A Processfor the Analysis of ‘thePhysics of Measurementand
Determination of MeasurementUncertainty in EMC Test Procedures
Edwin L. Bronaugh
EdB” EhK Consultants
10210 PrismDrive
Austin, Texas 78726-1364
USA
John D. M. Osbum
EMC Test Systems,LP
2205 Kramer Lane
Austin, Texas 78758
USA
Abstract - The coming application of uncertainty to EMC
DISCUSSIONOF THE TECHNICAL ISSUE
measurements
is described,and the terms are defined. ‘Ihe traditional
Uncertainty Described
conceptsof accuracyandprecisionare translatedto uncertainties,andthe
impact on EMC measummentsand the interpretationof results are
Uncerta* is a combiuationof the traditional measuresof test
described.The development
of actualuncer&intiesfor EMC measurements perknance. All of the abovementionedelementsare containedin one
is explainedandsuggestions
for improvinguncertainties
areincluded.
parameter.This parameteris a statisticalmeasureof test results,and it is
different than au absolutestatementof accuracy. IS0 Guide to the
INTRODUCTION
expressionof uncertaintyin measurement
[I] (refisrredto as the Guide in
A statementof uucertaintywill be requiredin future EuropeanUnion the rest of this paper)makesthe point that the real value of a measurable
(ELI)EMC submissions.‘Ihe fmal tbrm hasnot beendetermined,
however quantitycan neverbe known exactly,but can only be e&mated. This is
hecausethe deviationi+omidealof the measurement
Won
is also
oneiuterpretaticnmay havesign&ant impacton EMC testiug. Not only is
an uuhwn. The Guide describesaccuracyas a qualitativeconceptand
a statementof uncertaintyin the future for EU EMC submissions,
but it is
proposesuucertainty,which can be e&matedwith given probabilities,as
begkiug to appeariu US labomtoiy accmdkdiou programs,e.g., the
the qrrantiWvedescriptionof the variabilityofthe measuredvalue.
NVLAF 15O-seriesof handbooks. And, it is in other internatlo~l
accreditationprograms,e.g.,IS0 Guide25. Sooneror later, all EMC test
Determinatton of Uncertainty
lahmtories will haveto kucwthe uncertaintyoftbeir measuremeatts
and be
Methodsof determiningmm&a&y are discussedin the IS0 Guide,
preparedto report it almrg with test data and certiticatiou reports.
which containsthe world-wide(includingthe US) agreedupon methods.
Subcomm&e A of the CISPR has a standardsdevelopmentproject in
Thesemethodsaremorecomplexthanthe existingapproachusedin the US
progressto developan iutemationalstandardfor determining,stating,and
far EMC measuremsnts.
So fir only onecountryhaspublisheda definitive
applyinguuoutknty in EMC measurements.
standardfor applyingthe Guidesp&icaUy to EMC measurements.
Tkzditional and Current US Practice
In thesemethods,each elementin an EMC test is evaluatedfor its
contributionto the measurement
mcertaiuty. Au EMC test may comprise
Thepracticein the US derivesfrom the historicalUS approachto EMC
measuremeuts,
e.g., MR.-STD-4611462.ln thesestandards,measumment an antenna,a signalcable,a spectmmaualyzeror radio-noisemeter,a data
collecticcdevice(e.g., a computeror a plotter), and au operator. The
imtnmmts were requiredto maintaina measurement
accuracyof ti dE in
antenua is calibrated andthus has a calibrationuncertaintyin its traceability
amphde and zt2 % in frequency. Followiugthis idea, US practicehas
to a m&ma1 standard. lhe sigualcableloss has beenmeasuredwitb an
hem tc makea statementof measurement
quality basedon deli&ions of
ttttendantuncertainty.Iltespectmmanalyzerhasbeeucalibratedandhes
precision,repeatabii, and measurement
accuracy. Currentdafhitims of
been fbuud to be within its manutkhner-specifiedtolerances or
termsusedin this paperarecollectedat the endofthe paper.
Precisionwas usuallyffied asthe numberof correctdigitsiu a value, uncertaiuties.The data collectiondevicehas also beencalibratedin some
e.g., a numbernmm was said to be preciseto the third decimalplace. way andhas an uncertaintyassociatedwith it. The hmnanoperatoris the
Repeatabilitywas usually defined as the variability of successive most d&cult elementof the EMC test to evaluatefor uncertainty;the
measurements,
but was oflen not stated munerically. Measurement standardsandguidesdo not attemptto estimatethis. The actualprocessof
accuracywas a statementof absolutes,i.e., measuredvaluewithin +x dJ3 estimatingandcombiningtheseuucertaintiesis discussedlaterin this paper.
of true value.
