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Realization of the farad from the dc quantum Hall effect with digitally assisted impedance

bridges

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IOP PUBLISHING

METROLOGIA

Metrologia 47 (2010) 464–472doi:10.1088/0026-1394/47/4/013

Realization of the farad from the dc

quantum Hall effect with digitally assisted

impedance bridges

Luca Callegaro1, Vincenzo D’Elia and Bruno Trinchera

Istituto Nazionale di Ricerca Metrologica (INRIM), Str. delle Cacce 91, 10135 Torino, Italy

E-mail: l.callegaro@inrim.it

Received 9 March 2010, in final form 8 June 2010

Published 22 July 2010

Online at stacks.iop.org/Met/47/464

Abstract

A traceability chain for the derivation of the farad from dc quantum Hall effect has been

recently implemented at INRIM. The main components of the chain are two coaxial

transformer bridges: a resistance ratio bridge and a quadrature bridge, both operating at

1541Hz.

Both bridges are energized and controlled by a polyphase sinewave direct-digital-

synthesizer; the automated control of relative amplitudes and phases of the generator voltage

outputs permits principal and auxiliary balances of each bridge to be achieved. Such a

technique, which may be called digital assistance, is implemented for the first time in an

ohm–farad traceability chain.

The relative standard uncertainty in the realization of the farad, at the level of 1000pF, is

estimated to be 64 × 10−9. A first verification of the realization is given by a comparison with

the maintained INRIM capacitance standard, where an agreement within a relative combined

standard uncertainty of 420 × 10−9is obtained.

1. Introduction

A number of national metrology institutes worked on

measurement setups to trace the farad to the representation

of the ohm given by the dc quantum Hall effect [1–10].

The traceability chains employed involve a number of

experimental steps, usually requiring not less than three

different coaxial ac bridges.

networks of passive electromagnetic devices [11]: some of

them are fixed (transformers and single-decade inductive

voltage dividers) and several are variable (resistance and

capacitance boxes, multi-decadic inductive voltage dividers).

Bridges are balanced by operating on the variable devices to

reach equilibrium; that is, the detection of zero voltage or

current on a number of nodes in their electrical networks.

Variable devices, especially inductive voltage dividers, are

expensive; only a few models have been described [6,12–14]2

which permit remote control.

The bridges are complex

For this and other reasons,

1Author to whom any correspondence should be addressed.

2A commercial item is the Tegam mod. PRT-73.

a large number of existing implementations are manually

operated.

In most cases, the role of variable devices in a bridge

is to synthesize signals (voltages or currents) to be injected

in the bridge network to bring a detector position to

zero.The signals are isofrequential with the main bridge

supply, and can be adjusted in their amplitude and phase

relationships. The amplitude and phase of one (or more) of

the signals enter the measurement model equation, and must

be calibrated (main balance), but the others do not (auxiliary

balances).

Inthisview,itisstraightforwardtoconsiderthepossibility

of substituting in the bridge network most, or all, variable

passive devices with a corresponding number of active

sinewave generators, all locked to the same frequency but

independently adjustable in amplitude and phase.

digitalsynthesis(DDS)ofsinewaves[15]isawell-established

technique that permits the realization of such generators;

hence, in this sense, we may speak of digitally assisted

impedancebridges. Digitallyassistedimpedancebridgeshave

been considered both theoretically [16,17] and in a number

Direct

0026-1394/10/040464+09$30.00© 2010 BIPM & IOP Publishing Ltd Printed in the UK & the USA

464

Page 3

Realization of the farad from the dc quantum Hall effect

Figure 1. Graphical representation of the traceability chain for the realization of the farad unit from the quantum Hall effect.

of implementations [18–28]; some commercial impedance

meters are also digitally assisted.

In this paper, we consider for the first time the feasibility

ofacompleteohmtofaradtraceabilitychainbasedondigitally

assisted bridges. We constructed a resistance ratio bridge and

a quadrature bridge to measure capacitance (at the level of

1000pF) in terms of quantum Hall resistance (at the level of

RK/2 ≈ 12906.4?, where RKis the von Klitzing constant).

The bridges are automated, and a single measurement

can be conducted in a few minutes.

relative standard uncertainty of the capacitance determination

given by the traceability chain is 64 × 10−9(coverage

factor k = 1).

