Chapter 1

Chapter 1

Chapter 1 INTRODUCTION TO INSTRUMENTATION OBJECTIVES At the end of this chapter, students should be able to: 1. Explain the static and dynamic characteristics of an instrument. 2. Calculate and analyze the measurement error, accuracy, precision and limiting error. 3. Describe the basic elements of electronic instrument. 2

INTRODUCTION Instrumentation is a technology of measurement which serves sciences, engineering, medicine and etc. Measurement is the process of determining the amount, degree or capacity by comparison with the accepted standards of the system units being used. Instrument is a device for determining the value or magnitude of a quantity or variable. Electronic instrument is based on electrical or electronic principles for its measurement functions. 3 FUNCTION AND ADVANTAGES The 3 basic functions of instrumentation : Indicating visualize the process/operation Recording observe and save the measurement reading Controlling to control measurement and process

Advantages of electronic measurement Results high sensitivity rating the use of amplifier Increase the input impedance thus lower loading effects Ability to monitor remote signal 4 Typical Measurement System Architecture Noise and Interference Proce Proce ss ss or or Test Test

Sensor or Transducer Amp Signal Conditioner OUR TOPIC IS HERE Proces s Controller ADC

Converter PC comp and data storage and control over the process or experiment 5 Examples of Electronic Sensor applications New Solar Power Faucet by Sloan Valve 0.5 gpm aerator regulates water flow Electronic sensor automatically turns water on/off Integral temperature control

Uses infrared optical sensor 6 PERFORMANCE CHARACTERISTICS Performance Characteristics - characteristics that show the performance of an instrument. Eg: accuracy, precision, resolution, sensitivity. Allows users to select the most suitable instrument for a specific measuring jobs. Two basic characteristics : Static measuring a constant process condition. Dynamic - measuring a varying process condition. 7

PERFORMANCE CHARACTERISTICS Accuracy the degree of exactness (closeness) of measurement compared to the expected (desired) value. Resolution the smallest change in a measurement variable to which an instrument will respond. Precision a measure of consistency or repeatability of measurement, i.e successive reading do not differ. Sensitivity ratio of change in the output (response) of instrument to a change of input or measured variable. Expected value the design value or the most probable value that expect to obtain. Error the deviation of the true value from the desired value. 8 ERROR IN MEASUREMENT Measurement always introduce error Error may be expressed either as absolute or percentage of error

Absolute error, e = Yn X n where Yn expected value X n measured value Yn X n 100 % error = Yn 9 ERROR IN MEASUREMENT Relative accuracy, Yn X n A 1 Yn

% Accuracy, a = 100% - % error = A 100 Precision, P = 1 Xn Xn Xn where X-n value of the nth measurement -X n average set of measurement 10 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. Example 1.1 Given expected voltage value across a resistor is 80V. The measurement is 79V. Calculate, i. The absolute error ii. The % of error iii. The relative accuracy iv. The % of accuracy 11 Solution (Example 1.1) Given that , expected value = 80V measurement value = 79V

Yn X n i. Absolute error, e = = 80V 79V = 1V Yn X n 80 79 100 ii. % error = Yn = 80 100 = 1.25% Yn X n iii. Relative accuracy, A 1 = 0.9875 Yn iv. % accuracy, a = A x 100% = 0.9875 x 100%=98.75% 12 Example 1.2

From the value in table 1.1 calculate the precision of 6th measurement? Solution the average of measurement value 98 101 .... 99 1005 Xn 100.5 10 10 the 6 reading Precision = 1 100 100.5 1 0.5 0.995 100.5 100.5 th Table 1.1

No Xn 1 98 2 101 3 102 4

97 5 101 6 100 7 103 8

98 9 106 10 99 13 LIMITING ERROR The accuracy of measuring instrument is guaranteed within a certain percentage (%) of full scale reading E.g manufacturer may specify the instrument to be

accurate at 2 % with full scale deflection For reading less than full scale, the limiting error increases 14 LIMITING ERROR (cont) Example 1.6 Given a 600 V voltmeter with accuracy 2% full scale. Calculate limiting error when the instrument is used to measure a voltage of 250V? Solution The magnitude of limiting error, 0.02 x 600 = 12V Therefore, the limiting error for 250V = 12/250 x 100 = 4.8% 15