Impact of Expnakd Uncertainty Requirement
Determinationof compliancewith a specificationlimit was a statanert
The expandeduncertaintyis appliedto all EMC measuremeuts,
both
or showingthat the measuredlevel was at or belowthe specificationlimit,
emissionsand immuuity,but the applicationsare differ&. Taking the
i.e., beas 5 Alimit.
applicationapproachespousedby NAMAS and others,the measuredlevel
Future EU MeasurementRequirement
plusthe expandeduncertaintymustbe at or belowthe specificationlimit, if
oueis to statethat the EUT complies.‘Ibis impliesmoreEMC suppression
In the htnre, iuternationalstandards,includingthose of the EU, will
requirea statementof expandeduncertatnryto be includedwith every for “strong”signalsand increasesthe cost of EMC compliance,but it
the probabilityof sati&ctory future audits. Usingthe
measurement.This expandeduncertaintyis derivedfrom the combined markedlyiucreases
standarduuceitaiutksfor all of the elementsinvolvedin the measurement, sameapproachfor immunitytests,the measuredvalueminusthe expanded
and is chosenfor a level of confidence,e.g., 95 %, that the stated uncertaintymustbe at or higherthan the specificationlimit, This implies
moresuppression
of high-levels&al entrypointsand iucrease~ the costof
uncertaintycoversall measured
values.
compliance,but, again,it markedlyincreasesthe probabilityof satisfactory
The greatest impact will be in the method of determinationof
fbtureaudits.
wmpliauce. Currently,therearetwo interpretations
beingmade. That is, a
different approach is being taken by two diflbrent groups. One
UNDERSTANDINGTHE Fwwcs OF EMC MEAHJR!IMENTS
int~rpretaticnis that the measuredlevelplus the expandeduncertaintymust
he equalto or lessthan the speci&tion limit. The other interpretationis
Physical Measurements
that the measuredlevel must be at or belowthe specificationlimit. This
In a typical standardslaboratory, e.g., a NIST laboratory, one
secondinterpretatkmaversthat the specificationlimit includesthe expanded
measumndis measuredmany times and the statisticsof the measurement
uuoertaintyandthat thereneedbeno changeto existingspecificationlimits.
are calculated.The measurement
of physicalquantitiesoften resultsfrom
O-7803-3207-5/96/$5,00 0 1996lEEE
20 or moremeasurements
of the measurand.This numberof measurements
is unreasonable
for EMC comphencedem~stration. Onecan computethe
meen(average)of as few astwo measurements,
but moremeasurements
are
neededto computethe standarddeviation and other statistics’of the
messmend.The staudarddeviationof a sampleof manymeasurements
will
tend to be smallerthan the standarddeviationof a sampleof just a few
measurements.
This is explainedby the central limit theorem.
L&K Measurements
&/c)
u(x~)=J;;
(11, ami sh) = Chn-l- d2
(2)
wherez&J is an estimateof the variability of the averagevalue q of an
input 8mctionof qk The Type A evaluationis usuallynot practicalfor
EMC measurements
of a deviceor equipmentundertest (EUT), but it is
practicalas an wmluatimof some afthe EMC test equipment. Student’s-t
analysis,which is also scauetimes
used in a Type A evaluationof
unwrtaiuty,is coveredat lengthin the Guide.
A rectangulardistributionis impliedfor a measuringinstrumentwhen
its “accuracy”is simplystatedas -kx % or &X dB without any statistical
information, For the user, the true value of a measurement
could be
anywherewithin the rangefrom -x to +x witb equalprobability. When
mkiug a Type B evaluation,the standarduncertaintyu(y) of a rectangular
distributionis ekmatedby dividingthetotal rangeby twicethe square-root
of three,as in equation(3).
In usualEMC measurement
practice,the measurandis measuredonly
once;thus it is impossibleto calculatethe statisticsof the measurement.