Suchaccuracyhasnotyetbeenverifiedwithacomparison

with another farad realization. However, by completing the

chain with an older manual transformer ratio bridge [29], we

performed a comparison between the new realization and the

present national capacitance standard, maintained as a group

value at the level of 10pF with a relative standard uncertainty

The estimated

of 400 × 10−9(k = 1). The results are compatible within the

respective uncertainties.

2. The traceability chain

The traceability chain which has been set up, including the

steps for the comparison (section 5.5) with the maintained

capacitance standard, is shown in graphical form in figure 1.

Its steps are summarized here and will be described in more

detail in the course of the paper.

• ThequantumHalleffectisemployedtocalibratearesistor

RQhaving the nominal value RK/2 ≈ 12906.4? and a

calculable frequency performance.

• RQ is employed in an 8:1 resistance ratio bridge to

calibratetworesistancestandardsR1,2,withnominalvalue

4 × RK≈ 103.251k?.

• R1,2are employed in a quadrature bridge to calibrate the

product C1×C2of two capacitance standards C1,2with a

nominal value of 1000pF.

Metrologia, 47 (2010) 464–472

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L Callegaro et al

• in order to perform the comparison with the national

capacitance standard, maintained at the level of 10pF, a

capacitance ratio bridge is employed to perform a scaling

up to 1000pF and the measurement of C1and C2.

The resistance ratio bridge is calibrated with an

independent procedure (section 3.2); the capacitance ratio

bridge is operated with a step-up procedure which permits an

independent ratio calibration to be avoided (section 4).

2.1. The impedance standards employed in the chain

The standards employed in the traceability chain are the

following.

RQa quadrifilar resistance standard, having a nominal value

RQ = RK/2.3Its frequency performance and reactive

parameter are calculable from geometrical dimensions

[30]. Thestandardisthermostatedtoimproveitsstability.

Theoriginalstandardhasaninductanceof≈3µH;inorder

to reduce its phase angle, a small gas-dielectric capacitor

has been added in parallel to its current terminals.

R1,2two resistance standards with nominal value R1,2 =

4 × RK. Presently, two thermostated thin film resistors4

encased in a metal shield and defined as two terminal-

pair standards are employed. The casings are within a

single air bath, having 1mK temperature stability. Two

new standards with independent thermostats are under

construction. Thestandardsareemployedintheresistance

ratio bridge and in the quadrature by defining them at the

end of the connecting cables (which are considered parts

of the standards).

C1,2two gas-dielectric capacitance standards C1,2 = 1nF

are constructed from General Radio 1404-A standards,

re-encased in a thermostated bath at 23◦C with 1mK

stability and redefined as two terminal-pair impedance

standards.Reference [6] gives a detailed description.

The standards are employed in the quadrature bridge and

in the capacitance ratio bridge by defining them at the end

of the connecting cables.

2.2. Frequency and voltage corrections

Figure 1 gives also frequency and voltage values employed in

each step of the traceability chain.

The new instruments described here have a working

frequency of about 1541.4Hz: this particular frequency is

chosen in order to achieve balance of the quadrature bridge

(see section 3.3). The national capacitance standard is instead

maintained at about 1592Hz (that is, 10krad−1).

Different steps of the traceability chain should keep the

same excitation voltage or current of each standard employed.

However, two deviations from this general rule appear in the

chain in order to maximize the accuracy of each step.

The effects of frequency and voltage dependences of

the standards employed are taken into account in the

3NL engineering Type QF, serial 1294.

4Vishay VHA512 bulk metal foil precision resistors, ±0.001% tolerance,

0.6ppm◦C−1temperature coefficient.

Figure 2. Frequency performance of the RQresistor.

following way:

RQThe calculated frequency performance is shown in

figure2. Thecalibrationisperformedat35µA(≈0.45V),

but the working current of the ratio bridge is 22µA

(≈0.281VonRQ). RQhasaquadraticcurrentdependence

RQ(I) = RQ(0) · [1 + kI2], with k = 1.6A−2[31]. The

correction is not performed, but included as a term in the

uncertainty evaluation.

C1,2Indirect measurements of the frequency dependence have

been performed with the so-called S-matrix method

[32]: the estimated correction for a frequency shift from

1541Hz to 1592Hz is lower than 1 × 10−9, but an

uncertainty contribution has nevertheless been added to

the uncertainty budget (see section 6).

dependence of gas-dielectric capacitors has the form

C(V) = C(0) · [1 + αV2], with typical values of α <

1 × 10−10V−2[33–35], and is therefore negligible.

