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

**ABSTRACT** A new traceability chain for the derivation of the farad from dc quantum Hall effect has been implemented at INRIM. Main components of the chain are two new coaxial transformer bridges: a resistance ratio bridge, and a quadrature bridge, both operating at 1541 Hz. The bridges are energized and controlled with a polyphase direct-digital-synthesizer, which permits to achieve both main and auxiliary equilibria in an automated way; the bridges and do not include any variable inductive divider or variable impedance box. The relative uncertainty in the realization of the farad, at the level of 1000 pF, is estimated to be 64E-9. A first verification of the realization is given by a comparison with the maintained national capacitance standard, where an agreement between measurements within their relative combined uncertainty of 420E-9 is obtained. Comment: 15 pages, 11 figures, 3 tables

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**ABSTRACT:**An RLC bridge based on an automated synchronous sampling system has been developed using commercially available high-resolution analog-to-digital and digital-to-analog converters. This bridge allows the comparison of any kind of impedance standards in the four-terminal-pair configuration at frequencies between 50 Hz and 20 kHz within a range from 1 Ω to 100 kΩ. An automatic balance of the bridge is carried out using a downhill simplex algorithm. Consistency checks have been realized by comparing resistance, inductance, and capacitance standards at different frequencies. The consistency of the measured voltage ratio is better than 20 μV/V over the whole frequency range and even smaller than 5 μV/V around 1 kHz. Finally, the results of the calibration of a 10-nF capacitance standard have been compared to those obtained using a commercial high-accuracy capacitance bridge. The difference is smaller than the commercial bridge specifications over the whole frequency range.IEEE Transactions on Instrumentation and Measurement 08/2011; · 1.36 Impact Factor - SourceAvailable from: Luca Callegaro[show abstract] [hide abstract]

**ABSTRACT:**A current comparator impedance bridge, suitable for the comparison of four-terminal-pair impedance standards having similar phase angles (e.g., resistors or capacitors) in the audio frequency range at 1 : 1 and 10 : 1 nominal ratios, is here presented. The bridge is digitally assisted: Its accuracy is granted by an electromagnetic device, a high-permeability core current comparator, but the voltages and currents needed to achieve both principal and auxiliary equilibria are generated by programming a polyphase direct-digital-synthesis generator. The resulting implementation is neat and simple and does not include variable components such as decade dividers. The measurement is semiautomated: After an initial setting, the equilibrium can be achieved in a few minutes. Measurements performed on calculable resistors give a base accuracy of a few parts in 107 at kilohertz frequency, sufficient for calibration purposes, with the potential for further improvement.IEEE Transactions on Instrumentation and Measurement 01/2013; 62:1771-1775. · 1.36 Impact Factor

Page 1

arXiv:1003.1582v1 [physics.ins-det] 8 Mar 2010

Realization of the farad from the dc quantum Hall

effect with digitally-assisted impedance bridges

Luca Callegaro† §, Vincenzo D’Elia†, and Bruno Trinchera†

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

Torino, Italy

Abstract.

A new traceability chain for the derivation of the farad from dc quantum

Hall effect has been implemented at INRIM. Main components of the chain are

two new coaxial transformer bridges: a resistance ratio bridge, and a quadrature

bridge, both operating at 1541Hz. The bridges are energized and controlled with

a polyphase direct-digital-synthesizer, which permits to achieve both main and

auxiliary equilibria in an automated way; the bridges and do not include any

variable inductive divider or variable impedance box. The relative 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

national capacitance standard, where an agreement between measurements within

their relative combined uncertainty of 420 × 10−9is obtained.

§ Corresponding author (l.callegaro@inrim.it)

Page 2

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges2

1. Introduction

A number of National Metrology Institutes work on measurement setups to trace

the farad to the representation of the ohm given by the dc quantum Hall effect

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] . The traceability chains employed involve a number of

experimental steps, usually requiring not less than three different coaxial ac bridges.

The bridges are complex networks of passive electromagnetic devices [12]: some of

such devices 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

typically manually operated; only a few models have been described [13, 14, 7, 15]

? which permit remote control. Consequently, a large part of existing bridges 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 enters the measurement model equation, and must be calibrated (main

balance), but the others (auxiliary balances) don’t need a calibration.