LIMITING ERROR (cont) Example 1.7 Given for certain measurement, a limiting error for voltmeter at 70V is 2.143% and a limiting error for ammeter at 80mA is 2.813%. Determine the limiting error of the power. Solution The limiting error for the power = 2.143% + 2.813% = 4.956% 16 Exercise A voltmeter is accurate 98% of its full scale reading. i. If the voltmeter reads 200V on 500V range, what

is the absolute error? ii. What is the percentage error of the reading in (i). 17 Significant Figures Significant figures convey actual information regarding the magnitude and precision of quantity More significant figure represent greater precision of measurement Example 1.3 Find the precision value of X1 and X2? X n 101

X 1 98 ===>> 2 s.f X 2 98.5 ===>> 3 s.f 18 Solution (Example 1.3) X n 101 X 1 98===>> 2 s.f X 2 98.5===>> 3 s.f 98 101 X 1 Precision = 1 0.97 101 X 2 Precision = 1

98.5 101 0.975===>more precise 101 19 Significant Figures (cont) Rules regarding significant figures in calculation 1) For adding and subtraction, all figures in columns to the right of the last column in which all figures are significant should be dropped Example 1.4 V1 = 6.31 V + V2 = 8.736 V Therefore

VT = 15.046 V 15.05 V 20 Significant Figures (cont) 2) For multiplication and division, retain only as many significant figures as the least precise quantity contains Example 1.5 From the value given below, calculate the value for R1, R2 and power for R1? I = 0.0148 A ===> 4 s.f V1 = 6.31 V ===> 2 s.f V2 = 8.736 V ===> 3 s.f

21 Solution (Example 1.5) V 6.31V R1 1 426.35 426 ===> 3 s.f I 0.0148 A V2 8.736V R2 590.27 590 ===> 3 s.f I 0.0148 A

P1 V1 I 6.31V 0.0148 A = 0.09339 = 0.0934 ===> 3 s.f 22 Significant Figures (cont) 3) When dropping non-significant figures 0.0148 ==> 0.015 (2 s.f) ==> 0.01 (1 s.f) 23 TYPES OF STATIC ERROR

Types of static error 1) Gross error/human error 2) Systematic Error 3) Random Error 24 1. Gross Errors or Human Errors Resulting from carelessness, e.g. misreading, incorrectly recording Serious measurement errors can occur if an instrument is not read correctly. The digital instrument is on a 300 mA range, so its reading is in milliamperes. For the analog meter, the range selection must be noted, and the pointer position must be read from 25

the correct scale Absolute Errors and Relative Errors Percentage accuracy gives the relative error in a measured, or specified quantity. The absolute error can be determined by converting the percentage error into an absolute quantity 26 Accuracy, Precision, Resolution, and Significant Figures Accuracy (A) and Precision The measurement accuracy of 1% defines how close the measurement is to the actual measured quality. The precision is not the same as the accuracy of measurement, but they are related

Measurement precision depends on the smallest change that can be observed in the measured quantity. A 1mV change will be indicated on the digital voltmeter display above. For the analog instrument, 50 mV is the smallest 27 change that can be noted a) If the measured quantity increases or decreases by 1 mV, the reading becomes 8.936 V or 8.934 V respectively. Therefore, the voltage is measured with a precision of 1 mV. b) The pointer position can be read to within one-fourth of the smallest scale division. Since the smallest scale division represents 0.2 V, onefourth of the scale division is 50 mV.

