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1. Course : Measurements and Instrumentation Code : BEEE305L Sem.: Winter 2023-24 Module-1: Characteristics of Measurements (Lec-03) Faculty: Dr. Nitin Kumar Kulkarni Designation: Assistant Professor(Sr.) Department: School of Electrical Engg . (SELECT)_VITCC

2. List of Contents Static calibration Static characteristics of measuring instruments Sources of error in measurement (static error) Types of errors (briefly) Techniques of reducing error

3. Static Calibration Calibration: It is  the process of configuring an instrument to provide a result for a sample within an acceptable range (OR) It is defined as the act or process of marking a measuring instrument with the necessary gradations; the resulting markings or settings . Static calibration is the process by which static performance characteristics of a measuring instrument is obtained. Calibration procedure involves comparison of the particular instrument with either a primary standard or a secondary standard with high accuracy or instrument of known accuracy. For example, a calibration curve is shown here.

4. Performance indices of a measurement system A measurement instrument can be studied by obtaining its performance characteristics. Any instrument’s performance can be assessed by observing its behavior during static and dynamic conditions. In this context it is necessary to obtain static and dynamic characteristics of a measurement device. Static characteristics give a quality of measurement neglecting the dynamic aspects of the instrument. Dynamic characteristics give quality of measurement considering the dynamic aspects of the instrument.

5. Static characteristics Different parameters of static characteristics for the measurement system are: (i) Accuracy & Precision (ii) Sensitivity (iii) Reproducibility (iv) Drift (v) Static error (vi) Dead zone

6. Accuracy Accuracy is the closeness with which an instrument reading approaches the true value of the quantity being measured. Accuracy is expressed in multiple ways. Point accuracy: It is accuracy at one point on a scale. Accuracy as percentage of a scale: For an instrument with uniform scale, its accuracy is expressed in terms of scale range. For eg :- a thermometer which has a range of 500°C has accuracy of ± 0.5% of scale range. This is misleading since the error when thermometer reads 500°C is negligible but when the reading is 25°C the error is high i.e. it comes to 10% = (500/25)* ± 0.5% . Accuracy as a percentage of true value: It is mentioned as ± 0.5% of * true value . This system of expressing accuracy is much better than previous case. * True value: A value obtained by ‘ Examplar Method ’ i.e. method agreed upon by experts as being sufficiently accurate for the purpose.

7. Precision Precision is used in measurements to describe the consistency and reproducibility of the results. It is defined as the degree of similarity of repeated measurements. It is measured by a term known as ‘ precision index ’. High degree of precision does not mean high degree of accuracy since the measure values during taken for repeated experiments can show the same wrong value multiple times. It is a measure of the reproducibility of the measurements i.e. given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements. Precision is composed of two characteristics viz ; Conformity and Number of Significant figures .

8. Precision ( cont ….) Conformity: It is the ability of an instrument to produce the same reading, or it is the degree of similarity between the individual measurements. Number of Significant figures: Significant figures convey actual information regarding the magnitude and the measurement precision of a quantity. More are the significant figures higher is the precision. Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value . Eg : 256V has ‘3’ significant digits (number of non-zeros) 256.0V has ‘4’ significant digits 256.0V is more precise as compared to 256V More significant figures/digits means more precise is the measurement .

9. Sensitivity Sensitivity is an absolute quantity, the smallest absolute amount of change that can be detected by a measurement . The static sensitivity of an instrument/instrumentation system is the ratio of the magnitude of the output signal/response to the magnitude of input signal/quantity being measured. The reciprocal of sensitivity is called as inverse sensitivity/deflection factor. Static sensitivity = infinitesimal change in output/infinitesimal change in input . If the curve is straight line (calibrated line) then it is known as linear sensitivity .

10. Reproducibility & Drift Reproducibility is the degree of closeness with which a given value may be repeatedly measured. Perfect reproducibility means there is no drift . No drift means that with a given input the measured values are time invariant. Drift are of three types; zero drift, span drift and zonal drift . Zero drift: The whole calibration shifts from zero point of measurement due to undue warming up of electronic tube circuits. It can be prevented by proper zero setting. Span drift/Sensitivity drift: It is due to proportional change in the indication all along the upward scale. Zonal drift: It occurs for a portion of an instrument measurements i.e. restricted to a zone.

11. Drift types

12. Static error Static error is defined as the difference between the measured value and true value. Measured value is the quantity’s magnitude which is observed/calculated from the instrument’s reading. True value is approximately obtained by sufficiently extended series of measurements and also taking into account parameters conditions which may be applied . Static error = δ A = Am – At ; where, Am = measured value, At = true value respectively. δ A = ε = absolute static error quantity. Relative static error = absolute error/true value = δ A/At = ε r At = Am – δ A = Am - ε = Am – ε r At

13. Dead zone Dead zone is defined as the largest change of input quantity for which there is no output of the instrument.

14. Types of errors Gross errors : These are the error caused due to human mistake in reading instruments and recording and calculating measurement results Systematic errors : They are of ‘3’ types viz ; Instrumental, Environmental an Observational. Instrumental errors : These occur due to inherent shortcomings of the instrument, misuse of the instrument and loading effects on the instrument. Environmental errors : These occur due to the external conditions surrounding the instrument. Observational errors : These error occurs due to incorrect reading, and parallax. Random (Residual) errors : These errors occur by chance due to may be any factor.

15. Parallax Error

16. Few Techniques to reduce the errors Use instruments of higher precision. Improve the experimental techniques. Adjust the zero of the instruments properly. The value of the reading by standing straight to the instrument has been taken and not from the sides to avoid Parallax errors. Take its algebraic mean for a closer result by repeating the experiment several times. Take care of the environment if possible. In order to avoid gross errors carefully take the measurements.