In this view, it is straightforward to consider a substitution in the bridge network

of most, or all, variable passive devices with a corresponding number of active sinewave

generators, locked to the same frequency but adjustable in amplitude and phase

independently of each other. Direct digital synthesis (DDS) of sinewaves [16] is a

well-established technique that permit the realization of such generators; hence, in

this sense, we may speak of digitally-assisted impedance bridges when DDS generators

are used. Digitally-assisted bridges impedance have been considered both theoretically

[17, 18] and in a number of implementations [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29];

some commercial impedance meters are also digitally-assisted.

In this paper, we consider for the first time the feasibility of a complete ohm

to farad traceability chain based on digitally-assisted bridges.

resistance ratio bridge and a quadrature bridge, to measure capacitance (at the level

of 1000pF) in terms of dc quantum Hall resistance (at the level of RK/2 ≈12906.4Ω,

where RK is the Von Klitzing constant). The bridges are automated, and a single

measurement can be conducted in minutes. The estimated relative uncertainty of the

capacitance determination related to the traceability chain is 64 × 10−9.

This accuracy claim hasn’t yet been verified with a comparison with other farad

realization. However, by completing the chain with an older manual transformer ratio

bridge [30], 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 uncertainty of 400 × 10−9· The measurement results of the comparison are

compatible within the relative compound uncertainty.

We constructed a

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

Page 3

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges3

2. The traceability chain

The traceability chain which has been set up, including the steps for the comparison

(Sec. 6.5) with the maintained capacitance standard is shown in graphical form in

Fig. 1. Its steps are here summarized and will be described in more detail in the

course of the paper.

• The quantum Hall effect is employed to calibrate a resistor RQhaving the nominal

value RK/2 ≈ 12906.4Ω and a calculable frequency performance;

• RQ is employed in a 8:1 resistance ratio bridge to calibrate two resistance

standards R1,2, with nominal value 4 × RK ≈ 103.251kΩ, at the frequency

f ≈1541.4Hz;

• R1,2are employed in a quadrature bridge to calibrate the product C1×C2of two

capacitance standards C1,2with nominal value of 1000pF;

• in order to perform the comparison with the maintained 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;

• a small calculated frequency correction is applied to permit the comparison.

3. Impedance standards

The standards employed in the traceability chain are:

RQ a quadrifilar resistance standard, having a nominal value RQ = RK/2.¶

frequency performance and reactive parameter are calculable from geometrical

dimensions [31]: the result of the calculation is shown in Fig. 2. The standard

is thermostated to improve its stability. The original standard has an inductance

of ≈3µH; in order to reduce its phase angle, a small gas-dielectric capacitor has

been added in parallel to its current terminals.

R1,2 two resistance standards with nominal value R1,2 = 4 × RK. Presently, two

thin film resistors+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.

C1,2 two 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. Ref. [7] gives

a detailed description of the construction and characterization.

Its

4. Digitally-assisted coaxial bridges

The digitally-assisted bridges developed are a 8:1 resistance ratio bridge, and a

quadrature bridge. The coaxial schematics can be seen in Fig.

respectively. The bridges are based on the same design concept and share common

instrumentation: the polyphase generator (Sec. 4.1), the impedance standards (Sec.

3), and the detector. A photo of both bridges is shown in Fig. 5.

3 and Fig.4

¶ NL engineering Type QF, serial 1294.

+Vishay mod.VHA512 bulk metal foil precision resistors, ±0.001% tolerance, 0.6ppm/◦C

temperature coefficient.

Page 4

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges4

ac-dc?calculation

dc?potentiometer

ac-dc?correction?to

1541?Hzf

RR

QQ

=R

Q

acdc ac/dc

+ ?

2resistors

103.251?k

1541?Hz

?

?

R

f

1,2

resistance?ratio?bridge

2

1?nF?gas-dielectric

1541?Hzf

capacitors

?

C

1,2

frequency?corrections

100?pF?at?1592?Hz

10?pF?at?1592?Hz

two?terminal-pair?ac?bridge

two?terminal-pair?ac?bridge

Quantum?Hall?effect

in?dc

1

R

resistor

12906.4=/2

dc?calibration

?

?

quadrifilar

R

KQ

dc

quadrature?bridge

2

1?nF?gas-dielectric

f1592?Hz

capacitors

?

