CHAPTER 1 BASIC CONCEPTS OF INSTRUMENTATION AND MEASUREMENT

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CHAPTER 1 BASIC CONCEPTS OF INSTRUMENTATION AND MEASUREMENT 1.1 Classificatio of istrumets Aalog istrumet The measure parameter value is isplay by the moveable poiter.

1 CHAPTER 1 BASIC CONCEPTS OF INSTRUMENTATION AND MEASUREMENT 1.1 Classificatio of istrumets Aalog istrumet The measure parameter value is isplay by the moveable poiter. The poiter will move cotiuously with the variable parameter/aalog sigal which is measure. The reaig is iaccurate because of parallax error (parallel) urig the skill reaig. E.g: ampere meter, voltage meter, ohm meter etc. Digital istrumet The measure parameter value is isplay i ecimal (igital) form which the reaig ca be rea thru i umbers form. Therefore, the parallax error is ot existe a termiate. The cocept use for igital sigal i a igital istrumet is logic biary 0 a Characteristic of istrumets Figure 1.1 presets a geeralize moel of a simple istrumet. The physical process to be measure is i the left of the figure a the measura is represete by a observable physical variable X. Figure 1.1: Simple istrumet moel. 1

2 For example, the mass of a object is ofte measure by the process of weighig, where the measura is the mass but the physical measuremet variable is the owwar force the mass exerts i the Earth s gravitatioal fiel. There are may possible physical measuremet variables. The key fuctioal elemet of the istrumet moel show i Figure 1.1 is the sesor, which has the fuctio of covertig the physical variable iput ito a sigal variable output. Sigal variables have the property that they ca be maipulate i a trasmissio system, such as a electrical or mechaical circuit. Because of this property, the sigal variable ca be trasmitte to a output or recorig evice that ca be remote from the sesor. I electrical circuits, voltage is a commo sigal variable. I mechaical systems, isplacemets or force are commoly use as sigal variables. Other examples of sigal variable are show i Table 1.1. Table 1.1: Example physical variables The sigal output from the sesor ca be isplaye, recore, or use as a iput sigal to some secoary evice or system. I a basic istrumet, the sigal is trasmitte to a Display or recorig evice where the measuremet ca be rea by a huma observer. The observe output is the measuremet M. 2

3 There are may types of isplay evices, ragig from simple scales a ial gages to sophisticate computer isplay systems. The sigal ca also be use irectly by some larger system of which the istrumet is a part. Two basic characteristic of a istrumet is essetial for selectig the most suitable istrumet for specific measurig jobs: 1. Static characteristic 2. Dyamic characteristic Static characteristic of a istrumet are, i geeral, cosiere for istrumets which are use to measure a uvaryig process coitio. Several terms of static characteristic that have iscusse: 1. Istrumet A evice or mechaism use to etermie the preset value of a quatity uer observatio. 2. Measuremet The process of etermiig the amout, egree, capacity by compariso (irect or iirect) with the accepte staars of the system uits beig use. 3. Accuracy The egree of exactess (closeess) of a measuremet compare to the expecte (esire) value. 4. Resolutio The smallest chage i a measure variable to which istrumets will respose. Also kow as Threshol. 5. Precisio A measure of cosistecy or repeatability of measuremets, i.e. successive reaigs o ot iffer or the cosistecy of the istrumet output for a give value of iput. A very precise reaig though is ot perfectly a accurate reaig. X X Pr ecisio = 1 with X = measure value X X = average value or expecte value 6. Expecte value The esig value that is, most probable value that calculatios iicate oe shoul expect to measure. 7. Hysterisis The ifferet loaig a uloaig curve ue to the magetic hysterisis of the iro. E.g.: Occur to a movig iro voltmeter, it is slowly varies from zero to full scale value a the back to zero; the iput-output curve will be ifferet. 8. Dea Zoe/ba The total rage of possible values for istrumet will ot give a reaig eve there is chages i measure parameter. 9. Nomial value - Is some value of iput a output that ha bee state by the maufacturer for user maual. 3

