Instrumentation & Measurement Magazine 23-3 - 18

SI units as defined prior to May 2019. This was essentially a
measurement of kB because the relative uncertainty of h was
already known to negligible uncertainty from other types of
experiments.

Cross Correlation

Fig. 8. A Niobium based Johnson Noise Thermometry (JNT) chip. The chip
generates a voltage with a power spectral density similar to a 100 Ω resistor
at the temperature of the triple point of water. The US penny, which has a
diameter of about 19 mm, is for scale (photo courtesy of Dan Schmidt, NIST).

from which the temperature of the Johnson noise can be determined. In [25], S. P. Benz et al. provide a good explanation of the
pseudo-random noise generator and place it in the context of
earlier work on a Josephson arbitrary-waveform synthesizer.
The quantum noise source can be described by the following
equation:
SQ = a

N J2 fS
K J2

(21)

where NJ is the number of Josephson junctions in the circuit,
fs is a clock frequency, and a is a product of software parameters [25]. KJ = 2e/h is the Josephson constant, whose unit is
hertz per volt.
The electronics and software then provide the measurement ratio of the averaged PSDs:

SR
SQ

4 ( kBT ) X RK K J2  kB  T  16 X 
=   
 , (22)
2
a N J2 fS
 h  fS  a N J 

Every available technique must be used to eliminate extraneous noise sources from the PDF signals. Cross correlation
is used in JNT to minimize the effects of non-ideal low-noise
preamplifiers. The signal to be measured is sent through two
identical preamplifiers prior to further amplification and lowpass filtering. Each preamplifier adds a noise signal to the
output, but the extraneous noise sources from the preamplifiers are uncorrelated. At a later stage, the common signal (the
input signal to the preamplifiers) can be extracted by cross-correlation [24].

Integration Time
Finally, the uncertainty in the previous measurements of kB/h,
or of present measurements of T using JNT, is limited by the integration time, which should be as long as possible to reduce
statistical uncertainty [27]. Recent measurements of kB/h by
JNT, as discussed in [28], had integration times of 33 days and
100 days. The uncertainty budgets of both these measurements
are given in [29], where one can see that, despite several clever
improvements to the apparatus, the improvement in the total
uncertainty is due almost entirely to the integration time having been increased by a factor of 3, leading to a decrease in the
variance of the statistical uncertainty by the same factor. Why
go through all this trouble to decrease the relative uncertainty
from 3.9×10−6 to 2.7×10−6 [28]? Because, before it would recommend redefinition of the kelvin, the Consultative Committee
for Thermometry (CCT) set a goal of determining kB from at
least two different types of experiments, with the relative uncertainty of at least one of these experiments being less than
3×10−6 [29]. As it turned out, the JNT value also agreed within
uncertainties with the values determined by other technologies which met this goal [27].

Perspectives in JNT
showing how the measured PSD ratio and known T were used
to measure kB/h with respect to TTPW before the revision of the
SI on May 20, 2019. On that date, the constants kB and h were
defined to have exact numerical values, and therefore (13) now
shows how an arbitrary temperature T can be measured in
terms those constants [26]. The ratio in square brackets is composed of dimensionless numbers. For those interested in the
history of science, we note that both kB and h were invented
by Max Planck to describe the black-body curve of electromagnetic radiation at a given T. We also point out that the
measurement of kB/h reported in [24] was made using 1990
"conventional units" of voltage and resistance rather than
their corresponding SI units. Since May 20, 2019, use of the
conventional units has ended. However, it had been pointed
out 20 years earlier that the measurement of kB/h using JNT
could be made using conventional electrical units rather than
18

An integration time of 100 days is a tribute to the stability of
the equipment involved and the tenacity of the researchers,
but this type of heroic effort is unlikely to be repeated, now
that the kelvin has been redefined by fixing the numerical
value of kB [28]. Nevertheless, JNT will be a hot topic in the future. Several interesting possibilities are discussed in [23]. JNT
is a universal concept that applies in a broader temperature
range than any other type of thermometer. The resistor used
to sense the temperature can be calibrated in situ by a four-terminal measurement; removal of the resistor for recalibration is
unnecessary. The sensing resistor can therefore be exposed to
unusually harsh industrial environments. At cryogenic temperatures, superconducting quantum-interference devices
(SQUIDs) can be used to amplify the signals.
The CCT has published on-line documents describing methods to realize the definition of the kelvin. These are

IEEE Instrumentation & Measurement Magazine

May 2020

Instrumentation & Measurement Magazine 23-3

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 23-3