Error Analysis and Uncertainty of Capacitance Standards

1 Page 1 NIST Special Publication 250-52 .. NAT'LINST.OFSTAND&TECH m ErrorAnalysisandCalibration UncertaintyofCapacitance StandardsatNIST -35.43 -35.44-- -35.45-- "5 -35.46 > B -35.47 -P s o s o i: -35.49 -f E a. a -35.48 -- -35.... Open at page → 2 Page 2 #heNationalInstituteofStandardsandTechnologywasestablished in1988byCongressto"assistindustryin thedevelopmentoftechnology ...neededtoimproveproductquality,tomodernizemanufacturingprocesses,to ensureproductreliability...a... Open at page → 3 Page 3 NISTSpecialPublication250-52 NISTMEASUREMENTSERVICES: ErrorAnalysisandCalibrationUncertainty ofCapacitanceStandardsatNIST YMayChang ElectricityDivision ElectronicsandElectricalEngineeringLaboratory NationalInstituteofSta... Open at page → 4 Page 4 NationalInstituteofStandardsandTechnologySpecialPublication250-52 Natl.Inst.Stand.Technol.Spec.Publ.250-62,109pages(Jan.2000) CODEN:NSPUE2 U.S.GOVERNMENTPRINTINGOFFICE WASHINGTON: 2000 ForsalebytheSuperintendent ofDocume... Open at page → 5 Page 5 TABLEOFCONTENTS page ListofTables v ListofFigures vii ListofSymbols viii ABSTRACT 1 LINTRODUCTION 1 2.DESCRIPTIONOFSYSTEMSANDMEASUREMENTPROCEDURES 2 2.1Type-2CapacitanceBridgeandStandards 3 2.2Type-12CapacitanceBridge 3... Open at page → 6 Page 6 4.3.1.2 Analysis 24 4.3.2Two-TerminalMeasurementsofHigh-CapacitanceValues 25 4.3.2.1 BasicEquationsofBalance 25 4.3.2.2 Analysis 25 4.3.3Three-TerminalMeasurementsofLow-CapacitanceValues 26 4.3.3.1 BasicEquationsofBalanc... Open at page → 7 Page 7 ListofTables Page Table1.DialCorrectionsoftheType-2Bridge 40 Table2. StandardUncertaintiesinDialCorrectionsoftheType-2Bridge 41 Table3.CombinedUncertaintiesinDialCorrectionsUsingtheType-2Bridgeto MeasureCapacitorsofNomin... Open at page → 8 Page 8 Table14a.SummaryofComponentsofStandardUncertaintiesinMicaCapacitor DialCorrectionsforTwo-TerminalMeasurements 54 Table14b.SummaryofComponentsofStandardUncertaintiesinMicaCapacitor DialCorrectionsforThree-TerminalMeasurem... Open at page → 9 Page 9 ListofFigures page Figure1.BlockDiagramoftheFaradTransferandCalibrationProcessbyUsing theType-2Bridge 66 Figure2a.SchematicDiagramoftheNISTType-2CapacitanceBridge 67 Figure2b.SimplifiedCircuitDiagramoftheNISTType-2Capaci... Open at page → 10 Page 10 ListofSymbols 1.Type-2System aandb In-phaseandquadraturecorrectionsofthe1:1ratio. CjtoCg DialcapacitorsoftheType-2bridge. CjtoCg NominalvaluesofcapacitorsCjtoCg. CjtoCg RealvaluesofcapacitorsCjtoCg. Cg,Cj,&CjjReferenceca... Open at page → 11 Page 11 u^,u^,& Combined,TypeAandTypeBstandarduncertainties. Uand Expandedandtotal(assigned)uncertainties. Fg,Y^,& AdmittanceofC^,C^andc^- YandZ Effectiveadmittanceandimpedanceofthecapacitor,whereY=(1/Z). 2.TheType-12System Cjan... Open at page → 12 Page 12 i?landi?2 ValuesofratioresistorsRjand R^^andRj.2 Contactresistanceofthetwobalances. Standarduncertaintyduetoleadimpedance. Sjjp2andS|jp3StandarduncertaintiesduetocorrectionsofplatesP2andP3. s^^ Standarduncertaintyofexter... Open at page → 13 Page 13 ERRORANALYSISANDCALIBRATIONUNCERTAINTY OFCAPACITANCESTANDARDSATNIST Y.MayChang ElectricityDivision NationalInstituteofStandardsandTechnology ABSTRACT Thisdocumentpresentstheanalysisoferrorsourcesthatcontributetothetotalu... Open at page → 14 Page 14 