the precise measuremient of small capacitances-tbt

8/8/2019 The Precise Measuremient of Small Capacitances-TbT

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1958 Thompson:The PreciseMeasurementof SmallCapacitances 245and thegenerator revolutions given on the counter. By the Long Island Lighting Company at their Barrettsuitablecalibrationand selectionof constants, the Power Station.meter and counter are calibratedin terms of volt-sec- Five tests were run with indicating wattmeters inonds, watt hours,etc. each of three phases and with one Inductronic Watt-

For long periodsof time,such as 10 minutes or more, meter and integrator in phase A. The test time variedthe volt-secondsstoredin the capacitor at the end of a from one to three hours. The integrator was read at the

cycledo niothave to be read onthe

voltmeter.This is beginning and end

ofeach

testand the wattmeters were

because the counter indicationis largeand the small read every minute.amount of volt-seconds indicated on the voltmeter can The largestdifferencebetween the two watt-hourbe neglected.For shorterperiods of time, the sum of readings by each method was0.12per cent.The averagethevoltmeter and counter readings should be added to- differencefor al l five tests wa s 0.08per cent. It is be-getherto givethe totalvolt-seconds. lievedthat using Inductronic Wattmeters in the other

The basicaccuracy for normal periods of time (10 two phases and feeding the outputs to three integratorsminutes or more) is completely dependent upon the would have provided totalgenerator output in kilowattstabilityof the generator. This stabilityhas been ob- hours to an accuracy ofapproximately0.1per cent. Thetained by gooddesign practiceand 0.1per cent accuracy output of thethree wattmeters can alsobe connected tois maintained. one integrator to provide the total three-phase energy.

For short periodsof time,the accuracy of the instru- This may not be convenient where transformer connec-ment and readabilityof the counter are a factorand tion factorsmust be applied foreach phase and where itmust be considered.A more complete descriptionof the is desirableto know the load balance.precisionintegratoris given by Gilbert.6

The combination of Inductronic Wattmeter and in- IX. CONCLUSIONStegratorhas been testedunder actualfield conditions The product resolvercan be used forthemeasurementto determine its suitabilityfor measuring turbine effi- of volts,amperes, watts, and watt hours when used inciencies.This test was performed by the Engineers of conjunctionwith a precision integrator.It offers0.1

per cent accuracy over a wide power frequency range

6 R.W. Gilbert,"TheWeston Model1473PrecisionIntegrator," and provides a dc output which can be measured orWestonEng.Notes,vol.10 ,pp. 6-9;December,1955. used forcontrol.

The PreciseMeasuremientofSmallCapacitancesA. M. THOMPSONt

INTRODUCTION capacitor might provide values for theohm and related)HE practicalelectricalunits are based on the unitsmore accurate than those obtained by a direct

2I electromagnetic system, and the startingpointof electromagnetic determination.most "absolute"determinations has been thecon- An examination of a number of possiblecalculable

structionof an inductor and the calculationof its in- capacitorsshows that they have one thing in common:ductance from its mechanical dimensions. If a capacitorthe mechanical problem becomes easieras the capaci-is used as the startingpoint the capacitance is calculatedtance is reduced; and optimumdimensions would givedirectlyin electrostaticunits,and a knowledgeof the only a few picofarads.Considerable progresshas al-velocityof lightis necessary to convert to the practical ready been made with techniques for the measurementunits.Recent determinations of the velocityof lightare of small capacitances,and it has been considered thatconsidered to be accurate to the order of 1 in 106which these can be refinedsufficientlyto enable a 1-ohm re-is much better than has been claimed for absolute de- sistancestandard to be relatedto a capacitance of theterminations of the electricalunits.This fact, together order of 1 pF to an accuracy of 1 in 106.Accordingly, anwith the very much simpler geometry of somecalculableelectrostaticdetermination of the ohm based on a newcapacitors,suggests that a determination based on a type of calculablecapacitor'is being made, and much of

the development work has been completed.* Manuscript received by the PGI, August 14, 1958. 1A. M. Thompson and D. G. Lampard, "A new theorem in elec-

t Electrotechnology Div.,National Standards Laboratory, Chip- trostaticsan d its application to calculablestandards of capacitance,"pendale, Australia. NVature,vol. 177,p. 888; May, 1956.