The large nFrmberof EMC measurandsdoes not allow the repeated
measurement
of the measuraud,except in limited cases. To adequately
determinethe uncertaintyw-ill require repeatedmeasurements
of some
numberof valuesat any singleftequency.If ouly onemeasurement
is made
at eachfrequency,the usual hatim, neitherthe meannor the standard
deviationcaube calCuIated.Onemust haveat leastthreemeasurements
to
calcnhtethe standarddeviationof the valuesof the measuraud,but more
e+-eU(Y)= (3)
are neededif a reasonable
valueof ~certaiuty is to be established.One
2&
proposedidea is to measurethe levels of the ‘?.opsix” or ‘top ten” If the rangeis symmetrkal,le+l = (e-1 = e, (as in ?x %) the formula
fkquenciesseveraltimes. This.would lengthenthe EMC measurement
process,perhapsunduly. Regulatoryagenciesshouldconsiderthe economic siurplifies to equaticu (4).
burdenthatthis wouldplaceon industry.
(4)
In EMC measurements
a U-shapeddistributionoftenexistsfor VSWRcausedmcertaties. When there is VSWR on a tmnsmissionline, at
ftequmoieswherethe line is resonantthe “error”causedby the VSWR will
Measurement
uncertaintyis determinediu accordaucewith the IS0
he at a maximumdeviationeitherway from zero. Whenmakinga Type B
Guide. The Guide is a very tutorial docummncoutainingexplamticnsfor
the applicaticnof uncertaintyto every cukvable measurement.Several evahaticq the standarduncertainlyu(y) of a U-shapeddistributionis
edmatedby dividingthetotal rangeby twicethe square-root
oftwo, that is,
couutrieshave extractedand publishedi
fkoruthe Guide that
eachofthe standards
authoritiesbelievesto be appropriatefor usewithin its
e+-ecountryor witbin its standardslaboratories, For example:the NAMAS
u(Y)=(5)
2Jz
Executiveiu Englandhas publisheda standard,MS 81 [2]; the National
For mqmmehical values of e, the standard uncertainty is usually
Instituteof Stendardsand Tecbnology(NIST) has publishedTN 1297 [3]
c&dated ftom the worst-case
valueas:
for usewithin NIST, Australiais publishinga standardfor uncertaintyin
EMC measurements,
the EuropeanUnion has createda draft staudard,
prEN 50 222 [4]; the EuropesnComputerManufacturersAmocmtionhas
U(Y)=
publishedECMA-181[5]; and,CISPR Subcomm&eA is working on an
44
intemationalstandardfor uncertaintyin EMC measurements.NIS 81 For example,for mismatchuncertainty,e = 20L.og10(l~Ts~~F~~
dB, where
appliesspecifioallytc EMC mwsnremeuts,
as dcesprEN 50 222.
rs and rL are the reflectioncoetlicientsfor the sourceand load. ‘he
limitiugvaluee is uusymmetrical
aboutthe measuredresult,but it is usually
Fundamentalsof Uncertainty Computation
acceptable
to usethe largerofthe two limits, i.e., 20Loglc(l-]r&r~]).
There are two types of evahmtion,i.e., methodsof cakuhition or
The combinedstandarduncertaintyII~ is foundfrom a root-sum-square
of standard uncertuinty. These are calledType A evahmtion additionaccordingto the law ofpropagatirmof uncertaintyas givenin the
determination,
andTypeB evaluation.In Type A evaluation,the standarduncertaintyof a
Guide. For m contributions
this is shownin (7).
measumnd
is calculatedf&u the descriptivestatistics,or sometimes
from a
student’+t analysis,of a seriesof repeatedobservations.For practical
reasons,the standarduncertaintyof a measurandotten must be es&mted
from a knowledge(sometimes
au assumption)of the hind of distributionto
which it belongsor from experiencewith the kind of qua&y being Hardware Issues
evaluated.This is calleda Type B evahmtion.Iu &her words, a Type A
Wheu gather&ginhrmatim with which to computeor estimatethe
evalnatiouis calculatedfrom the statistics of a series of repeated
uucertaiuties,
you may find that the iustrumentation
speciiicationsdo NOT
observaticns,and a Type B evahmticnis determinedon the basis of
wutaiu the informationyou need;or the informalimrcmrtainedmay not be
assmned(or known)distributionsandexperience.
The componentsof uncertaintyevaluationsfor EMC measurements appropriatefor the computations. You must read the specificati~s
information.
geuerallyfall within one of the fbllowiug three distributions: normal carefully,audyou mayneedto contactthe factoryfor adequate
maynot havetheneedediuformation.
(Gaussian),rectaugular,or U-shaped.The normal distributionis the so- Also,someiustnmd manufacturers
called“MI curve”foundin any statisticstext. The rectangulardistribution AnaIysis Steps
is one in which any valuewithin the rangeof the distributionis equally
Oue set of suggested
stepsiu the aualysisfollows, but there may be
likely. The U-sbepeddistributionis one in which most of the valuesare
morethanwe way to proceed.
clusteredat bothendsof the rangeof the distribution.
