TEL304 — Measurements and Instrumentation: Lecture Note

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Course code: TEL 304 Course title: Measurements and Instrumentation Course credit load: 2 Units Series 1: Introduction to Measurement: Static and Dynamic Characteristics, and Types of Errors • Part 1.1: Introduction to Measurement Systems o Sub Part 1.1.1: Introduction to Measurement and Instrumentation o Sub Part 1.1.2: Significance of Measurement o Sub Part 1.1.3: Block Diagram of a Measurement System • Part 1.2: Static Characteristics I o Sub Part 1.2.1: Accuracy and Precision o Sub Part 1.2.2: Sensitivity and Linearity o Sub Part 1.2.3: Repeatability and Reproducibility • Part 1.3: Static Characteristics II o Sub Part 1.3.1: Resolution and Threshold o Sub Part 1.3.2: Drift and Stability o Sub Part 1.3.3: Dead Zone and Hysteresis • Part 1.4: Dynamic Characteristics and Types of Errors o Sub Part 1.4.1: Speed of Response and Measuring Lag o Sub Part 1.4.2: Fidelity and Dynamic Error o Sub Part 1.4.3: Types of Errors: Gross, Systematic, and Random Errors

Introduction This is the opening Series of TEL 304: Measurements and Instrumentation. This Series lays the foundation for the entire course, introducing measurement systems and their functional elements, before examining the static and dynamic characteristics used to specify and evaluate any measuring instrument, and the different types of error that can affect a measurement. The aim of this Series is to equip you with a sound understanding of the significance of measurement and the block diagram of a measurement system; the static characteristics of accuracy, precision, sensitivity, linearity, repeatability, reproducibility, resolution, threshold, drift, stability, dead zone, and hysteresis; the dynamic characteristics of speed of response, measuring lag, fidelity, and dynamic error; and gross, systematic, and random errors. We shall commence this Series by examining measurement systems and their functional elements. Next, we will consider the first group of static characteristics: accuracy, precision, sensitivity, linearity, repeatability, and reproducibility. Following that, our attention turns to the second group of static characteristics: resolution, threshold, drift, stability, dead zone, and hysteresis. Finally, we will conclude by examining dynamic characteristics and the different types of measurement error. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: explain the significance of measurement, • SLO 1.2: describe the block diagram of a measurement system and its functional elements, • SLO 1.3: define accuracy, precision, sensitivity, and linearity as static characteristics of an instrument, • SLO 1.4: define repeatability and reproducibility, • SLO 1.5: define resolution, threshold, drift, and stability, • SLO 1.6: define dead zone and hysteresis, • SLO 1.7: define the dynamic characteristics of an instrument: speed of response, measuring lag, fidelity, and dynamic error, • SLO 1.8: distinguish between gross, systematic, and random errors.

1.1 Introduction to Measurement Systems 1.1.1 Introduction to Measurement and Instrumentation Measurement is the process of comparing an unknown physical quantity against a known, standard reference quantity of the same kind, yielding a numerical value together with an appropriate unit, while instrumentation is the branch of engineering concerned with designing, constructing, and applying the instruments used to perform such measurements accurately and reliably. The physical quantity being measured is called the measurand, and every measurement is only as trustworthy as the standard against which the measuring instrument was itself calibrated, since an instrument can never be more accurate than the reference standard used to establish its own scale. Worked example: A digital thermometer reads a patient's body temperature as 37.2°C. Here, the measurand is the patient's body temperature, and the instrument's reading is only trustworthy to the extent that the thermometer was itself calibrated against a traceable temperature standard. Application: A sound understanding of measurement and instrumentation principles underlies virtually every branch of science and engineering, since design, quality control, process monitoring, and scientific research all depend fundamentally on the ability to measure physical quantities accurately and reliably. Fill in the blank: The physical quantity being measured is called the ________. An instrument can never be more accurate than the ________ against which it was calibrated. 1.1.2 Significance of Measurement Measurement is of fundamental significance throughout science, engineering, and industry, since it provides the objective, quantitative basis needed for scientific research, for verifying that a manufactured product meets its specified design tolerances, for monitoring and controlling industrial processes safely, and for ensuring fair trade through standardised weights and measures. Traceability, the unbroken chain of calibrations linking a working instrument back through successively more accurate reference standards to a recognised national or international standard, is what ultimately gives a measurement its credibility, allowing measurements made in different laboratories, countries, or times to be meaningfully compared with one another. Worked example: A factory's production-line micrometer is calibrated against a reference gauge block, which is itself periodically calibrated against a national standards laboratory's primary length standard, establishing an unbroken traceability chain for every length measurement made on that production line.