metrologist. Thecombinedstandarduncertainty,u^,isdefinedasthe"RSS"(root-sum-of-squares) ofbothtypes, as: r 2 , 2-,'/2 where isthecombinedstandarduncertainty,and andWj^areTypeAandTypeBstandarduncertainties,respectively. A... Open at page → 15 Page 15 100Hz,400Hz,and1kHz.TheotheristheType-12bridge,whichisaresistanceratiocapacitance measuringsystemforcalibrationofcapacitorsofnominalvaluesfrom0.001)iFto1^iFat frequenciesof66Hz,100Hz,400Hz,1kHz,and10kHz.Since1992,commerc... Open at page → 16 Page 16 mainlyusedtocalibratemica-dielectriccapacitorsofexposedbinding-postconnectorsintherange from0.001|iFto1|iF.Ingeneral,calibrationofcustomers'capacitors isperformedusingtwo measurements (ata1:1ratiooftheresistancearms)toel... Open at page → 17 Page 17 and areadmittancesof andC^^ ,respectively, r,-isthedialreadingofi dialapplyingvoltagetocapacitor c,-,where0<r,-< 1,in incrementsof0.1, V;istheadmittanceofc,-, • th g-istheeffectiveadmittanceassociatedwiththesettingsofthe... Open at page → 18 Page 18 (8) AssumingE^=lYasthereference,andbythedefinitionof1:1ratio,(E^I E^) -- 1,then: E^=-{l+a+ib), (9) whereaisthein-phasecorrectiontotheratio,and bisthequadraturecorrectiontotheratio. Theerrorsinthein-phaseandquadraturecorr... Open at page → 19 Page 19 10:1(and1:10)ratio,respectively. 3.2DialCorrections TheinternalcapacitorsoftheType-2bridgeareasetofeightthree-terminal aircapacitors,CjtoCg, withadjustabledials,asshowninFig.3.Onesideofeachcapacitorisconnectedtothedetect... Open at page → 20 Page 20 diandc/^^-^j^aredialcorrectionsofC^-andC^^-+j^ ,respectively, /«= 10istheratio,and cj^isthesumofdialreadingsgivingthecapacitancevalueatbalance,fork>i+l. ThebalanceequationforcalibratingC3(whereC3=1pF)withthe10pFreference... Open at page → 21 Page 21 whereVar( t/j )isthevarianceofthedialcorrectionofthethirddial,d^^, s^^isthein-phasestandarduncertaintyinthe1:10ratio,asgiveninEq.(11), 5„isthestandarduncertaintyofthereferencestandard, th r^^isthedialreadingforthe^dial,w... Open at page → 22 Page 22 5„„<7.2X 10"' pF. 3) Table 1givesasetoftypicaldataoftheaveragevaluesandstandarddeviationsofdial correctionsoftheType-2bridgefrom15measurementstakenoveraperiodofoneyear. Measurementrecordsshowthatonlythethreelowestdialsar... Open at page → 23 Page 23 3.3.1VoltageDependenceofStandards Thevoltagedependenceofagroupoften10pFcapacitorswasobservedin [6]bymeasuringtheir capacitanceanddissipationfactorsfrom100Vto200V.Usingtheaveragevaluesofthe measurements, aswellasthesystem... Open at page → 24 Page 24 Therefore,noadditionalerrorsduetofrequencydependenceareincurredexceptforcalibrations performedatfrequenciesotherthan1kHz. 3.3.3HysteresisEffectsinTemperatureCorrectionsofStandards EachNlST-made10pFfused-silicadielectricc... Open at page → 25 Page 25 Therefore,Eq.(23)canbewrittenas: Z= + ( G^./(oV )]+ j0) [ Ij- (C/w^C^ )], (24) Thus,theequivalentequationofadmittance,7=(1/Z)isexpressedas: Y= ((o^C^)/[(Rio)^C^+ )+ jG)C(G)^ Z-iC- 1)], (25) whereYistheeffectiveadmittance... Open at page → 26 Page 26 AG =3.94XlO-'^S<4X 10"'nS Table4givesasummaryoftheuncertaintiesduetoleadimpedanceformeasurementsofvarious nominalcapacitancevaluesatfrequenciesof100Hz,400Hz,and1kHz. 3.3.5UncertaintyintheReferenceStandard Therelativestab... Open at page → 27 Page 27 