The voltage

3. Digitally assisted coaxial bridges

The digitally assisted bridges developed are an 8:1 resistance

ratio bridge and a quadrature bridge. The coaxial schematics

can be seen in figures 3 and 4, respectively.

are based on the same design concept and share common

instrumentation: the polyphase generator (section 3.1), the

impedance standards (section 2.1), and the detector. A photo

of both bridges is shown in figure 5.

The bridges

3.1. Polyphase generator

Both bridges are energized (one at a time) by a polyphase

DDS generator; the schematic diagram is reported in figure 6.

The core of the generator is a commercial digital-to-analogue

(DAC) board5. The board is programmed for a continuous

generation of sine waves; each wave can be updated without

stopping the generation (large amplitude or phase changes are

achieved gradually to avoid steps in the output).

5National Instruments mod. NiDaq-6733 PCI board, eight DAC outputs,

variable reference input, 16 bit resolution, maximum sampling rate 1MSs−1,

voltage span ±10V.

466

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Realization of the farad from the dc quantum Hall effect

Figure 3. Simplified diagram of the 8:1 resistance ratio bridge.

Black rings along the mesh are current equalizers.

Figure 4. Simplified diagram of the two-terminal-pair quadrature

bridge.

Figure 5. A photo of the two bridges. On the left the quadrature

bridge; on the right the resistance ratio bridge. The instruments in

the middle are common to both bridges.

Sincethesinewavesarerepresentedbyanintegernumber

of samples (presently 628), the output frequency is finely

tuned by changing the common DAC update clock frequency,

typically ranging between 950kHz and 1MHz. The clock

is given by a commercial synthesizer6connected to the DAC

board by an optical fibre link [36] to minimize high-frequency

6Stanford Research System mod. DS345.

Figure 6. Schematic diagram of the sine-wave synthesizer, see

section 3.1 for details.

interference. The synthesizer is in turn locked to the INRIM

10MHz timebase; hence, the frequency uncertainty of the

polyphase generator is better than 1 × 10−10.

Five DAC channels are used.

energizing the bridge, the fifth gives a reference signal for the

lock-inamplifierwhichactsaszerodetector. Thefourchannels

enter purposely built analogue electronics which include for

each channel a line receiver (which decouples the computer

ground from the bridge ground), a 200kHz low pass two-pole

Butterworth filter to remove quantization noise and a buffer

amplifier with automatic control of dc offset [37] to avoid

possible magnetization of the electromagnetic components.

The analogue gain of each channel can be trimmed (see

section 5.2 for the trimming procedure).

Four are employed for

3.2. Resistance ratio bridge

A simplified coaxial diagram is shown in figure 3. Output

Va of the polyphase generator energizes the main isolation

transformer T having two secondary windings: one supplies

the measurement current, the other energizes the magnetizing

winding of the main ratio divider R.

Output Vc, and injection transformer Tchaving ratio Dc,

provides the main balance by adjusting R ratio. Output VW,

with transformer Twand injection capacitance CW, provides

Wagner balance. The detector D is the input of the lock-

in amplifier (in floating mode), manually switched between

detection points.

RQ is defined as a four terminal-pair impedance

standard [11]. The low-voltage port condition (V = 0,I = 0)

is given by the achievement of the main equilibrium. The

high-voltage condition (I = 0) is monitored by the detection

transformer Tvand the corresponding detector position; it is

achieved by adjusting the output Vb of the generator, with

drives on the injection transformer Tb.

R1,2isdefinedasatwoterminal-pairimpedancestandard,

at the end of its connection cables. The low-port condition

(V = 0) is achieved by the main equilibrium (although D is

not directly connected to R1,2, the low voltage–low current

internal connection of RQacts as a low-impedance T junction,

the same as is present in any two terminal-pair bridge).

Metrologia, 47 (2010) 464–472

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L Callegaro et al

The result of the measurement R1,2/RQ ≈ 8 can be

expressed as a function of7:

• the amplitude ratio |Vc|/|Va| and the phase difference

arg(Vc)−arg(Va) between the two voltage outputs Vcand

Vaof the polyphase generator;

• the complex deviation ? of the input–output ratio

k of R from its nominal value 1/9, expressed as

k = 1/9 + ?ph+ j?qd.

? is calibrated with a separate measurement setup [38],

which implements a bootstrap technique for the calibration of

inductive voltage dividers. The procedure has been validated

in an international intercomparison [39].

