Instrumentation & Measurement Magazine 23-3 - 17

bandwidth. We assume that R has no frequency dependence.
The Nyquist equation then describes the power spectral density (PSD), SR, in V2/Hz, of the voltage fluctuations across the
resistor:
	

Fig. 7. An example of an ac quantum Hall device made from epitaxial
graphene (image courtesy of Albert Rigosi, NIST).

Hall resistance at ac as an impedance standard is an appealing idea.
The most significant difference between ac and dc metrology is the fact in ac currents can flow across insulating
gaps via capacitive or inductive coupling. These couplings
are especially troubling if the defining device is in cryostat
which naturally requires long connections, prone to a lot of
coupling, relative to the room-temperature measurement devices. In 2007, researchers at the Physikalisch-Technische
Bundesanstalt (PTB), managed to solve these problems with
a shielded GaAs device [12]. The quantum Hall effect is since
a viable option to realize the farad. However, not many National Metrology Institutes (NMI) have been using the ac
quantum Hall effect as the basis of their impedance measurements. The reason is that GaAs quantum Hall chips that are
useable for ac are difficult to obtain. Graphene also, provides
an optimal solution for ac measurements. Graphene chips are
larger, thus having smaller edge-to-edge capacitance and they
can be fabricated in house at several NMIs. As is the case for
the dc quantum Hall measurement, the operating parameters
are more forgiving. The devices can be operated at higher currents, higher temperature, and smaller magnetic field. In 2020,
we hope to see some progress in the ac quantum Hall field.
Hopefully more and more NMIs will embark on a journey to
use the Quantum Hall device to realize impedance standards.
Fig. 7 shows a possible geometry for an ac quantum Hall device made from epitaxial graphene.

Johnson Noise Thermometer (JNT)
Johnson Noise was first described in 1927 and largely explained in 1928 [16]. It concerns voltage fluctuations V that
occur across a resistance R that is at a temperature T. In its
= 4 kBT  R
Δf
a  fresimplest form, the mean square fluctuations V 2 within
quency band Δ f:
	

V 2 = 4 kBT  R  Δf 	(18)

where kB is the Boltzmann constant, introduced above. Eq.
(18) is known as the Nyquist equation, and gives the mean
square voltage as a function of temperature, resistance, and
May 2020	

SR = 4 ( kBT ) R  .	(19)

A resistor can therefore serve as a convenient source of PSD
that is independent of frequency, i.e., "white noise." Alternatively, if the PSD is known, the absolute temperature T can be
determined. In this case, the device described by (19) becomes
a JNT. There are unique advantages to measuring temperature this way. However, the great disadvantages of an absolute
precision measurement are the need to measure SR against a
known PSD, the elimination of extraneous noise sources-e.g.,
from amplifiers, and the need to integrate the signal over long
times to reduce statistical uncertainty.
Nevertheless, the authors of [23] conclude that JNT "has
appeal for metrological applications at temperatures ranging from below 1 mK up to 800 K. With the rapid advances
in digital technologies, there are also expectations that noise
thermometry will become a practical option for some industrial applications, perhaps reaching temperatures above 2000
K." In [23], J. F. Qu et al. reviews the possibilities, giving ample references.

Redefining the kelvin
Because of the inherent difficulties in using a JNT, it was a remarkable achievement that such an experiment contributed
to the redefinition of the kelvin. For this, it was necessary to
measure the PSD of a resistance held at precisely 273.16 K, the
triple point temperature of water (TTPW). To be competitive
with other technologies being used to measure kB, the relative
uncertainty needed to be about 3×10−6, corresponding to about
800 μK uncertainty at 273 K. What follows is a brief description
of this remarkable measurement.

Resistor
The resistor is made from metal foils bonded to an alumina
substrate [24], a design that minimizes the dependence of R on
frequency. The nominal value is 100 Ω and is chosen to optimize the bandwidth over which SR is measured. The resistance
value R is measured in terms of the quantum-Hall resistance
RK = h/e 2 ≈ 25.8 kΩ, where h is the Planck constant and e is the
elementary charge. If we define the ratio X = R/RK, then (10)
becomes:
	

SR = 4 ( kBT )  XRK	(20)

PSD standard
Perhaps the most important innovation for these JNT measurements was the synthesis of a quantum PSD standard, SQ,
which depends on the Josephson effect [24]-[26]. Josephson
"junctions" are maintained at 4 K. Fig. 8 shows a photograph
of a chip with ten Josephson junctions. The technique results
in a pseudo-random noise source with megahertz bandwidth

IEEE Instrumentation & Measurement Magazine	17



Instrumentation & Measurement Magazine 23-3

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