Instrumentation & Measurement Magazine 23-6 - 5

example, in the pre-2019 SI the elementary charge, e, was related primarily to the Planck constant by e2 = 2h α/(μ0 c). So with
μ0 and c fixed exactly, we knew the elementary charge with respect to h to within half of the uncertainty of the fine structure
constant. In the revised SI with h, e and c now fixed exactly, μ0
will be realized with respect to α using the same equation.
The Rydberg constant and fine structure constant relate the
product of h and NA with the molar mass of the electron, NAh =
α 2M(e)c/(2 R∞), where M(e) is the molar mass of the electron. It
is indeed fortunate that the ratios of atomic masses, including
the electron, can be measured very accurately with Penning
traps and this equation can then be extended to other molar
masses including silicon [6]. This low uncertainty relationship
between h and NA means that while the Planck constant is used
to define the mass unit, the Avogadro constant can also be used
experimentally to determine a mass while adding only an infinitesimal incremental uncertainty.
So the apexes of traceability in the revised SI are the fixed values of the seven reference constants. They can be used in any
combination, with any laws of physics to obtain traceability and
they can be realized anywhere, anytime by anybody without
incurring additional uncertainties. Accessibility, redundancy, invariance and the lowest possible uncertainty are the key features
of the revised SI. The vast bulk of measurements need traceability but rarely have direct access to the apex of their measurement
units. For these users, the revised SI is the same as before-
business as usual. The revised SI will certainly impact those
pursuing the ultimate accuracies but it can also impact those that
want direct or simpler traceability even where uncertainties are
not critical. To highlight impacts we will describe several types
of mass or force measurements and mention some others.

Kibble Balance
Bryan Kibble first revealed the principles of the watt balance
in 1976 [9]. Kibble's concept was to abandon pursuit of the

precise dimensional characterizations of the coil and instead
measure the magnetic properties of the balance in a second
measurement phase using the same equipment.
A simplified schematic of a Kibble balance is shown in Fig.
3. Fig. 3a shows a simple beam balance with a test mass holder
and a coil on the left-hand side and a tare mass holder on the
right-hand side. The coil is suspended in a radial magnetic
field of flux density, B. The beam is adjusted to be balanced
with both the test and tare masses removed and zero current
passing through the coil. The tare mass is made to be approximately ½ of the test mass. A retro-reflector is rigidly attached to
the coil and a Michelson interferometer measures the distance
between the coil and the magnet.
In the first phase of the experiment, the weighing phase, the
instrument balances the gravitational force, mg, acting on the
test mass, against the electromagnetic force created by passing
a current, I, through a coil of length, L, immersed in a magnetic
field of strength, B:
	

m  g  I  BL	(1)

A servo control adjusts the coil current to keep the beam
horizontal by passing the current through a reference resistor,
R, and the coil. The test mass is alternately positioned on and
off the test mass holder and the current alternates from +I to -I.
In this way the difference in the coil currents is related to the
difference of the mass on the holder and thus, instrument zeros
and many magnetic effects are cancelled.
Fig. 3b shows the second phase of the experiment, the
moving phase, in which the masses have been removed. In
the moving phase, the coil is moved at a velocity, v, and the
voltage, VC, induced across the coil is measured. In this particular example, the beam movement is controlled by passing a
current through a second coil and magnet system on the righthand side which was not shown in Fig. 3a for clarity. The same

Fig. 3. (a) A simplified schematic of the weighing phase of the Kibble balance. (b) A schematic of the moving phase of the Kibble balance.
September 2020	

IEEE Instrumentation & Measurement Magazine	5



Instrumentation & Measurement Magazine 23-6

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 23-6

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Instrumentation & Measurement Magazine 23-6 - Cover1
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https://www.nxtbook.com/allen/iamm/25-9
https://www.nxtbook.com/allen/iamm/25-8
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