1. Define the speci$c .&UC measurement. Use the standardthat
The normal distribution implies a Type A evaluation. In this
A simplegeneric
determination
ofthe uncertainty
evaluation,severalmeasurements
are madeofthe measuraud,
andthe mean governsthe measurement.
and standarddeviationare computed.The standarddeviationof tbe mean of a laboratory is not acceptable;each specific test set up must be
evah@ed. Drawablochdiagmmwhichshowsallofthetest
valueof a numberof measurements
is the measurement
uncerta&y and is
imtnmmdon iu the system,includingcables,groundplanes,enclosures,
computedusingoneof the severalversionsof the well knownformulaefor
oranythingelsewhichcouldhaveauefktonthe~.
standarddeviaticmof themean(1) andstandarddeviationof the sample(2),
Determined per S&nab&
2. IdenhjS)the equipment which will “drive” the uncertainfy of the
measurement. The uncertainty of cablecalibrationis oftenoverlooked,as
is the uncertaintyof preamplifiercalibrationin emissions
measuremeuts.
If
a directionalcouplerandpowermeterareusedto monitorau immunitytest
signaI,their characteristics
will affectthe uncertaintyof the measurement,
while the uncertaintyof the power amplifiergain or the signalgenerator
outputwill not. Gn the otherbaud ifthe signalgeneratoroutputlevel is
usedto determinethe test signallevel,the0the uncertaintyof the signal
generatorandeveryotherelementin the chainwill aBbctthe uncertaiutyof
the measurement.
3. Assignment of individual uncertainties. After identifying the
elementsin the test set up that will a&ct the uncertainty,individual
uncertaintiesmust be computedor assignedfor each of them. From
speciticatious,information about the instrumsnt, and/or experience,
determiuethe variabilitiesor “errors”,the VSWReffects,etc. Decidefor
eachonewhat is the likely distributionand if the evaluationis Type A or
Type B. Calculateor estimatethe uncertaintyor uncertainties
which each
elementcontributesas suggested
above.
4. Combine indivtdual uncertainties to j?nd the combined stan&rd
by square-root
ofthe smn
uncertainty. Combinethe individualuncertainties
of the squaresaddition(RSS). For example,if therewerethreeiudividual
uucertainties,the combinedstandarduncertaintyu, would be found as
shownin (8).
Notethat thepositivesquare-root
is usuallyusedfor uc.
5. Compute the expandeduncertainty. The expandeduncertainty U is
usedtoestablishanestimateofthe~d~~thatthetruevalueofthe
measurandlies somewherewithin the span of uncertaintyarouud the
measuredvalue y, i.e., the true valueY = y f U. The expanded
uncerktty
q., wherethe coverage
factork is assigned
a valueasfollows:
a. R = 1, (+l a): 3 68 % of all measurements
fall withiu +-V;
b. k = 2, (S a): = 95 % of all measurements
fall within &V; and,
c. k = 3,(ti o):):99%ofallmeasurements&llwithinfU.
Most standardschoosek = 2 for a 95 % confidence
that the true value of
the measurand
will be within(or coveredby) thespanreported.
is
U
=
k
l
Completing the Evaluation
INTERPRETATION
OFUNCERTAINTY
DATA
Internationalstandardshaveusedstatisticalmethodsto determine
passfail criteriafor a longtime. The so-calledSO/SO
ruleor method(seeCISPR
16:1987163)allowse&matingif at least80 % of a producticoofproducts
will have emissionsthat are at or below the limit althoughone or two
samplesof the productionhave emissionsabovethe limit. The student’s-t
distributionis usedto evaluatesix samplesat the beg&ringof production.
On the basisof thesesix samples,the evaluationdetermines
with an 80 %
confidence
if at least80 % ofthe productionwill satisfythe limit.
In the past mostEMC testersin the US thoughtin termsof accuracy,
error,precision,andresolution.Theybelievedwhatthe standardssaid,that
is, the instnunentation
was requiredto havea certainaccuracyanda certain
precisionor resolution. If the in&mm& manufacturercertifiedthat its
insmuneaaation
metthe requirementa,
the EMC testeracceptedat tke value
a measuredlevelthat was belowthe limit. This wasthe approachfostered
by the milky standardsand by the earlier CISPRpublications. Then
EMCtestersbegautodiscoverthatthesameEUT measuredat several
dii3mat laboratoriesproduceddifkent results;not slightly diiferent,but
widelydiftbrsnt- oftenby 6 dF3,10 dl3, 12 dB or more! This usheredin an
era of concernfor accuracyand repeatabilityof measurements
which has
migratedto uncertaintyand reproducibilityof measurements.