C1,2

comparison

Figure 1. Graphical representation of the traceability chain for the realization

of the farad unit from the quantum Hall effect.

4.1. Polyphase generator

Both bridges are energized (one at a time) by a polyphase DDS generator; the

schematic diagram is reported in Fig. 6. The core of the generator is a commercial

digital-to-analogue (DAC) board∗.The board is programmed for a continuous

∗National Instruments mod. NiDaq-6733 PCI board, 8 DAC outputs, variable reference input, 16

bit resolution, maximum sampling rate 1MSs−1, voltage span ±10V.

Page 5

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges5

?

???

????????

??

?

?

?

?

?

?

?

??

Figure 2. Frequency performance of the RQresistor.

D

D

Va

Cw

Tw

R1,2

RQ

Vw

Vb

Vc

Tc

Tb

T

R

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

the mesh are current equalizers.

generation of sinewaves; each wave can be updated without stopping the generation

(large amplitude or phase changes are gradually achieved to avoid steps in the output).

Since the sinewaves are represented by an integer number 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 synthesizer♯ connected to the DAC board by an optical fibre link [32]

to minimize high-frequency interferences. The synthesizer is in turn locked to INRIM

10MHz timebase; hence, the frequency uncertainty of the polyphase generator is better

than 1 × 10−10.

Five DAC channels are used. Four are employed on the bridge network, the fifth

gives a reference signal for the lock-in amplifier which acts as zero detector. The four

channels enter a purposely-built analog electronics which include, for each channel, a

line receiver (which decouple the computer ground from the bridge ground), a 200kHz

♯ Stanford Research System mod. DS345.

Page 6

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges6

CW

Va

Vmag

Tw

Vc

Cc

R1

C1

C2

VQ

Vw

N

T

+E

-E

R2

D

A2

D

A1

RW

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.

low pass two-pole Butterworth filter to reduce the quantization noise, and a buffer

amplifier with automatic control of dc offset [33] to avoid possible magnetizations

of the electromagnetic components. The analog gain of each channel can be finely

trimmed.

4.2. Resistance ratio bridge

A simplified coaxial diagram is shown in Fig. 3. Output Vaof the polyphase generator

energizes the main isolation transformer T, which has two secondary windings: one

supplies the measurement current, the other energizes the magnetizing winding of the

main ratio divider R. RQis defined as a four terminal-pair impedance, whereas R1,2

is defined as two terminal-pair impedance. Output Vbof the generator, with injection

transformer Tb, adjusts the current in RQ. Output Vc, and injection transformer

Tc having ratio Dc, provide the main balance by adjusting R ratio. Output VW,

with transformer TWand injection capacitance CW, provides Wagner balance. The

Page 7

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges7

Vmag

V V

b

Vc

Vw

Q

,

Vref

PC

DAC?Board

GPIB

IN

A

Va

GPIB

Lock?in?Detector

Primary

timebase

10?MHz

Synthesized

Generator

Optical?link1?MHz

~

D

Gnd

Figure 6. Schematic diagram of the sinewave synthesizer, see Sec. 4.1 for details.

detector D is the input of the lock-in amplifier (in floating mode), manually switched

between detection points.

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

R1,2

RQ

= 8

?

1 +10

8

·

1

Dc

·|Vc|

|Va|cos[arg(Vc) − arg(Va)] −81

8ǫph

?

,

(1)

Eq. 1 takes into account also the complex deviation ǫ of the ratio k of R from its

nominal value 1/9, expressed as k = 1/9+ǫph+jǫqd. R is calibrated using a bootstrap

technique [34] validated in an international intercomparison [35].

4.3. Quadrature bridge

The quadrature bridge is shown in Fig. 4. The bridge measure the product C1C2in

terms of R1R2; it is an evolution of a similar bridge presented in [36].

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 center-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 fixed combining network N decouples the adjustments; detector points are

monitored with low-noise amplifiers A1 and A2 and the lock-in amplifier, manually

switched between the two detection points ††.

Output VW, with transformer TW and injection network CW-RW, provides

Wagner balance.