AlultICLDoJ0a1UfIX Ra


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1958 Thompson:The PreciseMeasurementof SmallCapacitances 247Y' Y2 y'12 Z12 Zll 2 22 12 Z

--

-z, z22-z122Y23 22 Z22 + Z2aIF '1 + Y2+Y3=O Y12 =z11Z22-z12

Y133_b Z11+Z,22 3 2 = z

Fig.3-Campbell's idealrationetwork.Fig.4-Equivalent circuitof 2-winding transformer.

Since llv1 Y3 z12 KiiY2 + Y2 Z 3 - \"l( ~~~~= P'

123= V23 _ zl22t 13V1+ Y2+ 13

theeffectivebridge ratio is Y1/Y2and this is independ- IDEAL TRANSFORMERent of thevalue of Y3.However, if Y3is varied so that RATIOS 1 ' P2 P1~2-the sum Y1+Y2+ Y3-*O the equivalent admittances z 2Yn,Y23-x and the bridge ratiobecomes independent >1 = 112 12 12of additionaladmittances shunting the ratio arms. 52 = Z2 - p2Z12Campbell pointed out that a transformer with two Fi. 5-qivln cirui of2wndn. rnsomr

Fig.4-Equivalent circuitof 2-windingtranisformer.

closelycoupled windings was very nearly equivalent tohis idealrationetwork.

Tranlsformerratioswith more than two windings may

be used, and these alsomay have such a low effective _ E limpedance that the effectof admittances shunting theratio arms is in most casesnegligibleand no balancing z, z2 =of the ground admittances is necessary.In addition, j A 1 P Ptransformers can give ratiosof extraordinary precision, | iand with multiple windings thereis considerable fiexi- Z11 Z22 3 i 92 l2bility in the design of measuring circuits.Some of thepossibleconfigurationsof transformer ratio arms and IDEAL TRANSFORMERtheirpropertiesare outlined in the next section. RATIOS 1 Pp3 PtP2p3l

TRANSFORMERRATIOARMS dj2 P2Z3 3Z1Th e simplest caseconsistsof two windings. If these z1, z13

have a commonconnection the equivalentcircuitshown = 2 Zin Fig.4 may be used.If thereis no commonconnection, z 1 1 2panl equivalent circuitbased on an idealtransformer is }2= 2sometimes useful.This is shown in Fig. 5, but thereisno unique circuitof this type and one of thetwo leakage z Z" iimpedances or the ratiomay be chosen to suita particu-lar application. Fig.6-Equivalent circuitof 3-windingtransformer.

For threewindingsthereis a unique equivalentcircuitbased on an idealtransformerwhich is very useful.This nected in series. The simplest circuitof this type isis shown in Fig.6. For more than threewindings there shownin Fig.7. If the windings have the same resistanceis no simple equivalent circuit. per turn and arewound to be symmetrical with respect

There are two types of bridge circuitin which a to a high permeability core,then multiratio windingstransformer may be used to givevery preciseratios.The can be produced such that no ratio departs from the

firsttype is obtained when the supply or detector is con- turns ratioby morethan 1 in 1O5,and where closeinter-

nected acrossal l the windings of the transformer con- leaving of the windings is possiblethis departure may



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248 IRE TRANSACTIONSON INSTRUMENTATION DecemberRATIO WINDINGS