Becausethe
true valueof a measurand
canuotbe known,the accuracyof a measurement
ofthat measmaud
cannotbe known. The useof a stat&&l approachwas
only a matteroftime, sincemeasurement
uncertaintyis statisticalin nature.
For years engineersand technicianswho testedequipmentrealizedthat
measurement
“error”seemed
to becomelargeror smallerfrom timeto time.
‘hey werejust eqeriencingthe randomnatureof uncertainty.
A statement
of uncertaintymeansthat a certainpercentage
of measured
valueswill fall within specifiedbounds;or that with a certaincoufidence
the
true valueof the measurandfalls betweenupper and lower boundsaround
therneasuredvalue.IftheexpandeduncertaiutyofatestislOdI3&=2),
onecanbe95%con6~thatifameasuredvalueislOdBbelwthe
spci6cationlimit,thetrue valuewill be at or belowthe limit. Thereis ouly
a 2.5 % chancethat thetrue valuewill be abovethe limit. 100% - 95 % =
5 %, but only oue of the two tails of the distributionis positive,thus the
above-limitprobabilityis only 5 % + 2 = 2.5 %.
VWILITY
Applythe developedexpanded
uucertaiutyto the measureddata. Note
that Uwill mostlikely vary with frequency,audthat U can be muchlarger
than expected,e.g., a rt5 dB or f10 dB for radiatedemissionsat 30 MHz
unlessgreatcarehasbeantakeuto reducethemeasurement
uncertainty.
NAMAS,inNISSl,andotherstakethepositionthattodeclarethatthe
EUT is satisktory, the measured
emissionvaluemustbe at leastLr below
the specificationlimit of themeasmemeut
standard.HoweverprEN so 222
disagreeswith this approach,statingthat the rmcerukty (I specitiedin
iuternationalstandards,e.g.,CISPR16,is built into the limit andthus does
not needto be addedseparately
to the measured
results. The outcomeof
this disagreemmt
remainsto be seen.
OFUNC~TAIJ~TY
DATA OVERFREQUENCY
Eledromagneiic propagationconditionsin the test facility vary with
fkequencyandfrom EUT to EUT. This variabilityis almostimpossibleto
predict mathematkahy,but must be estkted from judgmentbasedon
experience.An EUT may be viewedas a cokctiou of electricandmagnetic
dipolesof randomorientation.Generallythesedipolesare not spacedand
phasedinsuchaway~theyhavegain,buttheircambinedeffectscreate
a dipoleradiationpatternwhosedirectionand waveimpedance
vary widely
overthe typical test frequencyrange. Certainly,in the vicinity of 1 GHs
andhigher,someEUTs exhibitgaingreaterthan a dipole,but this is not a
lmiversaJ
chara~stic.
The measurement
antennaperformance
variesover its fiequeucyrange.
Its VSWR is higherat the bandedges,andita coupliugto the groundplane
SOURCESOF UNCERTAINTYDATA
varies over the fkquency baud. Groundplane couplingcan a%bctthe
Thereare severalsourcesof dataon the uncertaintyof instrumeutation VSWR, which iudirectly affects the antennacalibraticq and cau also
andaccessories
usedin EMCtesting. Thesesourcescan be groupedunder directlyaffectthe antenuacalibration,Most of this efkot is includedin its
manutkXurer’sinformation,c&brat& data, measurement
of component calibrationin a SOa system,provideda calibrationmethod,e.g., the
uncertainty,previousexperience,
and judgmentbasedon otherdata. The StandardSiteMethod[7l, which forcesthe calibrationgeometryto be the
most commonsourceis the manuikturer, howeverthese data usually sameas the measmmat geamebyis used. Even so, the calibration
require a Type B evaluationbecausethey appear to come from a uncertaintywill be larger near the baud edges. When the calibration
rectangulardishibutiou,e.g.,“accuracy”statedas kx %. The next most geometryis suchthat the resuhingantennafactorsare nearfree space,the
unnmon sourceis calibrationdata suchas that providedfor an antenna. calibration uncertainty will be c4-mhnt with the iustmmeutatim
The distributionof calibratim~data is usuallyrectangular,but it can be uncertainty;but, the uncertaintyof the measuredlevel is greaterwheuthe
geometry.obtainingthis dlsailed
normalor someothertypeof distributicn,dqmdiug on how it is stated.In autennaisusediuatypicalmeasurement
somesituatimsau instrumentation
component
or accessory
is subjected
to a uncertaintydata is generallynot cost effbctive;especiallyfor antenuas
for eachtesttkquency.