silicacapacitorinICLisassignedtobe0.72ppm,includingthecomponentsoftransformerratio, dialcorrections,andexternalbridgecomponents. Othercalculationsusingtheoil-bathtype capacitorasthereferencestandardutilizes^^=0.72ppmasth... Open at page → 28 Page 28 2) Sincetheassignedvalueoftheoil-bathtypefused-silicareferencecapacitorintheICLis measuredat1kHz,thereisanuncertaintycomponentof1.6ppmfromitsfrequency dependency,whenusingitasareferencetocalibrateothercapacitorsat100Hz.... Open at page → 29 Page 29 Table11containsthecalibrationuncertaintiesfortwotypesofHFcoaxialaircapacitors.Thelower- valuedtype,withnominalvaluesthatrangefrom1pFto20pF,hasarelativelyflatfrequency responsetoafewhundredmegahertz(seeFig.3inRef12).These... Open at page → 30 Page 30 toprovidecapacitanceandconductancevaluesofthemicacapacitorsbeingcalibratedbytheType- 12bridge. 4.1BasicEquationsofCapacitanceMeasurements Figure5bisasimplifiedschematicoftheType-12bridgeshowingthecomponentsforcapacitance... Open at page → 31 Page 31 tothedialreadingsareobtainedinaccordancewithEq.(36)andwiththefollowingprocedurefor switchingthecapacitors: Atdialreadingr= 0,allfourcapacitorsareconnectedtoarmCD,then Q =50pFand =0;therefore,C^=0. Atdialreadingr= 1,the5p... Open at page → 32 Page 32 4.2.1RatioResistors AccordingtothespecificationsfortheType-12bridge[13],themaximumboundsoferrorinthe1:1 ratioare±30ppm.Thus,accordingtoEq.(4),theuncertaintyintheratioof1:1isestimatedas: =17.3ppm<18ppm, (39) wheres^^isthe... Open at page → 33 Page 33 measurements, respectively. 2) Temperaturevariations Thetemperaturecoefficientsofairandmicacapacitorsare10ppm/°Cand45ppm/°C, respectively.ThetemperatureintheICLisalwaysmaintainedat(23±1)°C.Therefore, themaximumboundsofer... Open at page → 34 Page 34 ^rc^C-^dr+^tp^-^ds+-^tf ) '^nd (43) = (^mr ^+ ^mp ^ + ^ds ^ + '^mf ^ )^ (44) wheres^^and arethecombineduncertaintiesintheairandmicacapacitordials,respectively, whicharealsoincludedinTables13ato14b. 4.2.3ExternalBridgeCom... Open at page → 35 Page 35 twocomponents,whichareestimatedfromeachtypeofmeasurement, as: , 2 , 2X ('/2) "^br^^-^bp +'^bz ) ' (48) wheres^^^isequaltoeitherS)^^^ -^bpS' dependingonwhichplate(eitherP2orP3)isbeing ThesearegiveninTables15aand15d. used.... Open at page → 36 Page 36 Theratioresistorsarealwayssettobeequal,{R^=Rj)sothatEq.(52)becomes: q = ( -C,o), (53) whichistheequationusedtocalculatethevalueoftheunknowncapacitor. 4.3.1.2Analysis TherelationshipamongthevariancesofthetermsofEq.(52)can... Open at page → 37 Page 37 4.3.2Two-TerminalMeasurementsofHigh-CapacitanceValues (0.005^iF<C^^<1^iF) 4.3.2.1BasicEquationsofBalance Measurementproceduresofthistypearethesameasthoseforlow-capacitance values,exceptthat themicadialcapacitorsareneeded... Open at page → 38 Page 38 BysubstitutingEq.(62)and(=i?2)intoEq.(61),itbecomes: Var(q)<(C^s^^f+sJ + , (63) 2 2 wheres^^= +^^^0 • FromEq.(39),theuncertaintycontributedbytheratioresistors,s^^,forthetwo-terminalhigh- capacitancemeasurements is18ppm.(... Open at page → 39 Page 39 whereCj.j=2C^,and =2 aredialreadingsofinternalaircapacitorsatbalancewithC^, connectedtoarmADandtoarmCD,respectively. 4.3.3.2Analysis TherelationshipamongthevariancesofthetermsofEq.