Measurement 46 (2013) 1333–1339
Contents lists available at SciVerse ScienceDirect
Measurement
journal homepage: www.elsevier.com/locate/measurement
Review
Proposal for the direct comparison of the standards of,
capacitance and inductance to ac QHR
F. Castelli
Via Dino Compagni, 5 – 20131 Milano, Italy
a r t i c l e
i n f o
Article history:
Received 1 July 2011
Received in revised form 13 April 2012
Accepted 3 October 2012
Available online 26 October 2012
Keywords:
Quantized Hall resistance
Thompson–Lampard calculable capacitor
SI ohm
Quadrature and cryogenic current
comparator bridge
Inter-comparison method of standards
a b s t r a c t
The representation of the ohm by the quantum Hall effect permits the reproduction of the
farad unit by tracing capacitance to dc resistance. Many R–C bridge’s types are used in
these determinations. In effect a chain of some bridges must be used.
The proposed ‘‘direct comparison method’’ (DCM) is based on the definition of impedance and admittance and performs the detection of the equality of the rms value of voltage
drops and currents.
By DCM, at maximum operating frequency of 3 kHz, capacitance and inductance standards in the rage from 2 nF to 2 lF and from 30 mH to 1 H can be directly compared to
ac QHR.
These comparisons by DCM can be performed within few parts in 109 and a frequency
measurement currently performable within one part in 109–1010 and the detection of
the ratio of resistances and conductances performable within few parts in.
Ó 2012 Elsevier Ltd. All rights reserved.
Contents
1.
2.
3.
4.
5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.
Two- terminal connections for the QHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Basic principle of DCM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.
Zeroing procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.
Zero balance detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Applications of DCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.
DCM for comparing capacitance standards to ac QHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.
DCM for comparing inductance standards to ac QHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.
DCM for inter-comparing capacitance and inductance standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Uncertainty and test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.
Buffers’ calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A.
Test of the sensitivity and calibration of PTTCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E-mail address: franco.castelli@polimi.it
0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.measurement.2012.10.002
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F. Castelli / Measurement 46 (2013) 1333–1339
1. Introduction
The representation of the ohm by the quantum Hall effect permits the reproduction of the farad unit by tracing
capacitance to dc resistance [1,2]. In recent years, a few national metrology laboratories (NMLs) have been engaged in
attempts to compare quantized Hall resistance (QHR) devices with capacitors at audio frequencies to provide direct
determination of capacitance standards from the QHR. The
determination of resistance in terms of capacitance and
frequency is an essential stage in the route from the calculable capacitor to the SI ohm. A multiple frequency R–C
bridge [3,4] can be used to measure the ac resistance of
two or more resistors in terms of capacitance. If the resistors are sufficiently stable [5] they can be subsequently
measured in terms of ac QHR with the use of a transformer
ratio bridge and the results of the two bridge measurements can be combined to relate ac QHR to a capacitance
standard.
Both NMLs and secondary laboratories (SLs) maintain
the scale of ac resistance, inductance and capacitance
with sets of artifact standards. In NMLs, the traceability
chain for the impedance scale involves a set of coaxial
ac ratio bridges, the primary standard being the calculable capacitor. In SLs, the full set of standards is periodically calibrated by NML. NMLs have established a
measurement chain allowing calibration of capacitance
standards in term of the quantized Hall resistance QHR.
See in [6] the measurement chain of one of the more recent of these calibrations.
NML’s [7] for many years maintained the units of resistance and capacitance based on cross-capacitance measurements made with a Thompson–Lampard calculable
capacitor. The used design allows the farad to be related
to the International System (SI) units through measurements of length, and the SI ohm can be determined from
the calculable capacitor using a quadrature bridge based
on SI frequency standard.
Adoption of the QHR as reference standard in 1990 [8]
allowed the ohm to be maintained independently of the
farad, although the SI unit is still derived from the calculable capacitor [6].
The stability of resistance and capacitance standards [9]
is 10–50 times better than that of inductance standards,
this situation is thus sufficient to monitor the stability of
inductance standards by direct comparison with resistance
and capacitance standards. E.G. by means of a multifrequency double-balance L bridge, 1- and 10-nF capacitors
are linked to inductance standards whose values range
from 1 to 100 mH [10].
The illustrated proposal of the new comparison method
called the, ‘‘direct comparison method’’ (DCM) allows the
inter-comparison of capacitance inductance and resistance
standards of unequal rated values and their direct comparison to ac QHR. This is not performable by the, at present,
available impedance calibration proceedings.
The DCM allows these direct comparisons by a very
simple and accurate method performable, at maximum
operating frequency of 3 kHz, with the standards in the
rage, from 2 nF to 2 lF and, from 30 mH to 1 H, with
Fig. 1. Schematic diagram of the 2-terminal connection for the QHR.
sensitivity and resolution of few parts in 109 and a frequency measurement.
The DCM has been devised to exploit the chances of sensitivity in detecting the equality of rms currents and voltage
drops offered by the platinum thermoresistor thermal converter (PTTC) in its per difference form (PTTCD) [10].
The dc QHR is well established and is internationally accepted as a representation of the SI ohm. The quantized
Hall resistance is not exclusively a dc effect and has been
observed at audio- and radio-frequencies.
Metrological studies of the ac QHR attempt to deal with
several questions [12], in particular:
Can the ac QHR be used as a reference of ac resistance to
1 107 or better?
Is the ac QHR as accurate as the dc QHR?
Can the ac measurements improve our incomplete
understanding of the physics or the metrological limitations of the QHR?
Can an improved realization of the farad be maintained
using the ac QHR?
With alternating currents in the kilohertz frequency
range of 1–6 kHz the width of the plateau shows no significant frequency dependence [13].
In the course of the past ten years increased attention
has been paid to investigating the metrological applicability of the fact that the quantum Hall effect (QHE) can also
be observed when alternating current is supplied to a
quantum Hall device (QHD).
Measurements replicated at a number of laboratories
have shown that the unit of resistance can be reproduced
by means of AIGaAs/GaAs heterostructures with an uncertainty on the order of one part in 107 over a frequency
range from dc to at 1east 5 kHz. Nevertheless [9], QHDs
should be characterized carefully before being employed
as reference standards for impedance calibrations.
ID
727478
Title
Proposalforthedirectcomparisonofthestandardsof,capacitanceandinductancetoacQHR
http://fulltext.study/article/727478
http://FullText.Study
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