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UncertaintiesUncertaintiesUsing & CalculatingUncertainties for Electrical
Measurement
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementAll measurements, even the most accurate,
have an unknown inaccuracy or doubt.
The is known as the UCE!TA"T#As there is always an uncertainty with any
measurement we need to estimate this
amount. $e also need to calculate our
confidence in the estimate of uncertainty, which ishow sure we are that the true value is within the
uncertainty we have estimated.
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementAs an e%amle we may measure ' (olt and
be )*+ confident that we are within 'u(
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementUNCERTAINTY vs. ACCURACY
There is no connection between these terms.
Uncertainty is urely the unknown in anymeasurement.
Accuracy or Tolerance is the difference
between the desired value and the actualmeasured value.
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementE%amle
$ith a digital watch with ' second resolution
this resolution will limit the best uncertainty
to which you can tell the time -ie. ' second,
however the watch itself may only be
accurate to a few minutes.
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementThere are many sources of uncertainty in any
measurement which need to be combined
using statistical techni/ues to give a total.
0ifferent tyes of uncertainty need to be
treated differently to obtain an accurate
estimation.
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementTo calculate uncertainty you must first
identify all the sources of error, estimate the
si1e of the contribution from each source and
also decide on the tye of uncertainty for
each source.
There are two tyes of uncertainty Tye A 2 3ased on using statistics
e.g. reeated readings
Tye 3 2 3ased on other factors
e.g. manufacturers secifications
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Sources of Uncertainty inSources of Uncertainty in
Electrical Measurements.Electrical Measurements. "morted Uncertainty0rift of reference instrument
Temerature effects 4ead and thermal errors -0C volts !ounding errors due to resolution !eeatability
oise 5elf heating of high current shunts
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Imported UncertaintyImported Uncertainty
"morted uncertainty is taken directly from the
certificate issued by the laboratory which
calibrated the reference instrument. The robability distribution is 67!MA48
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Drift of reference instrumentDrift of reference instrument
0rift of reference instrument can be either taken form
historical data on the instrument or from the manufacture
secification for stability. "f the drift with time can be
redicted it is ossible to use a corrected figure for the
actual value of the reference with a reduced figure for
drift. 9owever it is more normal to use an 6un corrected8
figure.
The robability distribution is 6!ectangular8.
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Temperature EffectsTemperature Effects
The effect of temerature on many modern instruments is
often very small, and in many cases the instruments
secification covers a band of temerature without any
further addition. 5ome reference standards for e%amle resistors the
Temerature coefficient may be /uite imortant. The
figure for TC can be taken from the manufactures sec or
measured.
The robability distribution is 6!ectangular8.
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Lead and thermal errorsLead and thermal errors
(DC olts!(DC olts! Thermal emf can be difficult to evaluate. $ith a
little care and correct leads it is normal for
thermal EM: to be less than 'u(, or even .*u(
which is a figure often used in calculations.
The robability distribution is 6!ectangular8.
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"esolution of Measurement"esolution of Measurement "t is firstly imortant to understand that there is a big difference
between the resolution of a measuring instrument and that of areference source.
A source, such as a standard resistor may have no resolution at
all, but can still be very accurate, while for a measuringinstrument resolution is essential to achieve accuracy.
"t is only necessary to include measurement resolution in the
uncertainty calculation. ote if a 0MM is used to comare say
two resistors then the resolution must be entered twice.
The robability distribution is 6!ectangular8
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Com#ining UncertaintiesCom#ining Uncertainties "t is normal these days to use a sread sheet, in E%cel, taking a
temlate from M;;.
Use column ' for a descrition of source of uncertainty Use column < for the value of uncertainty usually in m Use column ; for a descrition of tye of =robability distribution Use column > for the divisor, < for a normal dist, '.?;< for rect Use column * for a coeficient used to convert say millvolts to microvolts Use column @ column-divisor % column*-coeff
Use the sum of s/uare to total column @ to get the Combined 5tandard
Uncertainty
To obtain the E%anded uncertainty -B
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Expressing Uncertainty ofExpressing Uncertainty of
MeasurementMeasurementE%amle
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Using $roCal to calculateUsing $roCal to calculate
UncertaintiesUncertainties
=roCal use three key elements to dynamically calculate
uncertainties as the test is run
' A table with imorted uncertainties and calibrator secifications
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Set Up Instrument Spec andSet Up Instrument Spec and
Imported UncertaintiesImported Uncertainties
Use =roset, select instrument Traceability in the file menu. 5elect the "nstrument re/uired 5elect the 6uncertainties button to access the table Enter the data, note default table e%ists for
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Set Up $rocedure TemplateSet Up $rocedure Template
Use =ro5et, select 6laboratory rocedures8 in the file menu. 5elect the "nstrument re/uired 5elect the rocedure sreadsheet temlate say for 0C voltage Enter the arameters to be calculated, note the imorted and
reference secification will always be added automatically. ote the rocedures for the main functions of the calibrator are
"nstalled as default
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Set Up Cali#ration $rocedureSet Up Cali#ration $rocedure
Use =roEdit, edit a rocedure and go to the 6"nstruments8 tab. Check the calibration instrument, lab. =rocedure and
uncertainty line. "f a Transmille calibrator is in use these items will be set
automatically, without having to be selected.
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Cali#rating %n InstrumentCali#rating %n Instrument Use =roCal, run a calibration "nut the reading and select enter the noise flicker in the dro
down bo% dislayed. "f re/uired, click on the UCE!T button to view the
uncertainty calculation.
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&here to 'et More Information&here to 'et More Information
UBA5 -www.UBA5.co.uk
ational =hysical 4aboratory
Transmille 4td -www.transmille.com