MCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions

Transcription

1 Faculty of Egieerig MCT242: Electroic Istrumetatio Lecture 2: Istrumetatio Defiitios

2 Overview Measuremet Error Accuracy Precisio ad Mea Resolutio Mea Variace ad Stadard deviatio Fiesse Sesitivity Rage Offset (bias) ad scale factor shift Liearity ad Liear Regressio Hysteresis Respose Time Real Time Gai

3 Measuremet Error Defiitio Error defied as ε = Y Where error i the th measuremet is defied as the differece betwee Y, the actual, true, defied or calculated value of the Quatity uder Measuremet ad is the measuremet

4 Accuracy The accuracy A of the th measuremet is defied as A 1 Y Y Percet Accuracy = 100 x A A measuremet is more accurate if it is closer to what is defied as the truth as compared to a referece stadard

5 Precisio of the th measuremet is defied as = N N where P N is the total umber of samples ad baris the MEAN Precisio is a measure of the reproducibility of the measuremet Precisio & Mea

6 Accuracy & Precisio From Measuremet Fudametals, Samplig Quality

7 Resolutio Resolutio is defied as the smallest uit of the quatity uder measuremet that ca be detected Example : if a measuremet is take of a quatity uder measuremet that ca vary betwee 0 ad 5 volts ad it is coverted ito oe of 4095 biary values (steps) the the resolutio is = 5 volts/4095 steps = volts per step A coverter of bits has 2 1 steps

8 Variace of a Populatio σ 2 1 N ( ) 2 x N = 1 The stadard deviatio is the square root of the variace

9 The stadard deviatio of a populatio is defied as This is the equatio to use if you have 100 percet sampled the etire populatio The stadard deviatio of a sample is defied as This is the equatio to use if you are dealig with a sample of the populatio ad tryig to estimate the etire populatio s characteristics N x N N S N S = = σ 2 1 ) ( 1 N x N N S N S = = σ 2 1 ) ( 1 1 Stadard Deviatio

10 From Statistics For Dummies by Deborah Rumsey Cautio these probabilities are for ormal distributios oly. Not all data fits a ormal distributio. It may be log-ormal, expoetial, etc which have differet iterpretatios.

11 Stadard Deviatios I A Normal Distributio The probability of a value beig betwee mea plus 3 sigma ad mea mius 3 sigma i a ormal distributio is 99.6% Source: Wikipedia Note This is two sided ca vary the same o either side of the mea ot all populatios of data are two sided

12 Fiesse The degree to which a quatity uder measuremet is iflueced by the measuremet process For example a thermistor or RTD ca heat to somethig beig measured at the same time it is measurig it

13 Sesitivity The sesitivity of the sesor is defied as the slope of the output characteristic curve or, more geerally, the miimum iput of physical parameter that will create a detectable output chage. I some sesors, the sesitivity is defied as the iput parameter chage required to produce a stadardized output chage. I others, it is defied as a output voltage chage for a give chage i iput parameter

14 Rage The rage of the sesor is the maximum ad miimum values of applied parameter that ca be measured.

15 Offset (Bias) ad Scale Factor The offset error of a trasducer is defied as the output that will exist whe it should be zero Alteratively, the differece betwee the actual output value ad the specified output value uder some particular set of coditios Offset is a liear error If a lie is y = mx +b, a offset is a error i the b term A scale factor error is a error i the slope A error i the m term A chage i scale factor ca also be viewed as a chage i sesitivity

16 From LabVIEW Data Acquisitio Basics Maual

17 Liearity The liearity of the trasducer is a expressio of the extet to which the actual measured curve of a sesor departs from the ideal curve. Figure 3 shows a somewhat exaggerated relatioship betwee the ideal, or least squares fit, lie ad the actual measured or calibratiolie (Notei most cases, the static curve is used to determie liearity, ad this may deviate somewhat from a dyamic liearity) Diagram from Sesor Termiology from Measuremet Fudametals.

18 Hysteresis A trasducer should be capable of followig the chages of the iput parameter regardless of which directio the chage is made; Hysteresis is the measure of this property. Figure 4 shows a typical hysteresis curve. Note that it matters from which directio the chage is made. Approachig a fixed iput value (poit B i Figure 4) from a higher value (poit P) will result i a differet idicatio tha approachig the same value from a lesser value (poit Q or zero). Diagram from Sesor Termiology from Measuremet Fudametals. Note that iput value Bca be represeted by F()1, F()2, or F()3 depedig o the immediate previous value clearly a error due to hysteresis.

19 Respose Time Sesors do ot chage output state immediately whe a iput parameter chage occurs. Rather, it will chage to the ew state over a period of time, called the respose time. The respose time ca be defied as the time required for a sesor output to chage from its previous state to a fial settled value withi a tolerace bad of the correct ew value. Separatig the respose time of the sesor from the respose time of the system is a critical issue I geeral sesors should be selected to have a much faster respose tha the system beig measured

20 Respose Time -Examples The curves below show two types of respose time. I Figure a the curve represets the respose time followig a abrupt positive goig stepfuctio chage of the iput parameter. The form show i Figure b is a decay time (Td to distiguish from Tr, for they are ot always the same) i respose to a egative goig step-fuctio chage of the iput parameter.

21 Real Time Real Time Systems are defied as those systems i which the correctess of the system depeds ot oly o the logical results of the computatio, but also o the time at which the results are produced May data acquisitio systems are real-time systems If you ca afford to ru it agai ad capture exactly the same coditios ad results (ot just similar), it is ot real time

22 Gai Gai is aother term for multiplicative amplificatio Typically represeted by a Triagle If a iput is 1 uit ad a output is 10 uits, the Gai is a factor of 10 Gai is also expressed i decibels (db) Decibels is calculated two ways For Voltage it is calculated as For Power Ratios it is calculated as 20 log10 ( 10 log10 V V referece ( ) P P referece )