(66)canbeestimatedby: Var(q)= C/2)^,,i'... Open at page → 40 Page 40 whereC^jand arevaluesoftheinternalaircapacitorsatbalancewiththeunknowncapacitor, connectedtoarmAD, andC^2 valuesoftheinternalaircapacitorsatbalancewithC ^ connectedtoarmCD, arevaluesoftheinternalmicacapacitorsatthesecond... Open at page → 41 Page 41 measurementsofthesamenominalvalues,exceptthatthecapacitanceoftheplate,P3,is0.006pF, andtheseareestimatedtobelessthan3ppmatfrequenciesof100Hzand1kHz.However,ata frequencyof10kHz,theseuncertaintiesincreasesubstantiallyforh... Open at page → 42 Page 42 q =[i?i/(i?,+/?2)](C^2+C^3) +C/^)[(Cr2-Cri)+(C,3-C,4)L (80) whereCj.jtoCj.4and to Qn3 micadialreadings,respectively,corresponding toeach measurement. Theratioresistorsarealwayssettobeequal =R2),soEq.(80)becomes: Q =(V2)... Open at page → 43 Page 43 measuretheunknowncapacitorofvalueequalto1|iiF.Thecombineduncertaintyinthemica capacitordialreadings,[(Vi)s^],isestimatedtobelessthan16ppm.Theuncertaintyintheair capacitancedialreadings,[(V2)s^.^],isestimatedtobe5ppm.(See... Open at page → 44 Page 44 maintainedat23°C±1°C.Uncertaintiesinunknowncapacitorsduetotemperaturechangesare dependentonthelengthoftimeneededtoperformmeasurementsandtoconnectadditional components. Ifanexternaldecadecapacitanceboxisneeded(suchasinthr... Open at page → 45 Page 45 SimilarmeasurementshavealsobeenperformedonfourNISTstandardsatfrequenciesof100Hz and10kHz,andstandarduncertaintiesoftheirpredictedvaluesarealsogivenintheTables 16aand 16b.TheType-12bridgeisemployedtoperformmeasurementsonm... Open at page → 46 Page 46 where istheconductanceoftheinternalmicacapacitorswithC^connectedtoarmCD, Gj-i istheconductancedialreadingswithoutconnectingC^, Gj.2istheconductancedialreadingswithC^^connectedtoarmCD,and Kgisthedividersetting. Forthecase... Open at page → 47 Page 47 Thisresistanceisconsideredasbeinginserieswiththeinternalcapacitanceofthedecadeswitches. Sincetherearetwoormorebalancesrequiredforeachmeasurement,andresultsarecalculatedfrom thedifferenceofthesereadings,themaximumboundsof... Open at page → 48 Page 48 4.6.4ResidualConductance Accordingto[14],themaximumboundsoferrorduetothelimitofresolutioninresidual conductanceinarmsADandCDarefunctionsoffrequencyandgivenas: ±^g,=±(0.02)// ^S, (93) where±^__arethemaximumboundsoferrordu... Open at page → 49 Page 49 4.7.1RepeatabilityofMeasurements Aspointedoutinsection4.4.1forrepeatabilityofcapacitancemeasurements,therangeofagiven "limit"forconductancemeasurements isalsocontainedinNISTinternaldocumentsforeach nominalvalueofcapacito... Open at page → 50 Page 50 6.ACKNOWLEDGMENTS TheauthorwouldHketoacknowledgethemembersoftheMCOMSubcommittee forCapacitance CalibrationServices;CarrollCroarkin(Chairman),BarryBell,NormanBelecki,AndrewKoffman, andJohnMayo-Wells fortheirvaluablesugges... Open at page → 51 Page 51 "CapacitanceStandardswithPrecisionConnectors,"TheGeneralRadioExperimenter, vol. 41,no.9,September,1967. "MoreCoaxialCapacitanceStandards,"TheGeneralRadioExperimenter, vol.42,no.5, May,1968. W.D.Voelker,"AnImprovedCapacit... Open at page → 52 Page 52 Table1. DialCorrectionsoftheType-2Bridge [Allvaluesarein( 10'^ pF ),exceptnominalvaluesofdials ] DialNo. 1 2 3 4 5 6 7 8 Nominal Value(pF) 1AA 100 1A 10 1 0.1 0.01 AAA1 0.001 AAAA1 0.0001 AAAAA 1 0.00001 4/25/94 5160.1 -... Open at page → 53 Page 53 Table2. StandardUncertainties inDialCorrectionsoftheType-2Bridge [Allvaluesarein(10'pF ),exceptnominalvaluesofdials ] DialNo. 