Y,

Pl= p)2Y

Fig. 7-Bridge circuitwith 2-winding transformer. PERMALLOY,=V STRIP-WOUNDC TOROIDALCORE

lP1 V

X 1lll

Il = p2'2ISUPPLY OR DETECTORWINDING

P2 VY2Fig.9-Cross sectionofelectromagnetically

screened ratiotransformer.

r 5 NWhichevertype of circuitis used,transformer ratioslp51 are best specifiedbythe ratiosobtained without an y ex -

T ) | | L3 1 =ternal loading and by a setof effectiveimpedances fromP1Pa, = P2PF'Y which the change in the ratiosdue to external loading

|2 l g ;/ / l l C Tmay be calculated.Such a specificationonly applies tothe particular method of connection, and it may varyslightlywith frequency and with the levelof excitation.

Fig.8-Bridge circuitswith 3-winding transformers. If a transformer has a largenumber of windings it is no tpracticableto compute and apply corrections for the

be as low as 1 in 106.Close interleaving alsoreduces the effectsof the separate loads on each winding, but the

effectiveimpedances, an d to keep these low a small num- effectiveimpedances must be determined to confirmber of turns should be used. that the loading errorsare within the desiredtolerance.The other type of bridge circuitwhich givesprecise This is best done by settingup the desired bridge circuit

ratiosis derived frornthe first by the addition of a sepa- and then determining the change in the balance causedrate winding for the supply or detector.The simplest by shunting a winding with a known admittance.circuitsof this type are shown in Fig. 8. This type ofcircuithas some advantages, but is best suited to the TRANSFORMERBRIDGESFORTHEMEASUREMENTcomparison of small admittances as the effectiveim- OFSMALLCAPACITANCESpedances of the ratio arms appear in serieswith the Siniceratio transformers are made to have a low ef-components being compared. As before,the ratiowind- fectiveimpedance to minimize loading errors,they doingsshould be svmmetrical with respect to a high per- not match the high impedances in the bridge when smallmeability core and alsoto the additionalsupply or de- capacitorsare being compared. In this case it is foundtector winding, but in this case the resistances of the that the maximumsensitivityresultsfrom the use of awindings do not affectthe open circuitratios.By elec- voltagetransformer only.A bridge of thistype, for thetromagnetically screening the ratiowindings from the comparison of two directcapacitances,is shownin Fig.core and the thirdwinding it is possibleto obtainiratios 10.The thirdterminal of the capacitors is connected towhich are the same as the turns ratiosto 1 in 107.Th e the ratiosideof the detector. One of the ground capaci-cross sectionof such a transformer is shown in Fig.9, tances is a shunt on the ratioarms which must be ofwhere the screening is provided by alternate copper and low effectiveimpedance if this shunt is to have a neg-permalloy C screens. ligibleeffecton the ratio.The other ground capacitance

Transformer ratioswhich are connected to the supply is a shunt on the detector so that it does not alter theproduce knlownvoltage ratios.They may operate with balance conditions but willhave an effecton the sensi-quite high fluxdensity, and are referredto as voltage tivity.The equivalent circuit ofthisbridge derived fromtransformers. Transformer ratiosconnected to the de- Fig.6 is shownin Fig.11.The balance conditions of suchtector define a current ratio and at balance operate at bridges may be analyzed in terms of the voltage distri-

very low flux density, and are referredto as current bution referredto the ratio sideof the detector.This

transformers. gives for the voltage at the detector.



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1958 Thompson:The PreciseMeasurementof SmallCapacitances 249C. ~~~~~~~~~~~~~Vi

Fig.10-Transformer bridge for the measturement vxofsmalldirectcapacitances. (a)

V,i Vi

Cl

VlYl+V2+V2 cxYo+ Y1+ Y2 Vx

(b)

Yb2 ~~~~~~~~~~~~~~V2vz ~~~~~~~~~~~~~~~~2

Fig.11I-Equivalentcircuitof bridgeshownin Fig.10. Kr 3

Vlyl + V2y2 CxV0 = VxYO+ Vi + Y2

At balance V0= 0 and (c)Fig. 12-Transformer bridgesfor small capacitances (a) Variable

Y,V2 capacitor.(b) Variableratio. (c) Multipleratiofixedcapacitors.