4 10. Bias A costat error that occur to istrumet whe the poiter ot startig from zero scale. 11. Rage A miimum a maximum rage for istrumet to operate a it is state by the maufacturer of the istrumet. 12. Sesitivity The ratio of the chage i output (respose) of the istrumet to a chage of iput or measure variable output S = iput Dyamic characteristic are cocere with the measuremet of quatities that vary with time. 1.3 Process of measuremet Measuremet is essetially the act, or the result, of a quatitative compariso betwee a give quatity a a quatity of the same ki chose as a uit. The result of measuremet is expresse by a umber represetig the ratio of the ukow quatity to the aopte uit of measuremet. The step take before measure: 1. Proceure of measuremet: Ietifie the parameter or variable to be measure, how to recor the result 2. Characteristic of parameter: Shoul kow the parameter that to be measure; ac, c, frequecy or etc. 3. Quality: Time a cost of equipmet, the istrumet ability, the measuremet kowlege a suitable result. 4. Istrumet: Choose a suitable equipmet; multimeter, voltmeter, oscilloscope or etc. Durig measuremet: 1. Quality: Make sure the chose, istrumet is the best, the right positio whe take result, the frequet of measuremet. 4

5 2. Safety first: Electric shock, overloa effect, limitatio of istrumet. 3. Samplig: See the chagig of parameter urig measuremet, which value shoul be take whe the parameter keep chagig. Take eough samples a it is accepte. The step take after measuremet: Every ata recore must be aalyse, statically, mathematically a the result must be accurately a complete. 1.4 Error i measuremet Error is efie as the ifferece betwee the true value (expecte value) of the measura a the measure value iicate by the istrumet. Error may be expresse either as absolute error or as a percetage of error. Absolute errors are efie as the ifferece betwee the expecte value of the variable a the measure value of variable. Absolute error, e = Y X where Y = expecte value X = measure value Absolute Error Percetage error = X100% Expecte value Y X or Percetage error = X100% Y 5

6 Relative accuracy, A = 1 Y X Y Percetage relative accuracy, a = 100 % Percetage error = A X 100% Example 1: The expecte value of the voltage across a resistor is 90 V. However, the measuremet gives a value of 89 V. Calculate: a) Absolute error b) Percetage error c) Relative accuracy ) Percetage of accuracy Solutio Expecte value of voltage across a resistor, Y = 90 V Measure value of voltage across a resistor, X = 89 V a) Absolute error, e = Y - X = = 1 V Y X b) Percetage error = X100% Y = X100% 90 = % 6

7 c) Relative accuracy, A = 1 Y X Y = = ) Percetage of accuracy, a = 100 X = % or a = 100% = % 1.5 Types of error Errors are geerally categories uer the followig three major heatig: 1. Gross Errors - Is geerally the fault of the perso usig istrumets a are ue to such thigs as icorrect reaig of istrumets, icorrect recorig of experimetal ata or icorrect use of istrumet. 2. Systematic Errors are ue to problems with istrumets, eviromet effects or observatioal errors. Istrumet errors It is ue to frictio i the bearigs of the meter movemet, icorrect sprig tesio, improper calibratio, or faulty istrumets. Evirometal errors Evirometal coitios i which istrumets are use may cause errors. Subjectig istrumets to harsh eviromets such high temperature, pressure, humiity, strog electrostatic or electromagetic fiels, may have etrimetal effects, thereby causig error. Observatioal errors - Those errors that itrouce by observer. Two most commo observatioal errors are probably the parallax error itrouce i reaig a meter scale a error of estimatio whe obtaiig a reaig from a scale meter. 7

8 3. Raom Errors are geerally the accumulatio of a large umber of small effects a may be of real cocer oly i measuremets requirig a high egree of accuracy. Such errors ca be aalyze statistically. 1.6 Statistical aalysis of error i measuremet How to aalyze a error? - use statistic metho Whe we measure ay physical quatity, our measuremets are effecte by a multitue of factors. Arithmetic mea the sum of a set of umbers ivie by the total umber of pieces of ata. Arithmetic mea, where x x x x x x = = x = 1 = th reaig take = total umber of reaigs Deviatio the ifferece each piece of test ata a the arithmetic mea. Deviatio, = x x Note: The algebraic sum of the eviatios of a set umbers from their arithmetic mea is zero. The average eviatio is a iicatio of the precisio of the istrumet use i measuremet or the sum of the absolute values of the eviatio ivie by the umber of reaigs. 8