3 4 5 6 7 8 2 1 Nominal ValueCi(pF) 1 0.1 0.01 0.001lE-04lE-05 10 100 MeanValue ofDial Correct... Open at page → 54 Page 54 Table3.CombinedUncertaintiesinDialCorrectionsUsingtheType-2BridgetoMeasure CapacitorsofNominalValuesof1pF,10pF,100pF,and1000pF NominalValue ofCapacitor(pF) 1 10 100 1000 No.ofDialsUsed Routinely 4 5 5 6 AssignedCombined... Open at page → 55 Page 55 Table4. Uncertainties inLeadImpedanceUsingtheType-2BridgetoMeasure CapacitorsatFrequenciesof100Hz,400Hz,and1kHz Frequency 1kHz 400Hz 100Hz NominalValue AC/C AC/C AC/C ofCapacitor(pF) (ppm) (ppm) (ppm) 1 «0.0002 «0.0002 «... Open at page → 56 Page 56 03 (N (U H <u o on N s C^ o (U Uo o.ti ^Z o o k3 o 00 in H CO J3 -o e cd +-> GO «^-( O c/o D > c o c o a, 00 > < OX) ^2 _c §-^I ^%"S to^ ^-a ^— 'on 3 OO C/0 3 (N C3 CQ ~" "O O(N (/2 —T3 3 K3 CQ 3 X3 D- - u CQ os Q H ^d Q... Open at page → 57 Page 57 o •ri M (U DO O 43 1^ I-H c» 3 CO o "C PQ cs 1 (U Oh H <L) :S 1^ CO c T3 r-t N c« in < O "73 -4— • «1-H f1 X w en t3 GO o > o c -I-' a, (D O X 0) > o o o lU 00 o is _c o o5I -ia PL, ^ % a> 3 tL, O —T3 3 O(N —T3 % (U 3 [i... Open at page → 58 Page 58 ^c OUOB §^:g o o o§^ o M3 OS O Om2 %.-S o o O is o o o^ P: ^ §^ 5^ o ^ OS T3 O CO > c o 4—" o X B Cl, CO 0) Id > 5 ^T3 en 3 o o o Io o ,-^o <=>^ o^ o CM o in o OS §5m 3<; IT) OS c O O 3 H U 00 c O i3 o o o ^s^g § °§^^ o—... Open at page → 59 Page 59 —.00 o o o o o S^ ^§5; o— oo p— ; O(N _a % .-5 H U c OX) o o o—00 ^ gs O O5m %"S-ia ^ s< o o o 10 Io ^o o^ S^Oooo o§^o00 o 00 10 00 o 3 m On a 00 o o oPoo o <^o oSo 00 >/-) 00 o C/2o —T3 % (U ^— ' c/5 3 00 c 00 o o o d p... Open at page → 60 Page 60 Table9.ExpandedandAssignedTotalUncertaintiesUsingtheType-2BridgetoMeasure Three-TerminalAirCapacitorsatFrequenciesof400Hzand1kHz (Allvaluesareinppm,exceptnominalvaluesofcapacitors) NominalValueof Capacitors(pF) 0.001 0.0... Open at page → 61 Page 61 Table10.ExpandedandAssignedTotalUncertaintiesUsingtheType-2BridgetoMeasure Three-TerminalAirCapacitorsat100Hz (Allvaluesareinppm,exceptnominalvaluesofcapacitors) NominalValueof Capacitors(pF) 0.01 0.1 1 10to1000 Componen... Open at page → 62 Page 62 Table11.ExpandedandAssignedTotalUncertaintiesUsingtheType-2BridgetoMeasure Two-TerminalCoaxialAirCapacitorsat1kHz (Allvaluesareinppm,exceptnominalvaluesofcapacitors) (Lower-Valued ) (Mid-Valued ) NominalValueof Capacitor... Open at page → 63 Page 63 Table12.ExpandedandAssignedTotalUncertaintiesofUsingtheType-2BridgetoMeasure Two-TerminalCoaxialMicaCapacitorsandOpen-CircuitTerminations at1kHz (Allvaluesareinppm,exceptnominalvaluesofcapacitors) CoaxialMicaCapacitors O... Open at page → 64 Page 64 Table13a.SummaryofComponentsofStandardUncertaintiesinAirCapacitorDialCorrections forTwo-TerminalMeasurements UnknownStandard ()iF) 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0 OlUL/CV.OIrrcU.Vd.lUC3Ol DialCorrection(... Open at page → 65 Page 65 Table13b.SummaryofComponentsofStandardUncertaintiesinAirCapacitorDialCorrections forThree-TerminalMeasurements UnknownStandard ()iF) 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0 StdDev.otrred.Valuesot DialCorrection(... Open at page → 66 Page 66 Table14a.SummaryofComponentsofStandardUncertaintiesinMicaCapacitorDialCorrections forTwo-TerminalMeasurements UnknownStandard (fiF) 0.01 0.02 0.05 0.1 0.2 0.5 1.0 Componentsof StandardUncertainties(ppm) (AtallFrequencies... Open at page → 67 Page 67 Table14b.SummaryofComponentsofStandardUncertaintiesinMicaCapacitorDialCorrections forThree-TerminalMeasurements UnknownStandard (jiF) 0.01 0.02 0.05 0.1 0.2 0.5 1.0 Componentsof StandardUncertainties(ppm) (AtallFrequenci... Open at page → 68 Page 68 Table15a.SummaryofComponentsofTypeBStandardUncertaintiesinCapacitanceMeasurementsUsing theType-12BridgetoMeasureTwo-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (Allvaluesareinppm -exceptnominalvaluesoftheunknowncapacitan... Open at page → 69 Page 69 Table15b.SummaryofComponentsofTypeBStandardUncertaintiesinCapacitanceMeasurementsUsing theType-12BridgetoMeasureThree-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (Allvaluesareinppm -exceptnominalvaluesoftheunknowncapacit... Open at page → 70 Page 70 Table16a.SummaryofComponentsofTypeAStandardUncertaintiesinCapacitanceMeasurementsUsing theType-12BridgetoMeasureTwo-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (Allvaluesareinppm-exceptnominalvaluesofunknowncapacitancest... Open at page → 71 Page 71 Table16b.SummaryofComponentsofTypeAStandardUncertaintiesinCapacitanceMeasurementsUsing theType-12BridgetoMeasureThree-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (Allvaluesareinppm -exceptnominalvaluesofunknowncapacitanc... Open at page → 72 Page 72 Table17a.SummaryofExpandedandAssignedTotalUncertaintiesinCapacitanceMeasurementsUsing .; , theType-12BridgetoMeasureTwo-TerminalMicaCapacitorsat100Hz,IkHz,and10kHz (Allvaluesareinppm-exceptnominalvaluesoftheunknowncapaci... Open at page → 73 Page 73 Table17b.SummaryofExpandedandAssignedTotalUncertaintiesinCapacitanceMeasurementsUsing theType-12BridgetoMeasureThree-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (Allvaluesareinppm-exceptnominalvaluesoftheunknowncapacitan... Open at page → 74 Page 74 Table18a.SummaryofComponentsofTypeBStandardUncertaintiesinConductanceMeasurementsUsing theType-12BridgetoMeasureTwo-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (Allvaluesarein -exceptnominalvaluesoftheunknowncapacitances... Open at page → 75 Page 75 Table18b.SummaryofComponentsofTypeBStandardUncertaintiesinConductanceMeasurementsUsing theType-12BridgetoMeasureThree-TerminalMicaCapacitorsat100Hz,1kHz,and10kHz (AllvaluesareinjiS-exceptnominalvaluesoftheunknowncapacita... Open at page → 76 Page 76 Table19a.SummaryofComponentsofTypeA,Expanded,andAssignedUncertaintiesinConductance MeasurementsUsingtheType-12BridgetoMeasureTwo-TerminalMicaCapacitorsat 100Hz,1kHz,and10kHz (Allvaluesarein -exceptnominalvaluesoftheunkno... Open at page → 77 Page 77 Table19b.SummaryofComponentsofTypeA,Expanded,andAssignedUncertainties inConductance MeasurementsUsingtheType-12BridgetoMeasureThree-TerminalMicaCapacitorsat 100Hz,1kHz,and10kHz (Allvaluesarein|uS-exceptnominalvaluesofthe... Open at page → 78 Page 78 Primary Capacitance Laboratory Impedance Calibration Laboratory ReferenceBank 4xlOpFOil-BathType Fused-SilicaCapacitanceStandards TransferStandard 10pFAir-BathType Fused-SilicaCapacitanceStandard ReferenceBank 4xl0pFOil-... Open at page → 79 Page 79 67 Open at page → 80 Page 80 -1 Ex Figure2b.SimplifiedCircuitDiagramoftheNISTType-2CapacitanceBridge. 68 Open at page → 81 Page 81 ^^^^^^^^ Ci|_C2LC2LC4LCj_C6\_Cjj_cj_ 100 10 1 10"' 10"2 iQ-' 10-'' 10-5 (pF) Figure3.InternalCapacitorsoftheType-2Bridge. G c R L, —^^/w c Figure4.LeadImpedanceofaCapacitorConnectedtotheBridge. 