁned? 23. Deﬁne primary and secondary stan- 30. What do you understand by electrical dards? standard? 24. What are primary standards? Where 31. List different types of electrical stan- are they used? dards. 25. What are secondary standards? Where are they used? Multiple Choice Questions 1. The closeness of values indicated by (a) noise (b) temperature an instrument to the actual value is (c) light (d) mains voltage deﬁned as 8. The ability of an instrument to re- (a) repeatability (b) reliability spond to the weakest signal is de- (c) uncertainty (d) accuracy. ﬁned as 2. Precision is deﬁned as (a) sensitivity (b) repeatability (a) repeatability (b) reliability (c) resolution (d) precision. (c) uncertainty (d) accuracy 9. The difference between the expected 3. The ratio of change in output to the value of the variable and the mea- change in the input is called sured variable is termed (a) precision (b) resolution (a) absolute error (c) sensitivity (d) repeatability (b) random error 4. The deviation of the measured value (c) instrumental error to the desired value is deﬁned as (d) gross error (a) error (b) repeatability 10. Accuracy is expressed as (c) hystersis (d) resolution (a) relative accuracy 5. Improper setting of range of a multi- (b) % accuracy meter leads to an error called (c) error (a) random error (d) % error (b) limiting error 11. Error is expressed as (c) instrumental error (a) absolute error (b) relative error (d) observational error (c) % error (d) % accuracy 6. Errors that occur even when all the 12. Gross errors occurs due to gross and systematic errors are taken (a) human error care of are called (b) instrumental error (a) environmental errors (c) environmental error (b) instrumental errors (d) random error (c) limiting errors 13. Static errors are caused due to (d) random errors. (a) measuring devices 7. A means of reducing environmental (b) human error errors is the regulation of ambient (c) environmental error (d) observational error 24 Electronic Instrumentation 14. Dynamic errors are caused by 15. Limiting errors are (a) instrument not responding fast (a) manufacturer’s speciﬁcations of (b) human error accuracy (c) environmental error (b) manufacturer’s speciﬁcations of (d) observational error instrumental error (c) environmental errors (d) random errors Practice Problems 1. The current through a resistor is 3.0 Which is the most precise measure- A, but measurement gives a value of ment? 2.9 A. Calculate the absolute error 6. A 270 Ω ± 10% resistance is con- and % error of the measurement. nected to a power supply source op- 2. The current through a resistor is 2.5 erating at 300 V dc. A, but measurement yields a value of What range of current would ﬂow if 2.45 A. Calculate the absolute error the resistor varied over the range of and % error of the measurement. ± 10% of its expected value? What is 3. The value of a resistor is 4.7 k-ohms, the range of error in the current? while measurement yields a value of 7. A voltmeter is accurate to 98% of its 4.63 K-ohms. full scale reading. Calculate (a) the relative accuracy, (i) If a voltmeter reads 200 V on and (b) % accuracy. 500 V range, what is the abso- 4. The value of a resistor is 5.6 K-ohms, lute error? while measuremen

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