9 Average eviatio, D = where 1, 2, 3... = absolute value of eviatios The staar eviatio is the square root of the sum of all the iiviual eviatios square, ivie by the umber of reaigs. Staar eviatio, S = *** For small reaigs (<30), the eomiator is - 1 Example: For the followig give ata, calculate a) Arithmetic mea b) Deviatio of each value c) Algebraic sum of the eviatios ) Calculate the average eviatio (As: 0.232) e) Calculate the staar eviatio (As: 0.27) Give x 1 = 49.7 x 2 = 50.1 x 3 = 50.2 x 4 = 49.6 x 5 = 49.7 Solutio a) The arithmetic mea, x1 + x2 + x3 + x4 + x5 x = = 5 = b) The eviatios from each value are give by 9

10 1 1 = x x = = 0.16 = x x = = = x x = = = x x = = = x x = = 0.16 c) The algebraic sum of the eviatios is tot = = 0 c) Average eviatio, D = 10

11 ) Staar eviatio, σ = 1.7 Limitig error Most maufacturers of measurig istrumet state that a istrumet is accurate withi a certai percetage of a full-scale reaig. For example, the maufacturer of a certai voltmeter may specify the istrumet to be accurate withi ± 2% with full-scale eflectio. 1.8 Measuremet error combiatios Whe a quatity is calculate from measuremets mae o two ore more istrumets, it must be assume that errors ue to istrumet iaccuracy combie i worst possible way. The resultig error is the larger tha the error i ay oe istrumet. Sum of quatities: E = (V 1 + V 2 ) ± ( V 1 + V 2 ) Differece of quatities: E = (V 1 - V 2 ) ± ( V 1 + V 2 ) Prouct of quatities: 11

12 Percetage error i P = (% error i I) + (% error i E) Quotiet of quatities: Percetage error i E/I = (% error i E) + (% error i I) Quatity raise to a power: Percetage error i A B = B (% error i A) Sum of Quatities Where a quatity is etermie as the sum of two measuremets, the total error is the sum of the absolute errors i each measuremet. As illustrate i Figure 1.2: V 1 ± V 1 R 1 E V 2 ± V 2 R 2 Figure 1.2: Error i sum of quatities equals sum of errors E = (V 1 + V 2 ) ± ( V 1 + V 2 ) Differece of Quatities 12

13 Figure 1.3 illustrate a situatio i which a potetial ifferece is etermie as the ifferece betwee two measure voltages. Here agai, the errors are aitive; E V 1 ± V 1 V 2 ± V 2 R 2 R 1 Figure 1.3: Error i ifferece of quatities equals sum of errors E = (V 1 - V 2 ) ± ( V 1 + V 2 ) Prouct of Quatities Whe a calculate quatity is prouct of two or more quatities, the percetage error is the sum of the percetage errors i each quatity. V 1 ± V 1 R 1 Figure 1.4: Percetage error i prouct or quotiet of quatities equals sum of percetage errors Percetage error i P = (% error i I) + (% error i E) 13

14 Quotiet of Quatities Here agai it ca be that the percetage error is the sum of the percetage errors i each quatity. Percetage error i E/I = (% error i E) + (% error i I Quatity Raise to a Power Whe a quatity A is raise to a power B, the percetage error i A B ca be show to be: Percetage error i A B = B (% error i A) Example: A 600V voltmeter is specifie to be accurate withi ± 2% at full scale. Calculate the limitig error whe the istrumet is use to measure a voltage of 250V. Solutio The magitue of the limitig error is 0.02 X 600 = 12 V 12 The limitig error at 250V is x 100% = 4.8% 250 Example: A voltmeter reaig 70V o its 100V rage a a ammeter reaig 80mA o its 150mA rage are use to etermie the power issipate i a resistor. Both these istrumets are guaratee to be accurate withi ± 1.5% at full-scale eflectio. Determie the limitig error of the power. (As: 4.956%) Solutio: 14

OBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to:

OBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to: OBJECTIVES Chapter 1 INTRODUCTION TO INSTRUMENTATION At the ed of this chapter, studets should be able to: 1. Explai the static ad dyamic characteristics of a istrumet. 2. Calculate ad aalyze the measuremet