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 error, accuracy, precisio ad limitig error. 3. Describe the basic elemets of electroic istrumet. INTRODUCTION Measuremet is the process of determiig the amout, degree or capacity by compariso with the accepted stadards of the system uits beig used. Istrumetatio is a techology of measuremet which serves scieces, egieerig, medicie ad etc. Istrumet is a device for determiig the value or magitude of a quatity or variable. Electroic istrumet is based o electrical or electroic priciples for its measuremet fuctios. FUNCTION AND ADVANTAGES The 3 basic fuctios of istrumetatio :- ν Idicatig visualize the process/operatio ν Recordig observe ad save the measuremet readig ν Cotrollig to cotrol measuremet ad process Advatages of electroic measuremet ν Results high sesitivity ratig the use of amplifier ν Icrease the iput impedace thus lower loadig effects ν Ability to moitor remote sigal 1
PERFORMANCE CHARACTERISTICS Performace Characteristics - characteristics that show the performace of a istrumet. ν Eg: accuracy, precisio, resolutio, sesitivity. Allows users to select the most suitable istrumet for a specific measurig jobs. Two basic characteristics : ν Static ν Dyamic PERFORMANCE CHARACTERISTICS Accuracy the degree of exactess (closeess) of measuremet compared to the expected (desired) value. Resolutio the smallest chage i a measuremet variable to which a istrumet will respod. Precisio a measure of cosistecy or repeatability of measuremet, i.e successive readig do ot differ. Expected value the desig value or the most probable value that expect to obtai. Error the deviatio of the true value from the desired value. Sesitivity ratio of chage i the output (respose) of istrumet to a chage of iput or measured variable. ERROR IN MEASUREMENT Measuremet always itroduce error Error may be expressed either as absolute or percetage of error Absolute error, e = X where expected value X measured value X % error = 100 ERROR IN MEASUREMENT Relative accuracy, % Accuracy, a = 100% - % error = A 100 X X Precisio, P = 1 X X X A =1 where - value of the th measuremet - average set of measuremet X 2
Example 1.1 Solutio (Example 1.1) Give expected voltage value across a resistor is 80V. The measuremet is 79V. Calculate, i. The absolute error ii. The % of error iii. The relative accuracy iv. The % of accuracy Give that, expected value = 80V measuremet value = 79V i. Absolute error, e = = 80V 79V = 1V X ii. % error = X = 80 79 100 = 1.25% 100 80 iii. Relative accuracy, = 0.9875 X A = 1 iv. % accuracy, a = A x 100% = 0.9875 x 100%=98.75% Example 1.2 Sigificat Figures From the value i table 1.1 calculate Table 1.1 the precisio of 6 th measuremet? Solutio the average of measuremet value 98 + 101+... + 99 1005 X = = = 100.5 10 10 No X 1 98 2 101 3 102 4 97 5 101 6 100 7 103 the 6 th readig 9 106 Precisio = 100 100.5 0.5 1 = 1 = 0. 995 10 99 100.5 100.5 8 98 Sigificat figures covey actual iformatio regardig the magitude ad precisio of quatity More sigificat figure represet greater precisio of measuremet Example 1.3 Fid the precisio value of X 1 ad X 2? X = 101 X1 = 98 ===>> 2 s.f X = 98.5 ===>> 3 s.f 2 3
Solutio (Example 1.3) Sigificat Figures (cot) X = 101 X1 = 98 ===>> 2 s.f X = 98.5 ===>> 3 s.f 2 98 101 X1 = Precisio = 1 = 0. 97 101 98.5 101 X = Precisio = 1 = 0.975 ===>more precise 2 101 Rules regardig sigificat figures i calculatio 1) For addig ad subtractio, all figures i colums to the right of the last colum i which all figures are sigificat should be dropped Example 1.4 V 1 = 6.31 V + V 2 = 8.736 V Therefore V T = 15.046 V 15.05 V Sigificat Figures (cot) Solutio (Example 1.5) 2) For multiplicatio ad divisio, retai oly as may sigificat figures as the least precise quatity cotais Example 1.5 From the value give below, calculate the value for R 1, R 2 ad power for R 1? I = 0.0148 A ===> 3 s.f V 1 = 6.31 V ===> 3 s.f V 2 = 8.736 V ===> 4 s.f V1 6.31V R1 = = = 426.35 = 426 Ω I 0.0148 A V2 8.736V R2 = = = 590.27 = 590Ω I 0.0148 A ( ) ( ) P1 = V1 I = 6.31V 0. 0148A = 0.09339 = 0.0934 ===> 3 s.f ===> 3 s.f ===> 3 s.f 4
Sigificat Figures (cot) 3) Whe droppig o-sigificat figures 0.0148 ==> 0.015 (2 s.f) ==> 0.01 (1 s.f) TPES OF STATIC ERROR Types of static error 1) Gross error/huma error 2) Systematic Error 3) Radom Error 1) Gross Error - cause by huma mistakes i readig/usig istrumets - caot elimiate but ca miimize TPES OF STATIC ERROR (cot) 2) Systematic Error - due to shortcomigs of the istrumet (such as defective or wor parts) - 3 types of systematic error :- (i) Istrumetal error (ii) Evirometal error (iii) Observatioal error TPES OF STATIC ERROR (cot) (i) Istrumetal error - iheret while measurig istrumet because of their mechaical structure (bearig frictio, irregular sprig tesio, stretchig of sprig, etc) - error ca be avoid by: (a) selectig a suitable istrumet for the particular measuremet applicatio (b) apply correctio factor by determiig istrumetal error (c) calibrate the istrumet agaist stadard 5