69 Open at page → 82 Page 82 70 Open at page → 83 Page 83 Figure5b.SimplifiedCircuitDiagramoftheType-12CapacitanceBridge. 71 Open at page → 84 Page 84 Figure6.ComponentsoftheType-12BridgeforTwo-TerminalLow-Capacitance ValuesMeasurements. 72 Open at page → 85 Page 85 ure7.ComponentsoftheType-12BridgeforTwo-TerminalHigh-Capacitance ValuesMeasurements. 73 Open at page → 86 Page 86 Figure8.ComponentsoftheType-12BridgeforThree-TerminalLow-Capacitance ValuesMeasurements. 74 Open at page → 87 Page 87 Figure9.ComponentsoftheType-12BridgeforThree-TerminalMeasurementsof Capacitorsupto0.5|iF. 75 Open at page → 88 Page 88 B D Figure10.ComponentsoftheType-12BridgeforThree-TerminalMeasurementsof CapacitorsLargerThan0.5|j,F. 76 Open at page → 89 Page 89 gure11.SimplifiedCircuitDiagramoftheType-12CapacitanceBridgeIncluding theConductanceComponents. 77 Open at page → 91 Page 91 APPENDIXA.UNCERTAINTYANALYSISOFTHECORRECTIONSTOTHE1:1RATIO Rewritethebalanceequationandthecorrectionstothe1:1ratiooftheType-2bridgeasshownin Eqs.(6)to(9)ofthetextasEqs.(Al)to(A4)as: E,Y^+E^(lriy,)+p,E^(Mlg.) =-E^Y^, (Al)... Open at page → 92 Page 92 10'^. Therefore,byeliminatingtheseterms,theapproximateequationfortheratiocorrections is: «i + j^i - [(L c.+L r„cJ +j(-l/0))/.5^ (L^/ + Z ]/ +Q, (A6) where and arein-phaseandquadraturecorrectionsapphedtothe1:1ratio. Thede... Open at page → 93 Page 93 MultiplyboththenumeratorandthedenominatoroftherighthandsideofEq.(All)by [(CgDf^+Q " J(QQ)] eliminatethesecondordertermsofDF^andDf^ .Eq.(Al1) becomes: [1/(Fg+Y^)]= (1/0)) {[ (C3DF^+q Z)F^)/(Cg+Q ' ] -j[l/(C3+ CJ]}. Inmeas... Open at page → 94 Page 94 Inordertoestimatethestandarduncertainties intheratiocorrections,afewassumptionsand approximations areneededtoapplytoEqs.(A15)and(A16).Ingeneral,allvaluesofZ)Fg,DF^^, df-,df^,x^,and arelessthan 10'^,andratiosof[x^I(DF^+DF... Open at page → 95 Page 95 4) Uncertaintiesestimatedfromtheinterpolationoflastdials Thesensitivityoftheconductancedialsissuchthatchangesofthe±1steponthefourthdial donotaffectthebalance.Thisintroducesastandarduncertaintytothein-phasecorrection of:... Open at page → 97 Page 97 APPENDIXB.CAPACITANCEDIALCORRECTIONSOFTHETYPE-12BRIDGE DataandanalysesofcapacitancecorrectionsforeachcapacitordialoftheType-12bridgeareincluded inthefollowingtables: TableB-1. DataandAnalysisofthe(0.1fiF/step )MicaCapaci... Open at page → 98 Page 98 TableB-2. DataandAnalysisofthe(0.1jiiF/step)MicaCapacitorDialCorrectionsofthe Type-12Bridgeat1kHz [AllvaluesareinpFexceptthedialswhicharein(fj.F/step)] Date^^^ial 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 O.X 6/67 9.522 20.953... Open at page → 99 Page 99 TableB-3. DataandAnalysisofthe(0.1p-F/step)MicaCapacitorDialCorrectionsofthe Type-12Bridgeat10kHz [AllvaluesareinpFexceptthedialswhicharein(fxF/step)] Date"-"»..