Resolution The measurement precision of an instrument defines the smallest change in measured quantity that can be observed. This smallest observable change is the resolution of the instrument. Significant Figures The number of significant figures indicate the precision of measurement. 28 Example 2.1: An analog voltmeter is used to measure voltage of 50V across a resistor. The reading value is 49 V. Find a) Absolute Error b) Relative Error

c) Accuracy d) Percent Accuracy Solution a) e X t X m 50V 49V 1V Xt Xm b) % Error 100% Xt 50V 49V 100% 2% 50V c) A 1 % Error 1 2% 0.98 d) % Acc 100% 2% 98%

29 Measurement Error Combinations When a quantity is calculated from measurements made on two (or more) instruments, it must be assumed that the errors due to instrument inaccuracy combine is the worst possible way. Sum of Quantities Where a quantity is determined as the sum of two measurements, the total error is the sum of the absolute errors in each measurement. E V1 VV1 V2 VV2 giving E V1 V2 VV1 VV2 30

Difference of Quantities The error of the difference of two measurements are again additive E V1 VV1 V2 VV2 V1 V2 VV1 VV2 Product of Quantities When a calculated quantity is the product of two or more quantities, the percentage error is the sum of the percentage errors in each quantity P EI E VE IVI EI EV I IV E VEVI since VEVI is very small, P EI EV I IV E 31

Example: An 820 resistance with an accuracy of 10% carries a current of 10 mA. The current was measured by an analog ammeter on a 25mA range with an accuracy of 2% of full scale. Calculate the power dissipated in the resistor, and determine the accuracy of the result. Solution 2 P I 2 R 10 mA 820 82 mW error in R 10% error in I 2% of 25 mA 0.5 mA 0.5 mA 100% 5%

10 mA %error in I 2 2 5% 10% %error in P %error in I 2 %error in R 10% 10% 20% 32 Deviation Difference between any one measured value and the arithmetic mean of a series of measurements May be positive or negative, and the algebraic sum of the deviations is always zero

d n x n x The average deviation (D) may be calculated as the average of the absolute values of the deviations. D d1 d 2 d 3 ... d n n 33 Standard Deviation and Probable of Error Variance: the mean-squared value of the deviations 2 2 2

d d ... d 2 n 2 1 n Standard deviation or root mean squared (rms) d12 d 22 ... d 2n SD or n

For the case of a large number of measurements in which only random errors are present, it can be shown that the probable error in any one measurement is 0.6745 times the standard deviation: Probable Error 0.6745 34 Example: The accuracy of five digital voltmeters are checked by using each of them to measure a standard 1.0000V from a calibration instrument. The voltmeter readings are as follows: V 1 = 1.001 V, V2 = 1.002, V3 = 0.999, V4 = 0.998, and V5 = 1.000. Calculate the average measured voltage and the average deviation. Solution V V2 V3 V4 V5

Vav 1 5 1.001 1.002 0.999 0.998 1.000 1.000 V 5 d1 V1 Vav 1.001 1.000 0.001V d 2 V2 Vav 1.002 1.000 0.002 V d 3 0.999 1.000 0.001V d 4 0.998 1.000 0.002 V d 5 1.000 1.000 0 V D d1 d 2 ... d 5 5 0.001 0.002 0.001 0.002 0

0.0012V 5 35 Instrument loading effect : Some measuring instruments depend for their operation on power taken from the circuit in which measurements are being made. Depending on the loading effect of the instrument (i.e. the current taken to enable it to operate), the prevailing circuit conditions may change. The resistance of voltmeters may be calculated since each have a stated sensitivity (or figure of merit), often stated in k per volt of f.s.d. A voltmeter should have as high a resistance as possible ( ideally infinite). In a.c. circuits the impedance of the instrument varies with frequency and thus the loading effect of the instrument can change. Example:

Calculate the power dissipated by the voltmeter and by resistor R in Figure 10.9 when (a) R=250 , (b) R=2 M. Assume that the voltmeter sensitivity (sometimes called figure of merit) is 10 k/V. 36 37 2. Systematic Error: due to shortcomings of the instrument (such as defective or worn parts, ageing or effects of the environment on the instrument) In general, systematic errors can be subdivided into static and dynamic errors. Static caused by limitations of the measuring device or the

physical laws governing its behavior. Dynamic caused by the instrument not responding very fast enough to follow the changes in a measured variable. - 3 types of systematic error :(i) Instrumental error (ii) Environmental error (iii) Observational error 38 Types of static error (i) Instrumental error - inherent while measuring instrument because of their mechanical structure (eg: in a DArsonval meter,

friction in the bearings of various moving component, irregular spring tension, stretching of spring, etc) - error can be avoid by: (a) selecting a suitable instrument for the particular measurement application (b) apply correction factor by determining instrumental error (c) calibrate the instrument against standard 39 (ii) Environmental error - due to external condition effecting the measurement including surrounding area condition such as change in temperature, humidity, barometer pressure, etc - to avoid the error :(a) use air conditioner (b) sealing certain component in the instruments