Application: Traceability is a mandatory requirement in regulated industries such as pharmaceuticals, aerospace, and metrology-dependent manufacturing, since a measurement that cannot be traced back to a recognised standard cannot be relied upon for safety-critical or legally binding decisions. Fill in the blank: The unbroken chain of calibrations linking an instrument back to a recognised standard is called ________. Measurement provides the objective basis for verifying that a product meets its design ________. 1.1.3 Block Diagram of a Measurement System A measurement system is conventionally represented as a block diagram of interconnected functional elements, beginning with a primary sensing element, which responds to the measurand and converts it into a suitable, usually electrical, signal, and typically continuing through a variable conversion element and a variable manipulation element, which respectively convert and amplify or otherwise process that signal. The processed signal is then usually carried, via a data transmission element, to a final data presentation element, such as an analogue meter, a digital display, or a data recorder, which presents the measured value in a form the observer can read and interpret directly, completing the measurement chain from the original physical measurand through to a readable result. Worked example: In a simple bulb thermometer, the mercury column acts as the primary sensing element, its thermal expansion is the variable conversion mechanism, and the calibrated glass scale itself serves as the data presentation element, all combined within a single physical device. Application: Breaking a measurement system down into its functional elements, rather than treating it as a single, indivisible device, allows a design or fault engineer to systematically analyse, troubleshoot, or improve any one stage of the measurement chain, from sensing through to final display, independently of the others. Fill in the blank: The functional element that first responds to the measurand is called the primary ________ element. The final functional element that presents the measured value to the observer is the data ________ element.

Figure 1.1: General block diagram of a measurement system. Pilot questions 1.1 1. Define measurement and instrumentation. (Linked to SLO 1.1) 2. Define traceability. (Linked to SLO 1.1) 3. State the purpose of a primary sensing element. (Linked to SLO 1.2) 4. State the purpose of a data presentation element. (Linked to SLO 1.2) 5. List the functional elements of a measurement system in order. (Linked to SLO 1.2) 1.2 Static Characteristics I 1.2.1 Accuracy and Precision Accuracy is the closeness with which an instrument's reading approaches the true value of the measurand, and is most commonly expressed either as a percentage of the full-scale reading or as a percentage of the true value itself, with the difference between the measured value and the true value known as the error. Precision is the closeness of agreement among a group of repeated measurements of the same quantity, reflecting an instrument's ability to consistently reproduce the same reading, and is

entirely distinct from accuracy: a precise instrument can, if improperly calibrated, consistently produce readings that are all equally inaccurate. Worked example: A voltmeter with a full-scale range of 100 V has an accuracy specification of ±2% of full scale. The maximum possible error at any point on the scale is therefore ±2% × 100 V = ±2 V. Application: Distinguishing clearly between accuracy and precision is essential when selecting or evaluating a measuring instrument, since an instrument that is highly precise but poorly calibrated, and therefore inaccurate, may appear trustworthy from its repeatable readings alone, while in fact being systematically wrong. Fill in the blank: Accuracy is the closeness of a reading to the ________ value. Precision is the closeness of agreement among ________ measurements of the same quantity. 1.2.2 Sensitivity and Linearity Sensitivity is the ratio of the change in an instrument's output signal, or reading, to the corresponding change in the measurand that caused it, sensitivity = Δoutput/Δinput, and a highly sensitive instrument produces a comparatively large output change for even a small change in the quantity being measured. Linearity describes how closely an instrument's actual calibration curve, relating its output to its input across the full measurement range, approximates a single straight line, and is usually expressed as the maximum deviation of the actual calibration curve from this best-fit straight line,

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