Instrumentation & Measurement Magazine 24-3 - 7

V n

h
f , (1)
2e

where h is the Planck constant, e is the elementary charge, f is
the frequency of the ac current and n is an integer number.
By biasing Josephson junctions in one of these steps one obtains a voltage standard whose value can be computed from
the frequency of the applied ac current and the defined value
of the fundamental constants h and e. For microwave frequencies (e.g., f ≈ 70 GHz), the size of the voltage steps would be
approximately 145 μV and a single junction would only be able
to produce small voltages. Practical voltage standards make
use of arrays containing thousands of Josephson junctions in
series to produce dc voltages in excess of 10 V.
Fig. 3 shows a schematic of a typical Josephson system and
how it is used in practice to calibrate common voltage standards such as a Zener reference. Modern Josephson arrays are
designed with several sections in series, each section being biased by a separate current source and having a binary-scaled
number of junctions (e.g., 1, 2, 4, 8, etc.). In this way, the overall step number n of the array can be chosen to be any number,
positive or negative, up to the total number of junctions in
the array. To measure the device under test (DUT), the array
would be biased to produce a reference voltage close to that of
the DUT and the small difference would be measured with a
sensitive voltmeter. The gain accuracy of the voltmeter is generally not a limiting factor and can be calibrated, for example,
by making a slight change in the frequency and measuring the
corresponding change in the voltage.
Josephson voltage standards have been in use now for
over four decades and can be found in most NMIs around the
Fig. 2. (a) Depiction of a Josephson junction biased with a combination
of a dc current and a microwave source. (b) I-V characteristic of an array
of 6 Josephson junctions in series without microwaves. The dotted line
represents the resistive characteristic that would be seen in the absence of
superconducting effects (normal tunnelling). (c) I-V characteristic of the same
array radiated with an 18.7 GHz source.

superconductors, the binding force of the Cooper pair arises
from the interaction of the electrons with the positive lattice of
the superconducting metal. Cooper pairs behave very differently from single (normal) electrons, and they form a highly
ordered electronic state in the superconductor which leads to
many effects, including the complete disappearance of electrical resistance.
Josephson predicted that in a tunnel junction with superconducting electrodes (now known as a Josephson junction),
Cooper pairs could tunnel across the barrier without breaking
and that this would give rise to several effects. Fig. 2a shows
the I-V characteristic of a Josephson junction being driven with
a dc current source. The plot shows that currents below a critical value Ic can flow through the junction with no voltage drop.
Furthermore, if a high frequency ac current (usually in the microwave range) is applied to the junction, the I-V characteristic
develops a series of zero-slope voltage steps, with the voltage
given by
May 2021

Fig. 3. Schematic of a typical Josephson array voltage standard. The array
voltage is adjusted to be approximately equal to that of the DUT (e.g., Zener
reference), and the small difference is measured with a digital volt meter
(DVM).

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