PI2 Measurement

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MeasuremeMeasurementsntsPart 1: Basic Principle ofBasic Principle of

MeasurementsMeasurements


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Learning objectives

To state sub-systems in a measurementsystem

To understand main function in each sub-system

To understand the basic properties ofmeasurement systems


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Basic components in a measurementsystem

Basic components in a measurement system are shown below:

It is also important to mention that a power supply is an important

element for the entire system.

Amplication and !onditioning


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INSTRUMENTATION CHARACTERISTICS

Shows the performance of instruments to beused.

Divided into two categories: static and

dynamic characteristics. Static characteristics refer to the

comparison between steady output and idealoutput when the input is constant.

Dynamic characteristics refer to thecomparison between instrument output andideal output when the input changes.


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STATIC CHARACTERISTICS

1. ACCURACY

Accuracy is the ability of aninstrument to show the exact reading.

Always related to the extent of thewrong reading/non accuracy.

Normally shown in percentage oferror which of the full scale readingpercentage.


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Example :

A pressure gauge with a range between

!" bar with an accuracy of # $% fs&full!scale' has a maximum error of:

$ x " bar ( # .$ bar

"

Notes: )t is essential to choose ane*uipment which has a suitable operatingrange.


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Example :

A pressure gauge with a range between

! " bar is found to have an error of# ."$ bar when calibrated by themanufacturer.

+alculate :

a. ,he error percentage of the gauge.b. ,he error percentage when the

reading obtained is -. bar.


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Answer :

a. Error ercentage ( # ."$ bar x " ( # ".$%

". bar

b. Error ercentage ( # ."$ bar x " ( # .$ % -. bar

,he gauge is not suitable for use for low range

reading. Alternative : use gauge with a suitable range.


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Example :

,wo pressure gauges &pressure gauge A and 0' have afull scale accuracy of # $%. Sensor A has a range of!" bar and Sensor 0 !" bar. 1hich gauge is moresuitable to be used if the reading is .2 bar3

Answer :Sensor A :

E*uipment max error ( # $ x " bar ( # .$ bar

"E*uipment accuracy4 .2 bar & in %' ( # .$ bar x " ( # $.5%

.2 bar


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Sensor 0 :

E*uipment max error ( # $ x " bar ( # .$ bar "

E*uipment accuracy4 .2 bar & in %' ( # .$ bar x " ( # $$%

.2 bar

+onclusion :

Sensor A is more suitable to use at a reading of .2 barbecause the error percentage $.5%' is smaller comparedto the percentage error of Sensor 0 $$%'.


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2. PRECISION

An e*uipment which is precise is notnecessarily accurate.

Defined as the capability of aninstrument to show the same reading

when used each time &reproducibility ofthe instrument'.



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Example :6 : result

+entre circle : true value

XXX

XXXX

XXX

XXX

XXX

X X

X

xxHigh accuracy, high precision

Low accuracy, high precision

Low accuracy, low precision


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Accuracy vs Precision

High Precision, but low

accuracy.

There is a systematic error"


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Accuracy vs Precision #!ont$

%igh accuracy means that the mean is close to the truevalue& 'hile high precision means that the standarddeviation ( is small"


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3. TOLERANCE

+losely related to accuracy of an

e*uipment where the accuracy of ane*uipment is sometimes referred to inthe form of tolerance limit.

Defined as the maximum error

expected in an instrument. Explains the maximum deviation of an

output component at a certain value.



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4. RANGE OF SPAN

Defined as the range of reading between

minimum value and maximum value forthe measurement of an instrument.

7as a positive value e.g..:

,he range of span of an instrumentwhich has a reading range of 8"9+ to" 9+ is - 9+.



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. !IAS

+onstant error which occurs during themeasurement of an instrument.

,his error is usually rectified through calibration.

Example :

A weighing scale always gives a bias reading. ,hise*uipment always gives a reading of " g even

without any load applied. ,herefore; if A with aweight of g weighs himself; the given readingwould be " g. ,his would indicate that there isa constant bias of " g to be corrected.



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". LINEARITY


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L#near#t$

)utput*eadings

Measured +uantity


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%. SENSI&ITY

Defined as the ratio of change in output towardsthe change in input at a steady state condition.

Sensitivity &>' ( ?@

?@i

?@: change in outputB ?@i : change in input

Example ":

,he resistance value of a latinum Cesistance,hermometer changes when the temperatureincreases. ,herefore; the unit of sensitivity forthis e*uipment is hm/9+.



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,ensitivity

&ar#at#'n '( t)e *)$s#+a, -ar#a,es

Most sensitive


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Example -:

ressure sensor A with a value of - barcaused a deviation of " degrees.

,herefore; the sensitivity of thee*uipment is $ degrees/bar.

Sensitivity of the whole system is &' (" x - x E x .. x n

1 . /0i0o


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Example:

+onsider a measuring system consisting of a transducer; amplifierand a recorder; with sensitivity for each e*uipment given below:

,ransducer sensitivity .- mF/9+

Amplifier gain -. F/mFCecorder sensitivity $. mF/F

,herefore;

Sensitivity of the whole system:

&' ( " x - x E ( .- mF x -. F x $. mF

9+ mF F

( -. mF/9+


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Example :

,he output of a platinum resistance thermometer&C,D' is as follows:

+alculate the sensitivity of the e*uipment.