3.3. Quadrature bridge

The quadrature bridge is shown in figure 4.

measurestheproductC1C2intermsofR1R2; itisanevolution

of a similar bridge presented in [40].

The main ratio transformer T has a magnetizing winding

(driven by generator output Vmag) and a primary winding

(driven by output Va). The secondary winding is a centre-

tapped bifilar winding providing two nominally equal outputs

+E and −E.

The double equilibrium of the quadrature bridge is

obtained by adjustments of the quadrature voltage (provided

by generator output VQ) and of a balancing current (provided

by output Vcand an injection capacitor Cc).

A combining network N decouples the adjustments;

detector points are monitored with low-noise amplifiers A1

and A2and the lock-in amplifier, manually switched between

the two detection points8.

Output Vw, with transformer Twand injection network

Cw–Rw, provides Wagner balance.

The bridge

7Thepresentsetuplacksforthemomentadedicateddivider; forRa100-turn

divider with taps each 10 turns has been employed, purposely calibrated using

as input its 90th turn. To permit the correct excitation of its magnetization

winding (which has 100 turns), the two secondary windings of T have been

used on different taps. This gives for R1,2/RQthe equation

R1,2

RQ

= 8

?

1 +10

8

·

1

Dc

·|Vc|

|Va|cos[arg(Vc) − arg(Va)] −81

8?ph

?

,

(1)

which has been employed for the calculations in this paper. R and T will be

replaced with a dedicated isolation transformer/divider, and equation (1) will

be slightly modified accordingly.

8Quadrature bridges are typically [11,41] equipped with a notch passive

LC filter placed between the detection point and the detector input. The

filter construction requires extreme care, since high-valued L can couple with

stray magnetic fields at the excitation frequency. The total harmonic level

at equilibrium has been measured to be 50µV at the input of amplifier A2.

The maximum error caused by harmonic content can be estimated taking

into account the harmonic rejection of A2 (>100dB) and of the digital

lock-in amplifier, Stanford Research Systems model SR830 (90dB), and the

bridge sensitivity. An equilibrium error of ≈3 × 10−9is thus estimated. A

conservative uncertainty of 6 × 10−9to take into account such possible error

has been added to the uncertainty budget of table 1.

The reading of the quadrature bridge can be expressed as

(see [11, chapter 6.2.2])

ω2R1R2C1C2= 1 + δ.

(2)

The real part Re[δ] of δ, which links principal values of

R1,R2,C1,C2(the imaginary part Im[δ] links resistance time

constants to capacitance losses) is given by the expression

Re[δ] =|Vc|

|VQ|ωCcR2sin[arg(Vc) − arg(VQ)],

where |Vc| and |VQ| are the amplitudes of phasors Vcand VQ,

and arg(Vc) and arg(VQ) are their phases.

Equation (3) does not take into account possible

asymmetriesoftransformerT;however,thesearecompensated

by interchanging the connections of the outputs of T to the

bridge network, and by averaging the two values of Re[δ]

obtained with the two equilibria.

(3)

3.4. Bridge operation

The bridges are operated in a similar way, with the same

control program. The user interface permits the amplitude and

relative phase of each generator output to be set; to achieve

equilibrium, an automated procedure [42] is implemented,

resulting in increased speed and ease of operation. Presently,

thedetectorinputmustbemanuallyswitchedbetweendifferent

detection points; despite this, equilibrium is reached from an

arbitrary setting in a few minutes; if the bridge is already near

equilibrium condition the equilibrium approach is faster.

4. Maintained capacitance unit

The Italian national capacitance standard is presently

maintainedasthegroupvalueofseveral10pFquartz-dielectric

capacitors [29]. The capacitance differences are periodically

monitored, and the group value is updated by drift prediction

and by participating in international comparisons [43].

The scaling from 10pF to 1000pF is performed with a

manual two terminal-pair coaxial ratio bridge [29] and a step-

upprocedure[44]whichallowsonetocompensateforpossible

deviations of the transformer ratio from its nominal value.

5. Results

5.1. Measurements of RQ

The representation of the ohm at INRIM is given [45] by the

dc quantum Hall effect on the i = 2 step, RK/2 ≈ 12906.4?.

A dc potentiometer [46] performs calibrations of resistance

standards. A time series of measurements of RQis shown in

figure 7: a significant, but predictable, drift of 5n??−1d−1is

estimated.