(ii) (iii) TPES OF STATIC ERROR (cot) Evirometal error - due to exteral coditio effectig the measuremet icludig surroudig area coditio such as chage i temperature, humidity, barometer pressure, etc - to avoid the error :- (a) use air coditioer (b) sealig certai compoet i the istrumets (c) use magetic shields Observatioal error - itroduce by the observer - most commo : parallax error ad estimatio error (while readig the scale) TPES OF STATIC ERROR (cot) 3) Radom error - due to ukow causes, occur whe all systematic error has accouted - accumulatio of small effect, require at high degree of accuracy - ca be avoid by (a) icreasig umber of readig (b) use statistical meas to obtai best approximatio of true value Example 1.6:A voltmeter havig a sesitivity of 1kΩ/V is coected across a ukow resistace i series with a milliammater readig 80V o 150V scale. Whe the milliammeter reads 10mA, calculate the i. Apparet resistace of the ukow resistace ii. Actual resistace of the ukow resistace iii. Error due to the loadig effect of the voltmeter Dyamic Characteristics Dyamic measurig a varyig process coditio. Istrumets rarely respod istataeously to chages i the measured variables due to such thigs as mass, thermal capacitace, fluid capacitace or electrical capacitace. The three most commo variatios i the measured quatity: ν Step chage ν Liear chage ν Siusoidal chage 6
Dyamic Characteristics The dyamic characteristics of a istrumet are: ν Speed of respose ν Dyamic error ν ν ω The differece betwee the true ad measured value with o static error. Lag respose delay Fidelity the degree to which a istrumet idicates the chages i the measured variable without dyamic error (faithful reproductio). LIMITING ERROR The accuracy of measurig istrumet is guarateed withi a certai percetage (%) of full scale readig E.g maufacturer may specify the istrumet to be accurate at ±2 % with full scale deflectio For readig less tha full scale, the limitig error icreases LIMITING ERROR (cot) LIMITING ERROR (cot) Example 1.6 Give a 600 V voltmeter with accuracy ±2% full scale. Calculate limitig error whe the istrumet is used to measure a voltage of 250V? Solutio The magitude of limitig error, 0.02 x 600 = 12V Therefore, the limitig error for 250V = 12/250 x 100 = 4.8% Example 1.7 A voltmeter readig 70V o its 100V rage ad a ammeter readig 80mA o its 150mA rage are used to determie the power dissipated i a resistor. Both of these istrumets are quarateed to be accurate withi ±1.5% at full scale deflectio. Determie the limitig error of the power. Solutio The limitig error for the power = 2.143% + 2.813% = 4.956% 7
Example 1.8 LIMITING ERROR (cot) Give for certai measuremet, a limitig error for voltmeter at 70V is 2.143% ad a limitig error for ammeter at 80mA is 2.813%. Determie the limitig error of the power. Solutio The limitig error for the power = 2.143% + 2.813% = 4.956% Stadard A stadard is a kow accurate measure of physical quatity. Stadards are used to determie the values of other physical quatities by the compariso method. All stadards are preserved at the Iteratioal Bureau of Weight ad Measures (BIMP), Paris. ν http://www1.bipm.org/e/home Four categories of stadard: ν Iteratioal Stadard ν Primary Stadard ν Secodary Stadard ν Workig Stadard Stadard Iteratioal Std ν Defied by Iteratioal Agreemet ν Represet the closest possible accuracy attaiable by the curret sciece ad techology Primary Std ν Maitaied at the Natioal Std Lab (differet for every coutry) ν Fuctio: the calibratio ad verificatio of secodary std Secodary Std ν Basic referece std used by measuremet & calibratio lab i idustries. ν Maitaied by the particular idustry. ν Each lab has its ow secodary std which are periodically checked ad certified by the Natioal Std Lab. Workig Std ν Pricipal tools of a measuremet lab. ν Used to check ad calibrate lab istrumet for accuracy ad performace. ν Eg: Std resistor for checkig of resistace value maufactured. ELECTRONIC INSTRUMENT Basic elemets of a electroics istrumet Trasducer Sigal Modifier Idicatig Device 1) Trasducer - covert a o electrical sigal ito a electrical sigal 2) Sigal modifier - covert iput sigal ito a suitable sigal for the idicatig device 3) Idicatig device - idicates the value of quatity beig measure 8
INSTRUMENT APPLICATION GUIDE Practice Selectio, care ad use of the istrumet :- Before usig a istrumet, studets should be thoroughly familiar with its operatio ** read the maual carefully Select a istrumet to provide the degree of accuracy required (accuracy + resolutio + cost) Before used ay selected istrumet, do the ispectio for ay physical problem Before coectig the istrumet to the circuit, make sure the fuctio switch ad the rage selector switch has bee set-up at the proper fuctio or rage A voltmeter has a accuracy of 98% i full-scale measuremet readigs. a) If the voltmeter gives measuremet readig of 200V at the rage of 500V, calculate the absolute error of the measuremet. b) Calculate the percet error for the readig i (a) 9