Instrumentation & Measurement Magazine 23-3 - 13

Fig. 4. The Fixed-Length Optical Cavity is housed in a copper block, which
helps to stabilize the temperature. In this photo, the upper plate of the block
has been removed (photo credit: NIST).

is also L. The resonance frequency is therefore different and n
is determined from this difference [4]. A short video explains
how the FLOC determines n [10].
Direct tests made several years ago with respect to NIST's
primary mercury standard demonstrated the superiority of the
FLOC at the lower end of the mercury manometer's range and
had better precision throughout the entire range [10]. A recent
feature in Nature Physics [11] gives an optimistic account of the
program to replace the primary mercury manometer, although
the conclusion of [9] is that much work still remains to be done
to displace what the authors refer to as "the mechanical pascal,"
by which they mean the pascal realized by force measurements.

Mass and Force Measurements Based
on the Planck Constant
The Kibble balance, invented by the first contributor to the Basic Metrology column, Bryan Kibble [12], is an apparatus that
can be used to realize the unit of mass from the Planck constant.
Two building blocks are necessary to assemble a Kibble balance: a balance and quantum electrical standards. The balance
itself is an electromechanical device that allows to counteract
the weight of a mass standard with a force that is generated by
a current carrying coil immersed in a magnetic field. The ingenious insight of Bryan Kibble was the fact that the conversion
factor between the current in the coil and the resulting force is
May 2020	

identical to the conversion factor between voltage and velocity,
when the same system is used as a generator. In this mode, the
(electrically) open coil is moved vertically through the magnetic field, while simultaneously measuring the coil's velocity
and the electro motive force that appears between the coil's
ends. By doing this with great care, the so-called geometric
factor of the Kibble balance can be measured to with uncertainties that are smaller than a part in 108 (for the world's best
Kibble balances that is). And, by applying the geometric factor to the force mode, a device that converts current to a force
with slightly larger uncertainties. In short, a known force can
be generated relying upon measurements of voltage, current,
and velocity.
To measure voltage and current, the quantum electrical
standards are used. The quantum Hall effect provides a resistance standard that is an integer fraction of h/e2, about 25
812.807 kΩ. Here, h is the Planck constant, and e the elementary charge, two of the seven defining constants of the SI. Note:
a Kibble balance does not need to be directly connected to a
quantum Hall resistor; a standard resistor that has been calibrated against a quantum Hall resistor is all that is needed.
By routing the coil current through this standard resistor, a
voltage drop occurs. The resistive voltage drop, as well as the
induced voltage in the velocity mode, can be precisely measured with the help of the Josephson effect [4]. This quantum
mechanical phenomena that occurs at a tunnel barrier between two superconducting layers provides a voltage that is
h
proportional to f , where f is the frequency of a microwave
2e
current driven through the tunnel barrier. By combining two
measurements of voltage with the quantum Hall resistor, the
elementary charge drops out, but the Planck constant remains.
Hence, force can be written as:
	

F=

f 2h
β ,	(8)
v 1

where β1is a known numerical factor that contains the number
of Josephson junctions used, the integer in the quantum Hall
effect and the ratio of h/e2 to the standard resistor used in the
Kibble balance.
The Kibble balance is first and foremost a machine for a
traceable force measurement; only by knowing the local gravitational acceleration g can it be used to realize mass, via the
weight, mg. As an aside, the alternative method to realize the
unit of mass at the kilogram level, the X-ray crystal density
(XRCD) method does not require g. Here, the mass of a silicon crystal is given by a large known number multiplied by
the electron mass which is precisely known, albeit with an insignificant uncertainty, from determinations of the Rydberg
constant. In absence of a precise knowledge of g, the Kibble
balance can be used to measure force and the XRCD method to
measure mass. By combining both measurements, the local acceleration can be obtained. Of course, there are other ways to
obtain g, for example by measuring the free fall acceleration of
a mass in a vacuum chamber.
The Kibble balance and the XRCD method are usually
seen as a replacement for the international prototype of the

IEEE Instrumentation & Measurement Magazine	13



Instrumentation & Measurement Magazine 23-3

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