(c) use magnetic shields (iii) Observational error - introduce by the observer - most common : parallax error and estimation error (while reading the scale) - Eg: an observer who tend to hold his head too far to the left while reading the position of the needle on the scale. 40 3) Random error - due to unknown causes, occur when all systematic error has accounted - accumulation of small effect, require at high degree of accuracy - can be avoid by (a) increasing number of reading

(b) use statistical means to obtain best approximation of true value 41 2- Systematic Errors versus Random errors Systematic Errors Instrumental Errors Friction Zero positioning Environment Errors Temperature Humidity Pressure Observational Error Random Errors

42 Dynamic Characteristics Dynamic measuring a varying process condition. Instruments rarely respond instantaneously to changes in the measured variables due to such things as mass, thermal capacitance, fluid capacitance or electrical capacitance. 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 behavior of the instrument is important. 43 Dynamic Characteristics

The dynamic behavior 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: Step change Linear change Sinusoidal change 44 Dynamic Characteristics Step change-in which the primary element is subjected to an instantaneous and finite change in measured variable. Linear change-in which the primary element is following the measured variable, changing linearly with time.

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. 45 Dynamic Characteristics The dynamic performance characteristics of an instrument are: Speed of response- The rapidity with which an instrument responds changes in measured quantity. Dynamic error-The difference between the true and measured value with no static error. Lag delay in the response of an instrument to changes in the measured variable. Fidelity the degree to which an instrument indicates the changes in the measured variable without dynamic

error (faithful reproduction). 46 Standard A standard is a known accurate measure of physical quantity. Standards are used to determine the values of other physical quantities by the comparison method. All standards are preserved at the International Bureau of Weight and Measures (BIMP), Paris. Four categories of standard: International Standard

Primary Standard Secondary Standard Working Standard 47 Standard International Std Defined by International Agreement Represent the closest possible accuracy attainable by the current science and technology Primary Std

Maintained at the National Std Lab (different for every country) Function: the calibration and verification of secondary std Each lab has its own secondary std which are periodically checked and certified by the National Std Lab. For example, in Malaysia, this function is carried out by SIRIM. 48 Standard Secondary Standard Secondary standards are basic reference standards used by measurement and calibration laboratories in industries. 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 particular industrial laboratory with a certification of measuring accuracy in terms of a primary standard. Working Std Used to check and calibrate lab instrument for accuracy and performance. For example, manufacturers of electronic components such as capacitors, resistors and many more use a standard called a working standard for checking the component values being manufactured. 49 ELECTRONIC INSTRUMENT Basic elements of an electronics instrument

Transduce r Signal Modifie r Indicatin g Device 1) Transducer - convert a non electrical signal into an electrical signal - e.g: a pressure sensor detect pressure and convert it to electricity for display at a remote gauge. 2) Signal modifier - convert input signal into a suitable signal for the indicating device

3) Indicating device - indicates the value of quantity being measure 50 INSTRUMENT APPLICATION GUIDE Selection, care and use of the instrument : Before using an instrument, students should be thoroughly familiar with its operation ** read the manual carefully Select an instrument to provide the degree of accuracy required (accuracy + resolution + cost) Before used any selected instrument, do the inspection for any physical problem Before connecting the instrument to the circuit, make sure the function switch and the range selector switch has been set-up at the proper function or range 51


Define the terms accuracy, error, precision, resolution, expected value and sensitivity. State three major categories of error. A person using an ohmmeter reads the measured value as 470 ohm when the actual value is 47 ohm. What kind of error does this represent? State the classifications of standards. What are primary standards? Where are they used? What is the difference between secondary standards and working standards? State three basic elements of electronic instrument. 54 THE END


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