programof measurements
aimedat dekmking its uncertainty,i.e., a Type whichmustbe readjusted
Automaticncanbe both a baneanda boonfor EMC testiug. It creates
A evaluaticn. In somecases,the uncertaiutymust be estimatedfrom
camplimticus,such as more test setup complexityand possiblymore
experience
or judgment.
contributionsto uncertainty.It hasthe capacityto producemorebad data
Easter,so it requiresmuchmoreattentionf&u boththetest engineerandthe
testoperatortothewaythetatissetupandperformed.Gntheotherband,
247
it allows faster, more consistentmeasurements
which are less likely to
containblundersthan are manualmeasuremeuts.Automationalso can
provide the data to make better statistical estimatesof measurement
uncertaiuty.
individualunitsproducesthreeindividualuncertainties
which add up to 43
timesthe individualuncertainties.But, calibratingthemtogetherproduces
only oneuucertaiutyof magnitudeapproximatelyequalto eachof the three
individualuncertainties.
Avoid Type B evaluationsby doingyour own repeatedmeasuremeuta.
‘Ilms insteadof an estimatedrectangularuncertainty,the uncer&ainty
becomes
normal(Gaussian).
EXAMPLE UNCERTAINTY
EVALUATION
Au exampleof a typical uncertaintybudgetis shownin Table 1. This
budgetis for verticallypolarizedradiatedemissionsmeasurements
at a 10 m
CONCLUSIONS
distanceusing somelikely valuesof uncetiiuty taken from NIS 81 [2],
Uncertainty
and
expanded
uncertaintyare in your future. ‘Theway
appendixII. Table 1 doesnot takeinto accountthe e&c& of ambid noise
andthe repeatabilityofthe ELJT. Onecouldarguewith someof the values expandeduncertaintyis to be appliedhas yet to be debzmiued. If not
of individual~certaiuty givenin the table. when makingsucha budget, handledcarefully, uncertaintycan easily becomea numbersgame for
andinstrumentmauufacturers.
alwaysusevaluesof uncertaintythat are kuowuto be true or are the best commercialEMC testlaboratories
estimatespossible Figure 1 showsa block diagramof the uucertaintycontributingelementsfor Table 1.
Beginnow to considerthe impactof uncertaintyon your measurement
cperation. Obtainand studycopiesof the IS0 Guide, TN 1297,and NIS
8 1. Ratherthaukwing the measuredvalueplus expandeduncertaintyplus
a companymargin at or below the specificationlimit, considerusing a
coveragefactor k = 3 so that only the measuredvalue plus expanded
uncertaintymustbe at or belowthe specificatiouiii.
Or, hopethat the
prEN 50 222 approachwins.
SUMMARY
The requirementfor the inclusionbf expandeduncertaintywith each
mwsuremantinanEMCtestofanykind,isonthetimehorizon.
This
requiremeztt
will impactthe EMC comm&ty iu severalways,but overthe
longerterm, in a very positivemanner. It will improvethe quality of
c.ompuancemeasurementa.
‘Ihe authorswish to thaukEMC Test Systems,LP, and EdBTMEMC
Consuhauts
for supportiu thewriting andprese&tion of this paper.
viousassessment
of s(a)
from5 repears;
only 1
-C!ES
[l] IS0 : 1993,Guide to the Expression of Uncertaintyin Measurement.
[2] NIS 81 : 1994,The Treatment of Uncertainty in EMC Measurements.
NAMAS Executive, National Physical Laboratory, Teddiugtou,
Middlesex,TWl 1 OLW,England.
[3] NIST TN 1297: 1994,Guidelinesfor Evaluating and Expressing the
Uncertainty of NIST Measurement Results, by Barry N. Taylor and
ChrisE. Kuyatt.
[4] prEN 50 222 : Sep. 1995,Standardfor the evaluation of measurement
Antenna
resulk%taking measurementuncertainly into account.
[5] ECMA-181 : 1992,Uncertain@ of Measurement as Applied to Type
Approval of Products, EuropeanComputerMarmfWwersAssociation.
[6] C.I.S.P.R.16 : 1987,specification for radio inte@rence measuring
apparatus and measurementmethodr, $9, p 81.