The reading of the quadrature bridge can be expressed as (see Ref. [12], ch. 6.2.2)

ω2R1R2C1C2= 1 + δ

(2)

††The notch filter for harmonics rejection, commonly employed in other setups [12, 11], has proven

unnecessary because of the high harmonic rejection (−90dB) of the digital lock-in amplifier employed,

Stanford Research Systems model SR830, and of A1and A2. The residual effect has been considered

as an uncertainty contribution, see Sec. 7.

Page 8

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges8

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|ω CcR2sin[arg(Vc) − arg(VQ)]

(3)

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

are their phases.

Eq. 3 does not take into account possible asymmetries of transformer T; however,

these are compensated by exchanging 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.

4.4. Bridge operation

The bridges are operated in a similar way, with the same control program. The user

interface permits to set the amplitude and relative phase of each generator output;

to achieve equilibrium, an automated procedure [37] is implemented, resulting an

increased speed and ease of operation. Presently the detector input must be manually

switched between different detection points; despite this, equilibrium is reached from

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

condition the procedure is faster.

5. Maintained capacitance unit

The Italian capacitance national standard is presently maintained as the group value

of several 10pF quartz-dielectric capacitors [30].

periodically monitored, and the group value is updated by drift prediction and by

participating to international comparisons [38]. The scaling from 10pF to 1000pF

is performed with a manual two terminal-pair coaxial ratio bridge [30] and a step-

up procedure which permits to compensate for possible deviations of the transformer

ratio from its nominal value.

The capacitance differences are

6. Results

6.1. Measurements of RQ

The representation of the ohm at INRIM is given [39] by the dc quantum Hall effect

on the i = 2 step, RK/2 ≈ 12906.4Ω. A dc potentiometer [40] performs calibrations

of resistance standards. A time series of measurements of RQis shown in Fig. 7: a

significant, but predictable, drift of 5nΩΩ−1d−1is estimated.

6.2. Characterization of the polyphase generator

As shown in Sec. 4.2 and 4.3, the reading of each bridge is given by a mathematical

expression whose input quantity is the complex ratio of the nominal settings of two

generators (Vc/Vafor the ratio bridge, Vc/VQfor the quadrature bridge). The tracking

of the different outputs of the generator (under proper loading conditions) has been

adjusted and calibrated; the deviations from nominal values are within a few parts in

104. Since the impedance standards deviate from their nominal values by less than a

Page 9

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges9

??

??

?

?

?

?

??

??

Figure 7. Time drift of the quadrifilar resistor RQ.

few parts in 10−5, and their relative phases have been adjusted, the contribution to

final accuracy of each bridge caused by the generators can be kept near 1 × 10−8.

The stability and noise of the polyphase generator can be inferred from drifts of

detector readings of the bridge after an equilibrium. Fig. 8 show the time evolution

of the detector reading at the combining network of the quadrature bridge, which is

affected by all generator output drifts.

?

?

?

?

?

?

?

?

Figure 8.

quadrature components) at the combining network detection point of the

quadrature bridge, after an equilibrium operation (for t = 0).

Typical time evolution of the detector reading (in-phase and

6.3. Ratio bridge measurements

Fig. 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.

Page 10

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges10

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

9 shows the repeatability of measurements over a few days.

?

?

?

?

??

?

?

?

?

?

??

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

over a period of 400 days. Data is expressed as relative deviation (in parts per

106) from the nominal ratio [R2/RQ]nominal= 8.

6.4. Quadrature bridge measurements

Fig. 10 shows the measurement of δ (see Eq. 2) with the quadrature bridge over the

same time period of Fig. 9. The drift is the compound drift of the standards R1, R2,

C1, C2. The inset of Fig. 9 shows the repeatability of measurements over a few days.

?

??

?

?

?

?

?

?

?

?

???

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.

Page 11

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges11

6.5. Final result, and comparison with the maintained capacitance standard

Fig. 11 shows the geometric mean of C1and C2from the nominal (1000pF) value. The

result is computed from all data previously described. The observed drift is attributed

to coumpond drift of C1and C2.

In the same figure, the result (with uncertainty bars) given by a step-up

measurement from the maintained national capacitance standard is shown; a visual

agreement can be appreciated. This measurement is performed at the frequency of

1592Hz and should be corrected to 1541Hz because of the frequency dependence of

C1and C2. Indirect measurements of such dependence, performed with the so-called

S-matrix method [41] give a correction below 1 × 10−9. An uncertainty contribution

associated with the correction has been nevertheless added to the uncertainty budget

(see Sec. 7).