Answer :

Draw an input versus output graph. Grom that graph;the sensitivity is the slope of the graph.

> ( ?@ graph ( &H!-' ohm ( - ohm/9+?@i slope &-!"' 9+

nput#2!$ )utput#)hm$

3 3

133 .33

.33 433

/33 533

433 633


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/. 0EA0 SPACE 0EA0 !AN0

Defined as the range of input reading when thereis no change in output &unresponsive system'.

Dead Space

)utput*eading

Measured7ariables

- +



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. RESOLUTION

,he smallest change in input readingthat can be traced accurately.

Iiven in the form J% of full scale&% fs'K.

Available in digital instrumentation.



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1. THRESHOL0

1hen the reading of an input isincreased from Lero; the input readingwill reach a certain value beforechange occurs in the output.

,he minimum limit of the input readingis JthresholdK.



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0YNAMIC CHARACTERISTICS

Explains the behaviour system ofinstruments system when the inputsignal is changed.

Depends on a few standard inputsignals such as Jstep inputK; JrampinputK dan Jsine!wave inputK.


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Step )nput

Sudden change in input signal from steadystate.

,he output signal for this ind of input isnown as Jtransient responseK.

nput

Time


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Camp )nput ,he signal changes linearly.

,he output signal for ramp input isJramp responseK.

nput

Time


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Sine!wave )nput

,he signal is harmonic.

,he output signal is Jfre*uency responseK.

nput

Time


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*esponse time

)ne 'ould lie to have ameasurement system 'ithfast response"

n other 'ords& the e8ect ofthe measurement system onthe measurement should be

as small as possible"


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EAMPLE OF 0YNAMICCHARACTERISTICS

Cesponse from a -ndorder instrument:)utput

100%

90%

10%

trTime


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EAMPLE OF 0YNAMICCHARACTERISTICS

Cesponse from a -ndorder instrument:

". Cise ,ime & tr '

,ime taen for the output to rise from"% to 2 % of the steady state value.

-. Settling time &ts'

,ime taen for output to reach a steady

state value.

, f


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,ensor Performance!haracteristics

Trans(er Fun+t#'n5

The functional relationship bet'een physical input signal and electrical outputsignal" 9sually& this relationship is represented as a graph sho'ing therelationship bet'een the input and output signal& and the details of thisrelationship may constitute a complete description of the sensorcharacteristics" or e;pensive sensors 'hich are individually calibrated& this

might tae the form of the certied calibration curve"Sens#t#-#t$5

The sensitivity is dened in terms of the relationship bet'een input physicalsignal and output electrical signal" The sensitivity is generally the ratiobet'een a small change in electrical signal to a small change in physicalsignal" As such& it may be e;pressed as the derivative of the transfer function

'ith respect to physical signal" Typical units : &',ts6e,-#n" A Thermometer'ould have


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A++ura+$5=enerally dened as the largest e;pected error bet'een actual and idealoutput signals" Typical 9nits : >elvin" ,ometimes this is ?uoted as a fraction ofthe full scale output" or e;ample& a thermometer might be guaranteedaccurate to 'ithin @ of ,) #ull ,cale )utput$

H$steres#s5

,ome sensors do not return to the same output value 'hen the input stimulusis cycled up or do'n" The 'idth of the e;pected error in terms of themeasured ?uantity is dened as the hysteresis" Typical units : >elvin or of,)

N'n,#near#t$ 8'(ten +a,,e9 L#near#t$:5

The ma;imum deviation from a linear transfer function over the specieddynamic range" There are several measures of this error" The most commoncompares the actual transfer function 'ith the best straight lineC& 'hich liesmid'ay bet'een the t'o parallel lines 'hich encompasses the entire transferfunction over the specied dynamic range of the device" This choice ofcomparison method is popular because it maes most sensors loo the best"

, P f


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N'#se5All sensors produce some output noise in addition to the output signal" Thenoise of the sensor limits the performance of the system based on the sensor"Doise is generally distributed across the fre?uency spectrum" Many commonnoise sources produce a 'hite noise distribution& 'hich is to say that thespectral noise density is the same at all fre?uencies" ,ince there is an inverse

relationship bet'een the band'idth and measurement time& it can be saidthat the noise decreases 'ith the s?uare root of the measurement time"

Res',ut#'n5

The resolution of a sensor is dened as the minimum detectable signalEuctuation" ,ince Euctuations are temporal phenomena& there is somerelationship bet'een the timescale for the Euctuation and the minimum

detectable amplitude" Therefore& the denition of resolution must includesome information about the nature of the measurement being carried out"

!an9;#9t)5

All sensors have nite response times to an instantaneous change in physicalsignal" n addition& many sensors have decay times& 'hich 'ould represent

the time after a step change in ph sical signal for the sensor output to deca

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