[7] ANSI C63.5 : 1988, American National Standardfor electromagnetic
L
TestSite
Figure 1. Block Diagram of Test for Table 1 Analysis.
compatibility - radiated emission measurements in electromagnetic
interference (IEM4 control - calibration of antennas. [Extensively
TIJEHUMANELEMENTINMEASUREMENTS
A concentrating
humanoperatorcan adaptto measurement
conditions
in “real time” thus producingthe best data. An inattentiveoperator
producesthe worst data, usually in the form of unrepeatableor
umeproducibleresults. Automationof measuremeuts
can reduce or
eliminatethe bad data, if the automatingsoftwareis well written, but it
makesthe test complexitygreater,createsmore individualcontributorsto
uncertainty,and takesmore plarmtngand setuptime. However,it allows
more measurermarts,
improved statistics, and measurementsby less
sophisticatadopemtors.
MANAGINGUNCERTAINTY
VALUES
Calibratesimplein&tune& togetherto produceonetmc.&a&y value.
For example,calibrating a cable plus a preamplifierplus a cable as
248
revisedversionto be publishedin late 1996.1
DEFINITIONS
FromIS0 Guide to the exuressionof uncertain@ in measurement
Uncertainty (of measurement):
1, A parameter,associated
with the resultof
a measurement,
that characterizes
the dispersionof the valuesthat could
reasonablybe attributedto the measuran&2, the spreadof valuesaboutthe
mwsnromentresult withiu which the value of the measuraudmay be
expectedtobefom3,a measureof the possibleerror in the e&mated
valueofthe measuIsmd
asprovidedby the resultof a measuremeut.
Standard uncertain@: unwtainty of the result of a measurement
expressed
as a staodarddeviation.
Tvpe A evaluation (of staudarduncertainty):methodof evaluationof a
standardunwrtairdyby the statisticalanalysisof a seriesofobsenations.
.
Type B evaluation (of standarduncertaiuty):methodof evaluationof a
standarduncertaintyby meansotherthanthe statisticalanalysisof a series
of observations.
Combined standard uncertain@ standarduncertaintyof the resultof a
measuremmt
whenthat result is obtainedfrom the valuesof a numberof
other quantities,equalto the positivesquareroot of a sum of terms,the
termsbeingthe vaiaucesor covariauces
of theseotherquantitiesweighted
accordingto how the measurement
result varies with changesin these
quantities.
Expanded uncertatn@ quant@ de6ning the intervalaboutthe resultof
a measurement
within whichthe valuesthat couldreasonablybe attributed
to the measurand
maybe expected
to he with a highlevelof confidence.
Coveragefactor: numericalfactor usedas a multiplierof the combined
standarduncertaintyin orderto obtainan expanded
uncertainty.Note - A
coveragefactor,k, is typicallyin the range2 to 3, but may rangelower for
specialpurposes.Whenk = 2 the con6dence
levelapproximates
95 %.
From the VJM - International vocabularv of basic and peneral terms in
metrolon kuntained in the IS0 Guide)
body or substance
that
Measurable quantity: attributeof a phenomenon,
may be distiuguished
qualitativelyanddetermined
quamitatively.
Value of a quantity: magnitude of a specific quantity generally
expressed
as a unit of measurement
multipliedby a number,e.g.,546 mm,
2.5 W, -120 dB(pV/m)
True value of a quant@: valueperfectlyconsistent
with the defhrition
of a givenspecificquantity.Note-true valuesareby natureindetermiuate.
Conventional true value of a quantity: v&e attributedto a specific
quantityand acceptedsometimes
by convention,as havingan uncertainty
appropriatefor a givenpurpose,e.g., Avagadroconstantis (6.022 136 7
f0.000003
6) x 1023 mol-1.
Measurement: set of operations
havingthe objectof determiuinga valueof
a quantay.
Principle of measurement: scientific basis of a method of
tIWdL5Wement.
Method of measurement: logical sequence
of operaticms,
in generic
tams, used in the perfbrmanceof measurements
accordingto a giver
principle,e.g.,substitutionmethod,dif&r&ial method,null methodetc.
Measurementprocedure: set of operations,in specific terms, used in
the performanceof particularmeasurements
accordingto a givenmethod.
Note - usually in sufhcientdetail to enablean operatorto carry out a
measurementwithout additionalinformation.
Measurand: Specific quantitysubjectto measurement.