5.2. Characterization of the polyphase generator

The analogue electronics of the generator introduces, for each

channel, an analogue gain and a phase rotation. As shown

in sections 3.2 and 3.3, the bridges’ measurement equations

468

Metrologia, 47 (2010) 464–472

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Realization of the farad from the dc quantum Hall effect

Figure 7. Time drift of the quadrifilar resistor RQ.

Figure 8. Typical time evolution of the detector reading (in-phase

and quadrature components) at the combining network detection

point of the quadrature bridge, after an equilibrium operation (for

t = 0). An Allan deviation analysis shows a 1/f behaviour for both

components. The deviation of detector reading from null gives a

bridge error, with a sensitivity of ≈2V−1; an error scale is also

reported in the graph.

(equations (1) and (2)) depend on amplitude ratios and phase

differences of the voltage outputs of two channels (Vc and

Vain the ratio bridge; Vcand VQin the quadrature bridge).

Therefore, the bridges’ accuracy is determined by amplitude

and phase matching of these channels, not by the absolute

accuracy of each channel setting.

Amplitude matching is trimmed by acting on the

electronics, and measured with a two-channel ac voltmeter to

be better than 5 × 10−5. Phase matching is verified with an

auxiliarycircuit(see[11,figure4.50a])tobetterthan100µrad.

Theverificationisperformedundernormalloadingconditions

(with the bridge circuit connected to the generator).

With these amplitude and phase tracking errors, if the

impedancestandardsdeviatefromtheirnominalvaluesbyless

thanafewpartsin10−5,thecontributiontothefinalaccuracyof

eachbridgecausedbythegeneratorscanbekeptnear1×10−8.

The mid-term stability and noise of the polyphase

generator can be inferred from drifts of detector readings of

Figure 9. Results of measurement of R2/RQwith the 8:1 resistance

ratio bridge over a period of 400 days. Data are expressed as

relative deviation (in parts per 106) from the nominal ratio

[R2/RQ]nominal= 8.

Figure 10. Results of measurement of δ ≡ ω2R1R2C1C2− 1 with

the quadrature bridge over a period of 400 days. The inset shows the

repeatability of the measurement over a few days.

Figure 11. Comparison between quadrature bridge and step-up

procedure.

Metrologia, 47 (2010) 464–472

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L Callegaro et al

Table 1. Measurement steps of the ohm–farad traceability chain: relative uncertainty expression (contributions and root-sum-square RSS).

Contribution to uncertaintyType

ur

Note

1. Calibration of RQat 1541Hz

Dc calibration of RQ

Phase correction of RQ

Frequency dependence

Current dependence

Short-term stability

RSS

2. Resistance ratio bridge

Noise

Main balance injection

4TP impedance definition

4TP cable corrections

2TP contact resistance repeatability

Residual loading on main IVD

Main IVD ratio

Non-coaxiality

RSS

3. Quadrature bridge

Noise

Frequency

Main balance injection

Distortion

Residual offset after inversion

2TP contact resistance repeatability

2TP capacitance repeatability

Non-coaxiality

RSS

n??−1

25

12

3

2

10

30

n??−1

10

12

10

1

1

10

45

5

50

nFF−1

20

0

12

6

3

1

1

5

25

A, B

B

B

B

B

Calibration with dc QHE

1 × 10−5loss angle of 10pF capacitor

10% of calculated frequency deviation

[31]

Estimated drift is 5 × 10−9day−1

A

B

B

B

B

B

B

B

Std. of the mean of ten measurements

5 × 10−4of a 25 × 10−6injection

See [11]

BPO repeatability, 100µ?

Bootstrap calibration [38]

Calibration of R1and R2

A

B

B

B

B

B

B

B

Std. of the mean of ten measurements

Lock to INRIM 10MHz frequency standard

5 × 10−4of a 25 × 10−6injection

Harmonic amplitude and lock-in rejection ratio

Average of difference of direct and reverse meas.

BPO repeatability, 100µ?

Calibration of (C1C2)1/2

the bridge. Figure 8 shows the time evolution of the detector

reading at the combining network of the quadrature bridge,

which is affected by all generator output drifts.

The harmonic content of the generated signals has been

measured on the bridges in working condition, on the high-

voltage port of the impedance standards; the spurious-free

dynamicrangeis90dB(tobecomparedwithasignal-to-noise

and distortion ratio (SINAD) of 98dB of an ideal 16bit DAC).