Y2 V1There are a number of ways by which the separate

P2/P1 capacitance and conductance balances may be obtained,if zi and Z2are both zero.Small correctionsdue to finite and someof these are described in the next section.values of zi and Z2are given with sufficientaccuracy by CapacitanceBalancethe relations

V, = pjE[1- zi(ya + Y1) There are threemain practicalforms of the generalbridge,and these are illustratedin Fig. 12 for the

V2= - p2E[1- Z2(Yb+ Y2)] capacitance balance.In the first of these a subdividedso that capacitor is used with a singlefixedratio.The capacitormay be of the switched decade type and there is no

- = - [2 P2 limit to the subdivision which may be continued by- - -

[I + Z1(ya+ yl)-

Z2(yb+ Y2)I. addingfurtherdecades.However,this requiresten2 VI Pi separate capacitorsper decade if they are to be indi-More complicated bridges may be analyzed in the same vidually intercompared by substitution,so that such away, sincein al l cases capacitor becomes bulky and expensive. In the second

ZvE Yn, form a singlefixedcapacitoris used and the ratiois ad-V/ - u t b e Th sudvso avial on asinl trans->'1 former is limitedby thenumberof turns,and additional

and the bridge is balanced when transformers are necessary if subdivision beyond 1 in- O ~~~~~~~1000s required. In the thirdform there is a limited sub-n- j *~=0 divisionof the ratio, and a number of fixedcapacitors

In general,the corrections due to finitetransformer im- are switched separately among these subdivisions.Thepedances are of the same form as forthe case above, but equivalent of a decade capacitor is obtained by sub-

moreterms are

necessary sinceall the ratiosare affecteddividing

one of the ratiowindings into tenequal

partsby a load on one winding, and switching a singlefixedcapacitor for each decade.



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250 IRE TRANSACTIONSONINSTRUMENTATION DecemberCombiniations of the above techniques may be used G2 yl2

to obtain the bestsolutionto a particularmeasurement G 2problem. I AAA-2 =Conductance Balance cn C2

A conductanicebalance may be provided by tech- 3niques similarto those used for capacitance, but since

IFG = G2

the phase anglesof the capacitors and of the transformer C, C2ratiosthat we are consideringare very small,a four-dial _G C2voltage divider and a fixedconductance standard are Ci+C2usually adequate. It is difficultto obtain a very small Fig. 13-T network fora smalldirectconductanceconiductance of good phase angleas a singlecomponent. ofgoodphaseangle.If a relativelylargeconductance is used then the sensi-tivity may be reduced considerably. The equivalent of La smalldirectconductance of good phase anglemay be X I- 2obtained by the use of a T network such as the oneshown in Fig. 13. In practiceG1 is a largeconductance TCof good phase angle and Ci such that GK


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1958 Thompson:The PreciseMeasurementof SmallCapacitances 251C Y

02

C I 2D

on th eseparatetwo-e Fig.16-Comeparisonof 3-terminalcapacitorswithCa 0b ~~~~~~~~separationiof thegrou-ndleads.

Fig.15-Three-terminal capacitorwithone finite leadi fpedanceanidapproxim-Fateequivalen-itcircuit.