?

?

?

?

????

??

?

?

?

?

?

Figure 11. Comparison between quadrature bridge and step up procedure.

7. Uncertainty

Tables 1–3 give the uncertainty expression corresponding to the measurements

described in Sec. 6:

• Tab. 1 lists the uncertainty contributions related to the various measurements

and standards employed in the new traceability chain;

• Tab. 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

representation of the ohm given by the quantum Hall effect in dc regime;

• Tab. 3 gives the uncertainty budget for the comparison described in Sec. 6.5 and

shown in graphic form in Fig. 11.

8. Conclusions

The paper described a new traceability chain for the realization of the farad from

the quantum Hall effect, which include two bridges, a resistance ratio bridge and a

Page 12

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges12

Table 1.

uncertainty expression (contributions and root-sum-square RSS)

Source of uncertainty

1: Calibration of RQ@ 1541Hz

DC calibration of RQ

phase correction of RQ

Frequency dependence

Short-term stability

RSS

Measurement steps of the ohm-farad traceability chain:relative

Type

ur

Note

nΩ · Ω−1

25

12

3

10

30

nΩ · Ω−1

10

12

10

1

1

10

45

5

50

nF · F−1

20

0

12

6

3

1

1

5

25

A, B

B

B

B

Calibration with dc QHE

1 × 10−5loss angle of 10pF capacitor

10% of calculated frequency deviation

Estimated drift is 5 × 10−9/day

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

Noncoaxiality

RSS

A

B

B

B

B

B

B

B

Std of the mean of 10 measurements

5 × 10−4of a 25 × 10−6injection

See [12]

BPO repeatability, 100µΩ

Bootstrap calibration [34]

Calibration of R1 and R2

3: Quadrature bridge

Noise

Frequency

Main balance injection

Distortion

Residual offset after inversion

2TP contact resistance repeatability

2TP capacitance repeatability

Noncoaxiality

RSS

A

B

B

B

B

B

B

B

Std of the mean of 10 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, 100µΩ

Calibration of (C1C2)1/2

Table 2.

standards from dc quantum Hall effect with the new traceability chain:

uncertainty expression.

Source of uncertainty

ur× 10−9

Calibration of RQ @ 1541Hz

25

Resistance ratio bridge

50

Short-term stability of R1 and R2

10

Quadrature bridge

25

RSS

64

Measurement of the geometric mean (C1C2)1/2of the capacitance

Note

Tab. 1, #1.

Tab. 1, #2.

TC of 2 × 10−6K−1; 5mK std over 1h

Tab. 1, #3.

quadrature bridge, based on a polyphase sinewave generator. The bridges do not

contain variable passive components like multi-decadic inductive voltage dividers or

impedance decadic boxes; the equilibrium is obtained by direct digital synthesis of

the necessary signals. In the present implementation the bridge operation is semi-

automated and the equilibrium is reached in short time.

The total relative uncertainty of the traceability chain is estimated to be

Page 13

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges13

Table 3. Comparison between the measurement with the new traceability chain,

and the maintained capacitance national standard.

Source of uncertainty

1: Calibration of RQ@ 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

Type

ur

Note

nF · F−1

400

40

100

4

5

64

419

B

B

B

B

B

B

2 measurements

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

1541Hz to 1592Hz, gas-dielectric

Tab. 2

64 × 10−9at the level of 1000pF, therefore adequate for a national metrology institute.

A first verification of the realization accuracy is given by a comparison with the

maintained capacitance national standard, but an international comparison is being

planned in the next months.

Future improvements of the implementation will include the installation of

individually thermostatted resistance standards for R1 and R2, and the complete

automation of the bridges with a remotely-controlled coaxial switch. Since the digital

assistance of primary impedance bridges has proved as a successful approach, the

realization of a digitally-assisted 10:1 ratio bridge for scaling 1000pF to maintained

10pF standards is under consideration.

Acknowledgments

The authors are indebted with their colleagues F. Francone and D. Serazio for the

physical construction of the electromagnetic devices; and to C. Cassiago for the

calibration of RQ.

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