5.3. Resistance ratio bridge measurements

Figure 9 shows the measurement of R2/RQwith the resistance

ratio bridge (the result of R1/RQ, not shown, is very similar)

over a period of more than one year of operation. The ratio

drift is caused by the compound drift of both R2and RQ. The

inset of figure 9 shows the repeatability of measurements over

a few days.

5.4. Quadrature bridge measurements

Figure 10 shows the measurement of δ (see equation (2)) with

the quadrature bridge over the same time period of figure 9.

ThedriftisthecompounddriftofthestandardsR1,R2,C1,C2.

The inset of figure 9 shows the repeatability of measurements

over a few days.

5.5. Final result, and comparison with the maintained

capacitance standard

Figure 11 shows the geometric mean of C1and C2from the

nominal (1000pF) value. The result is computed from all

Table 2. Measurement of the geometric mean (C1C2)1/2of the

capacitance standards from dc quantum Hall effect with the new

traceability chain: standard uncertainty expression.

Contribution to uncertainty

ur× 10−9

30

50

10

Note

Calibration of RQat 1541Hz

Resistance ratio bridge

Short-term stability of

R1and R2

Quadrature bridge

RSS

Table 1, #1

Table 1, #2

TC of 2 × 10−6K−1;

5mK std. over 1h

Table 1, #325

64

data described previously. The observed drift is attributed to

compound drift of C1and C2.

In the same figure, the result (with uncertainty bars for

coverage factor k = 1) given by a step-up measurement from

themaintainednationalcapacitancestandardisshown;avisual

agreement can be appreciated.

6. Uncertainty

Tables 1–3 give the uncertainty expression corresponding to

the measurements described in section 5:

• Table 1 lists the uncertainty contributions related to the

variousmeasurementsandstandardsemployedinthenew

traceability chain.

• Table 2 gives the uncertainty budget for the measurement

of the geometric mean (C1C2)1/2of the 1000pF

capacitance standards C1and C2in terms of the INRIM

470

Metrologia, 47 (2010) 464–472

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Realization of the farad from the dc quantum Hall effect

Table 3. Comparison between the measurement with the new traceability chain and the maintained national capacitance standard.

Contribution to uncertaintyType

ur

Note

1. Calibration of RQat 1541Hz

10pF maintained group value at 1592Hz

Capacitance bridge, 10pF to 100pF step-up

Capacitance bridge, 100pF to 1000pF step-up

Short-term stability of 1000pF capacitors

Frequency correction

New traceability chain, (C1C2)1/2

RSS

nFF−1

400

40

100

4

5

64

419

B

B

B

B

B

B

Two measurements

TC 4 × 10−6K−1; 1mK controller stability

1541Hz to 1592Hz, gas-dielectric

Table 2

representationoftheohmgivenbythequantumHalleffect

in the dc regime;

• Table 3 gives the uncertainty budget for the comparison

described in section 5.5 and shown in graphical form in

figure 11.

All uncertainties are given for a coverage factor k = 1.

7. Conclusions

The paper has described a traceability chain for the realization

of the farad from the quantum Hall effect, which includes

two bridges, a resistance ratio bridge and a quadrature

bridge, based on a polyphase sine-wave generator.

bridges do not contain variable passive components like

multi-decadicinductivevoltagedividersorimpedancedecadic

boxes; the equilibrium is obtained by DDS of the necessary

signals. In the present implementation the bridge operation

is semi-automated and the equilibrium is reached in a

short time.

The total relative standard uncertainty of the traceability

chain is estimated to be 64 × 10−9(k = 1) at the level

of 1000pF, sufficient for a national metrology institute, in

particular if one considers the large cost reduction with

respect to traditional implementations. A first verification of

the realization accuracy is given by a comparison with the

maintained national capacitance standard, but an international

comparison is planned in the near future.

Future improvements of the implementation will include

the installation of individually thermostated resistance

standards for R1 and R2, and the complete automation of

the bridges with a remotely controlled coaxial switch. Since

thedigitalassistanceofprimaryimpedancebridgeshasproved

to be a successful approach, the realization of a digitally

assisted10:1ratiobridgeforscaling1000pFtomaintain10pF

standards is under consideration.

The

Acknowledgments

TheauthorsareindebtedtoFFranconeandDSerazio(INRIM)

forthephysicalconstructionoftheelectromagneticdevices; to

CCassiago(INRIM)forthecalibrationofRQandtoFOverney

(METAS, Switzerland) for the communication listed as [31].

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