enyough.The groundloopimpedancemay be increasedconsiderablyby threadingthecoaxial leadsthrougha Ghighpermeabilitycore,and this should have no effecton theseparatetwo-terminal pairparameters. The addi- -____________tionaladmittance that resultsfrom thecompletionof a Fig t circuitfo ra sml unane

to 109 pF nd isnot dtectale i a lo voltge brdgev ent crren 1Eqivalen cicior1mp Thsmlhuiaal e mae

ground loopis given in the Appendixas YaYbrrrb/Zo.If of a capacitancebridge.reasonable values are substitutedin this expression,namely, Th e noiseproducedby G at room temperature may be

m a = Yib = 100 pF ra= rb = 10n representedby an equivalentcurrent generator whoseroot mean square value is rmsi=1.3X10i10Guf)t2. If

and Zo = 1 mH ,this additionaladmittance is equivalentG= 10bi ho and the bandwidth Af=1 cps this equiva-to 10r9pF and is not detectable in a low voltagebridge, lent current is 4 X -15 amp. This should be compared

The impedanceof each separateleadgivesrise to the with a current of 10-14amp produced by 1 voltacrosssame type of error as the impedanceof the ratio arms. 1 ppF at a frequencyof 1592 cps.This is a relativeerror which is onlysignificantwhen A thermionic tube amplifierconnected directlytomeasuring largecapacitancesand does not se t a lower the bridgeis the best detector for the measurementoflimitto capacitancemeasurements. small capacitances.If a gridresistoris used to control

For thecomparisonofunequalcapacitances,the error the gridbiasit should be of theorder of t0 ohms. Thein

the ratioof the transformer must be determined. If

amplifiershould be tuned and the

usualprecautionsthe nominal-ratio is n to the error can be determined taken against microphonyand interference.A very nar-by intercomparingn +1 equalcapacitorsby substitu- row bandwidth may be obtained by the use of a phasetionan d then using n in parallelagainstthe remainingsensitivedetector and low-passfilter or integratingcir-one to form a knowncapacitanceratioof n to 1. The cuit. The measured noisecharacteristicof an amplifieraccuracyof this process requiresthecapacitances to be with selectedtubes is shown in Fig.18as a function ofstrictlyadditive,and is limitedby the stabilityof the the total capacitanceat the input.It should be notedrelativecapacitances.Withsimilarcapacitorsand reason- that thereare noiselimitationsto both the current andable temperature stability,an accuracy of1i in 106is the voltagesensitivity.When largecapacitancesarereadilyobtained. Small capacitors10-100 pF are most being comparedthe voltagesensitivityis usuallyade-convenient and with these the loading errors are small. quate,but greatersensitivitymay be obtained by usingA shieldedratiotransformer of thetype shownin Fig.9 a suitablecouplingnetwork between the bridgeand themay be used as a standard to calibrateother ratiosbY detector amplifier.The most directway of increasingusing the ratioof a pairof capacitorsas a transfer. the sensitivityis to increasethe voltage suppliedto the

SENSITIVITYc e thr h l c obridge.Voltagesup to about 100 are easilyobtained,butSENoITIVITYne t c is c u cabove thislevelthe transformersbecomerathercumber-If the type of bridgeshown in Fig. 12 is initiallY some or their effectiveimpedances are increased,and

balanced and then unbalanced by a small change in C, their loadingerrorsbecome significant.The improve-

ofyniselinathisciruit iste conductmhoanceG=his mapiaFlmttin.h ensitivitylimitasuineh isueaboutbe ofpFw



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252 IRE TRANSACTIONSONINSTRUMENTATION December-1 3 4m m

10 _o ~~10

E V E X E REFERENCE A 0. Imm

o

O8 1IC4 Fig. 19-Three-terminalcapacitaniceprobe for the nmeasurenmelntI-: of mechanical displacements.