Influence vntiry: quantitythat is nat includedin the specikationof
the measurandbut that nonetheless
affectsthe resultof the measurement,
e.g., frequencyin the measurement
of an alternatingelectricpotential
di.Rerence,
or temperatureof a micrometer
usedto measurehmgth.
Result of measuremenf: value attributedto a measurand,obtainedby
measurement.
Notes- 1 whentheterm “resultof a measuremmt~
is used,it
shouldbe ma& clear whetherit refersto the indication,the uncorrected
resul&or the correctedresult,andwhetherseveralvaluesare averaged;2 a
complek statementof the result of a measurement
includes&rmaticm
abouttheuncertaintyof measurement.
Uncorrecfed result resultof a measurement
beforecorrectionfor the
assumed
systematicerror.
Corrected result: result of a measurement
aftercorrectionfor assumed
qdematic error.
Repeatability (of resultsof measurements):
closeness
of the agreement
betweenthe resultsof successivemeasurements
of the samemeasurand
carriedout subjectto all of the followingconditions:
the samemeasurement
249
procedure;the sameobserver;the samemeasuringinstrument,usedunder
the samewnditions;the samekxation; repetitionover a short period of
time.
closenessof agreement
Reproducibility (of resultsof measurements):
betweenthe resultsof measurements
of the samemeasurandwherethe
measurements
arecarriedout underchangedconditionssuchas:principleor
m&hod of measuremmt;observer; measming instmment; location;
wnditionsof use;time.
Uncertainty (of measuremtmt):
a parameter,associated
with the resultof a
measurement,
that characterizes
the dispersionof the valuesthat could
reasonablybe attributedto the measurand.Note - the uncertaintymay be
arrivedat from eithera TypeA or TypeB evahmt.ion.
betweenthe resultof
Accuracy of measurement: closenessof the agreement
a measuremmt
anda true valueof the measurand.Notes- 1 accuracyis a
qualitativeconcept- the accuracyof a measurement
is indekxmkte; 2 the
term “precision”shouldnot be usedfor “accuracy”.
emmt): resultof a measurememt
minusa true valueof
Error (of measur
the measurand.Notes - 1sinceatruevahrecannotbedetermined,in
practicea conventionai
true value is used,if available;2 the quantityis
sometimescalledabsoluteerror of measurement
when it is necessaryto
distinguishit fkomrelativeerror.
Relative error (of measurement):error of &asurement dividedby a
true value of the measurand. Note - since a true value caunot be
determined,
in practicea convmtionaltrue valueis used if available.
Random error: result of a measurement
minusthe meanresult of a
ts of the samemeasurand.Note large numberof repeatedmeasuremen
carriedout under“repeatability”
cemhtions.
Systematic error: mean result of a large numbfx of repeated
d minusa true valueof the measurand.
measurements
ofthe samemeasuran
Notes - 1 carriedout under “repeatability”conditions;2 like true value,
systematicerror and its causescannotbe completelyknown; 3 for a
mmsuriugirshurnent,see“bias”(VIM 5.25).
Correction: valuethat, addedalgebraicallyto the uncorrectedresultof a
measurement,
compensates
for an assumedsystematicerror. Notes- 1 the
wrrdon is equalto the negativeof the assumedsystematicerror; 2 some
s@ematic
errors may be e&mated
and compensated
by applying
appropriatecorrections,but sincethe systematicerror can& be known
perfectly,the wmpmsationcannotbe complete.
Correction factor: numerical factor by whichthe uncorrectedresultof a
measuremmt
is multipliedto compensate
for an assumedsystematicerror,
e.g., in EMC measurements,
the loss in a signal cable which is usually
measured
andstatedin decibelsandaddedto an uncormctedresultwhichis
also measuredand statedin decibels. Note - sincethe systematicerror
cannotbe knownperfectly,the tzmpeadon cannotbe complete.
From IEEE Std 100-1988
Precision: the quality of being exactlyor sharply defmedor stated,a
measureof theprecisionof a represer&tionis the numberof distinguishable
alternatives
from whichit was selected,
whichis some&es indicatedby the
number of signi.6cantdigits it contains. mere is almost a page of
defmitionsfor precision;thesewerethemostgeneraldefmitions.]
Resolution: 1 the least value of the measuredquantity which can be
distinguishad; 2 the degree
to whichnearlyequalvaluesof a quantitycanbe
discriminated;
3 the degreeto which a systemor a devicedistinguishes
betweendues of a qmmtity. were are two pagesof deiiniticmsfor
resolution; these were the de5iticms most aligned with EMC
measuremmts.]