^ial 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 O.X 6/67 16.633 40... Open at page → 100 Page 100 TableB-4. DataandAnalysisofthe(0.01)a.F/step)MicaCapacitorDialCorrectionsofthe Type-12Bridgeat100Hz [AllvaluesareinpFexceptthedialswhicharein(fiF/step)] Date"""^^Dial 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 O.OX 6/6... Open at page → 101 Page 101 TableB-5. DataandAnalysisofthe(0.01|j.F/step)MicaCapacitorDialCorrectionsofthe Type-12Bridgeat1kHz [AllvaluesareinpFexceptthedialswhicharein(fiF/step)] Date"^"^Dial 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 O.OX 6/67... Open at page → 102 Page 102 TableB-6. DataandAnalysisofthe(0.01jiF/step)MicaCapacitorDialCorrectionsofthe Type-12Bridgeat10kHz [AllvaluesareinpFexceptthedialswhicharein(|j,F/step)] Date^^Dial 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 O.OX 6/67 0... Open at page → 103 Page 103 TableB-7. DataandAnalysisofthe(1000pF/step)AirCapacitorDialCorrectionsofthe Type-12Bridge (AllvaluesareinpF ) Date^>^Dial 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 6/67 0.060 0.010 0.189 0.109 0.189 0.154 0.334... Open at page → 104 Page 104 TableB-8. DataandAnalysisofthe(100pF/step)AirCapacitorDialCorrectionsofthe Type-12Bridge (AllvaluesareinpF ) Date^^-^^Dial 100 200 300 400 500 600 700 800 900 1000 '6/67 -0.003 0.125 0.092 0.075 0.067 0.200 0.167 0.165 0... Open at page → 105 Page 105 TableB-9. DataandAnalysisofthe(10pF/step)AirCapacitorDialCorrectionsofthe Type-12Bridge (AllvaluesareinpF ) Date^"\Dial 10 20 30 40 50 60 70 80 90 100 6/67 0.007 -0.057 0.005 0.047 0.059 -0.015 0.047 0.059 -0.004 0.007 1... Open at page → 107 Page 107 APPENDIX C.CONDUCTANCEDIALCORRECTIONSOFTHETYPE-12BRIDGE DataandanalysesofconductancecorrectionsforeachmicacapacitancedialoftheType-12bridgeare includedinthefollowingtables: TableC-1. DataandAnalysisofConductanceCorrectio... Open at page → 108 Page 108 TableC-2. DataandAnalysisofConductanceCorrectionsof(0.1^iF/step)MicaCapacitanceDial oftheType-12Bridgeat1kHz (Allvaluesarein0.001|j.S,exceptthedialwhichis0.1|j,F/step) DIAL 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 O.X 0/0/ /I... Open at page → 109 Page 109 TableC-3. DataandAnalysisofConductanceCorrectionsof(0.1jj,F/step)MicaCapacitanceDial oftheType-12Bridgeat10kHz (Allvaluesarein0.001fiS,exceptthedialwhichis0.1fj,F/step) DTAT 01 02 01 04 05 06 07 08 09 0X O/O/ 4yz.JUo 1JJ... Open at page → 110 Page 110 TableC-4. DataandAnalysisofConductanceCorrectionsof(0.01uF/step)MicaCapacitanceDial oftheType-12Bridgeat100Hz (Allvaluesarein0.001|liS,exceptthedialwhichis0.01|j,F/step) DTAT 001 003 004 005 006 007 008 w.wo 000 0OY o/o/... Open at page → 111 Page 111 TableC-5. DataandAnalysisofConductanceCorrectionsof(0.01uF/step)MicaCapacitanceDial oftheType-12Bridgeat1kHz (Allvaluesarein0.001\xS,exceptthedialwhichis0.01|iF/step) DIAL AA1 0.01 AAO O.OZ AA^ 0.03 AAyl 0.04 AAC AA/C 0.... Open at page → 112 Page 112 TableC-6. DataandAnalysisofConductanceCorrectionsof(0.01uF/step)MicaCapacitanceDial oftheType-12Bridgeat10kHz (Allvaluesarein0.001|j,S,exceptthedialwhichis0.01^F/step) DlAT 001 007 003 004 005 006 007 008yj,yjo 009yj.yjy... Open at page → 114 Page 114 THESP250SERIESONNISTMEASUREMENTSERVICES* SP250-1 SpectralRadianceCalibrations PB87179883 SP250-2 FarUltravioletDetectorStandards PB87227609 SP250-3 RadiometricStandards intheVacuumUltraviolet PB87227625 SP250-4 FrickeDos... Open at page → 115 Page 115 THESP250SERIESONNISTMEASUREMENTSERVICES*-Continued SP250-45 RadiationProcessingDosimetryCalibration Services:ManualofCalibrationProcedures SN003-003-03514-9 $4.00 SP250-46NISTMultifunctionCalibrationSystem SN003-003-0351... Open at page → 116 Page 116 OCOS 0)CD9 COwo^ .o -c «^E 32raO Open at page →