0- , 1 *,*.-EIo1 Y 2B

10 100 1000 A BINPUT CAPACITANCE pF 3

Fig.18-Noise charaLcteristics ofa thermionic tube amplifier; EO= Lofrequency 1592 cps,bandwidth 1 cps. I

applicatioiisbecome practicable.Apart from measure- Fig.20-Network representinga 3-terminal admittancepplications ~~~~~~~~~~~~~~witheparatecoaxialleadsand ground loop.ments where the capacitance itself is ofprimary interest,thereare numerous possibilitiesfor the applicationof3-terminalcapacitancetransducers to measurement circuited)the voltage drop in the input leadis (Y+Ya)zaproblems. As an example, consider the sensitivitythat and in the output leadYZb.The resultingcurrent con-could be obtained with a capacitance probe for the tributionto i2 would bemeasurement of mechanical displacement. The probe -(Y + Ya)Zay - YZb(Y+ Yb).could take the form of a small diskwith guard as shownin Fig.19.A disk diameter of 4 mm spaced 0.1mm from Hencethe reference surface would givea directcapacitance of i21 pF. The gap would easilysupport 100 voltsgivinga YAB= - = Y[1- Y(Za+ Zb)- YaZa- YbZb](1 )sensitivityof 10-7pF. This corresponds to a change of Eonly 10-1 mm in the

separationof the

surfaces.Capaci- and

thisis the equivalent

transferadmittance as an

iso-tance probesof this type and otherswith sphericalends latedtwo-terminal pairnetwork. The potentialappear-have been particularlyusefulin theassembly of a pre- ing between terminals A' and B' is approximatelycisecalculablecapacitorwhere measuring sensitivities jira+t2rbwhere ra and rb are the resistancesof the outerof a few microinches were required.They have thegreat conductors,sincethereis very little inductive couplingadvantage that they do not contact the referenceto an externalcircuit including the outers,providedsurface. theseare not too thick.HenceVA'B'W-(Y+ Ya)ra+ Yrb.If

theexternalcircuitis now closedand Eo=0, the currentAPPENDIX in the ground loop is io= VA'B'jZOwhere Z0is the im-

A 3-terminal admittaincedefinedat terminals 1, 2, pedance of the ground loop.The voltage drops in theand 3 is connected by coaxialleadsto separate coaxial leadsdue to this current in the outers only areioraandterminations AA' and BB'. It is required to findthe iorband the resultingaddition to i2 is ioraY+iorb(Y+ Yb).transferadmittance YABand the effecton this admit- Hence, the additional admittance due to connectingtance of an additionalcircuitjoiningA' and B'. This A'B' isnetwork, shown in Fig.20, may be solved in terms of 1the loop currents indicatedand associatedloopim- - [Y(r(,+ rb) + Yara][Y(r.+ rb) + Ybrb]pedances, but there is some effortinvolved in reducing Zothe result. Because of the very small effectof the lead /ra + rb\ Yimpedances (usuallyra+rband thefirst termimposing the current distributionthat such potential is much smaller than the leads correctionsgiven bydrops would givein the rest ofthe network. For 1 volt (1).The term YaYbrarb/Zois independent of Y and mustapplied to AA' andlfor io=0 the lead currents are be considered when very small capacitances are beingii~ Y+ Ya and i2~ Y. If the leadimpedances areza and compared.Zb(as measured from one end with the other end short When two admittances are joined in parallelso that



9/9

1958McGregor,et al.: NewApparatusat theNBS for AbsoluteCapacitanceMeasurement 255the ground leadsform a loop,thecurrent in thisgrounidiniducedin theground loopfrom stray fields,the result-loopis due to the differencebetween the two separate ing currentin the ground loopwould contributethevalues of VA'B'that would be obtained before making equivalent of an additioilaladmittancethe parallelconnection. In this case,the additionalad-mittance independent of Yand Y' is z- [Y(r,+ rb ) + Ybrb].

-[Yara - Ya'ra'F[Ybrb-Yb rb'] If the erroraYbrbJZois not

tobe

detected,then the

Z6 voltage inducedin the groundloop should be lessthanaindin somecasesit may be worthwhile to balailcethe about Zo/rbtimesthe voltage senisitivityof the detector.leadsand the ground admittances. If thereis a voltage With a few turns oli a high permeability core Z0orb>100.

