Instrumentation & Measurement Magazine 23-3 - 15

trivial. In the electrostatic case, the movable capacitor plate
needs to be servoed to different positions where the capacitance must be measured in order to obtain the capacitance
gradient. Each of the measurements occurs statically, and no
synchronization is required.
An advantage of the magnetic actuator in the Kibble balance is that it can be used to make forces in both directions. The
force is proportional to the current and by reversing the direction of the current, the direction of the force can be reversed.
This is not the case for the electrostatic capacitor, where the
force is proportional to the square of the potential difference.
Hence, if one capacitor plate is grounded, the force will be the
same, whether there is a positive or negative voltage of the
same magnitude applied to the other plate. The force is always
in the direction that maximizes the capacitance. Lastly, the
Kibble balance is ideally suited for larger forces (millinewton
to newton), whereas the electrostatic balance is ideally suited
for smaller forces (mirconewton and below). This can be easily seen, by the fact that geometric factor in the Kibble balance
ranges from about 1 T m to 1000 T m, while dC is about 10−9
dz
F/m. Hence, 1 mA in a coil of a Kibble balance produces a force
between 1 mN and 1 N. A potential difference of 100 V in the
electrostatic balance, however, only produces a force of 5 μN.
What are our expectations for 2020 regarding these technologies? Fig. 5 shows a comparison of different methods to
measure mass. The data points represented by the red circles
are taken from the entries that the NIST has at the calibration
measurement capability database maintained at the International Bureau of Weights and Measures (BIPM). In blue and
cyan are shown the uncertainties that were achieved with two
Kibble balances named NIST-4 and KIBB-g1. The former is a
Kibble balance that is optimized to measure 1 kg mass pieces
and was formerly used to help established the now fixed value
of the Planck constant. The latter is a table top Kibble balance

that can be used to weigh 1 g masses. The intention for this balance is to bring Kibble balance technology to the factory floor.
The uncertainties shown at the smaller mass range are obtained with the electrostatic force balance. These uncertainties
are smaller than the uncertainties that are obtained with the
traditional subdivision method.
The challenge for metrology in 2020 is twofold: First, to develop primary realization of the unit of mass in the range from
10 mg to 100 g. In this range, the subdivision of mass standards
still outperforms the primary realization methods. Second, to
achieve larger penetration of the existing technology. At NIST,
efforts are under way to build a Kibble balance for 100 g masses
with a stated relative uncertainty goal of a few parts in 108.
Such a Kibble balance should be lower cost than a 1 kg balance
and could be a good alternative for smaller national metrology
institutes to realize the unit of mass. A larger penetration includes not only Kibble balances on the factory floor but also the
application of these traceable measurement devices for other
applications. One area that researchers at NIST are actively
engaged in is measuring laser power with an electrostatic balance. There, the momentum transfer of light in reflection will
cause a force on a mirrored surface that is measured with an
electrostatic balance.

The Quantum Hall Effect for Resistance
and Impedance Measurements

The quantum Hall effect was discovered by Klaus von Klitzing
in 1980 [13]. Klitzing carried out measurements of electronic
transport in silicon field effect transistors at low temperatures
when he discovered the quantization of the Hall resistance,
the quotient of transversal voltage to longitudinal current
in the presence of a magnetic field. This resistance is quantized at a submultiple of the von-Klitzing constant RK = h/e2,
which has a convenient exact value, which is approximately
25 813 Ω. The value is convenient in the sense that
it is close to the geometric
mean of 10 μΩ and 1 TΩ,
a range that encompasses
most electrical resistors
used in technology. In the
SI, the Planck constant and
the elementary charge are
both fixed, and hence, the
von-Klitzing constant can
be calculated to arbitrary
precision.
For the quantum Hall
effect to occur, three conditions must be met: the
system must feature a twodimensional electron gas;
Fig. 5. Relative uncertainty of mass measurements from 50 μg to 5 kg. The red filled points are from the calibration
must be sufficiently cold;
measurement capability (CMC) of NIST. These points are obtained by a work-down and work-up down from the mass
and must be immersed in
assigned to a prototype. NIST-4 and KIBB-g1 are two Kibble balances, the former working with 1 kg standards, the latter
a strong magnetic field
with 1 g standards. The green circles represent relative uncertainties that were obtained with the NIST electrostatic force
that is perpendicular to
balance (EFB).
May 2020

IEEE Instrumentation & Measurement Magazine 15

Instrumentation & Measurement Magazine 23-3

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