NewApparatusat theNationalBureauofStandardsforAbsoluteCapacitanceMeasurement*M. C. McGREGORt,J. F. HERSH$,R. D. CUTKOSKY,F. K. HARRIS, ANDF. R. KOTTER

INTRODUCTION work of Thompson and his group at the NationalT HE use of tightlycoupled inductiveratio arms Standards Laboratory of Australia.By combining the

ratherthan resistiveratioarms in a 4-arm bridge best techniquesfor constructing ratio transformers,for the comparison of impedances was suggested completely shielded3-terminal capacitorsand detec-

by Blumlein' in 1928,and theuse of a 3-winding trans- torsof high sensitivity,together with a cylindricalcrossformer in such a bridge circuitwa s described by Starr2 capacitor as a calculablestandard, there is now promisein 1932.Other bridgesusingBlumlein's principlehave of being able to assign values to capacitance standardsbeen describedby severalworkers3 in the past 30 years. comparable with, or perhaps even better than, the ac-Historically,it is of interestto note that conjugate curacy assigned to our present standards of electro-bridgesmakinguse of 3-winding transformers were de- motive foreeand resistanee.scribedby Elsas4in 1888 for resistancecomparison and Thepresentpaper deseribesa transformer bridge eon-by Trowbridge5in 1905 forcapacitance and inductance structedat the National Bureau of Standards formeas-comparisons. uring the directcapacitance of 3-terminal capacitors

Thus the basicprincipleof operationand thegeneral ranging in values up to 1 yf and having a leastcount ofarrangement of transformer bridgeshave been known 1 lspf. Although the transformers and network com-for many years. However, the possibilitiesof such ponents describedbelow were designed specificallyforbridgesfor the precisecomparison of very low value operation at 1 kc, the operation is by no means limitedcapacitorshad never been fullyexploitedbefore the to this frequency.Voltage output of the ratio trans-formers constitutesthe most seriouslimitationat lower

frequencies,but it is reasonableto suppose that, with* Manuscriptreceived bythePGJt,AUlUNsn,uustr14,i1958relatively minor modificationls,satisfactoryoperationt National Standards Lab.,Chippendale,N.S.W., Australia. reailymnr odfctos,aifcoyopain$ GeneralRadio Co.,Concord,Mass. should be possibleover theaudio-frequencyrange to at National Bureau ofStandards,Washington,D. C. least10 kc.IBritishPatent No. 323037.2 A.T. Starr,"A noteon impedancemeasurement,"W. Eng.and While some of the presentbridge components differ

Exp.W.,vol.9, pp. 615-617;November, 1932. sbtnilyfromtercutrat t N L tsolC H. Young, "Measuring inter-electrodecapacitances,"Bell substantially om their counterparts at NSL it shouldLabs.Rec.,vol.24,pp.433-438;December,1946. be understood that no more is involved generally than

H. A.MIClarkand P. B.Vanderlyn,"A.C.bridgeswithinduc- modifications and in some cases improvements of de-tivelycoupled ratioarms," Proc.lEE, vol. 96,pp. 365-378; May,1949. signsalready proven by Thompson and his group

C. XV1.Gatley and J. G. Yates, "Bridges with coupled inductive in Sydney.ratioarms for the comparison of standards of resistance orcapaci- Thr a enltl eaie n o m t olsetance," Proc.IEE, vol.101,pp.91-100;March, 1954. Teehsbe itedtie nomto ulse

tVA.,M.OThompson,"A,bridgBefor7themeasuroembentof pemt- up to now concerning these components, an d the present4A.Elsas,"Ueber Widerstandsmessungen mitdemnDifferential-paper must be considered primarily as a discussion of

ind5uctor,"Ann.riPhys.,vnol.3e5,dipfp.82n8-a83t3r;ar18f8o8.mretheconstructionaldetailsand performance of theNBS

vol. 20,pp. 65-76;1905.trnfme-aibid.

the precise measuremient of small capacitances-tbt

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