Instrumentation & Measurement Magazine 23-2 - 5

number of junctions individually biased. These systems could
generate voltages of 10 mV at most and required specifically
designed resistive dividers to compare with the best voltage
standards at that time, the Weston cells.
The quantized voltage (1) arising on one Josephson junction is usually smaller than 150 μV. To increase the output
voltage, JJs are connected in series and a common bias current is passed through them. The parameters of the junctions
and the conditions of their operation are adjusted so that
the voltage (1) is set on each junction, and the total voltage
is equal to:

U = NVJ (2)

where N is the number of JJs. Equation (2) imposes strict constraints on the spread of JJs normal resistances Rn and critical
currents Ic, as well as high requirements for uniform irradiation with an external signal with a frequency f. At the same
time characteristic voltage of the junctions fc = KJIcRn should be
adjusted based on f, Ic and Rn.
State-of-the-art technologies of LTS JJs, as well as advances
in the design of microwave and millimeter wave integrated
circuits for applications in the voltage standards, have allowed
the development of the conventional dc Josephson voltage
standard (CJVS) on the one hand, and more advanced standards on the other hand: the programmable Josephson voltage
standard (PJVS) and Josephson arbitrary waveform synthesizer (JAWS), also known as the ac Josephson voltage standard
(ACJVS). Different types of LTS JJs are used in these applications and different synchronization schemes with external
signal as well. Below we briefly discuss various voltage standards built on integrated superconductor circuits from LTS JJs.

DC Josephson Voltage Standards
The first practical voltage standards were based on the arrays
of superconductor - insulator - superconductor (SIS) junctions
with hysteretic IVC. Major progress in increasing the number
of synchronized junctions connected in series was obtained according to Levinsen and coauthors who exploited the so called
"zero crossing steps" [10], i.e., voltage steps whose value is
quantized over a range of currents that covers positive and
negative values, including the condition of zero direct current
(dc) bias. These zero-current-crossing voltage-steps allowed
the junction uniformity problem to be circumvented by biasing the array at, or near, zero dc current.
The elaboration of the technology of the SIS JJ Nb/AlAlOx/Nb [11] with hysteretic IVC in 1982, as well as the
proposed [12] integration of arrays of such junctions in a microstrip line with a fin-line antenna, provided synchronization
of a large number of series connected JJs by electromagnetic
radiation of the millimeter wave range. As a result, the first
large scale superconducting integrated circuits with N = 14000
SIS niobium junctions, each working on n ≈ 5 steps were developed. Such circuits are used in dc conventional Josephson
voltage standards with output voltages up to U = 10 V with
step current margins about ΔI ≅ 20 μA and combined relative
April 2020

uncertainties (1-5) × 10−9. DC voltage standards are commercially available [13].
At present, the quantum LTS dc voltage standards are
widely used in National Metrology Institutes (NMIs) to reproduce the dc volt, to calibrate directly the new solid-state
voltage standards (Zeners) at 1 V and 10 V and precision
digital voltmeters. They also replaced the former "artifact" primary standards based on Weston cells [14], [15]. They formed
the base of the Recommendation 1 (CI-88) which established
the new representation of the volt based on the Josephson effect and, along with the development of the quantum Hall
resistance standards, began the process of redefining the SI
ampere [16].

AC Josephson Voltage Standards
Despite world recognition of the dc voltage standards based
on SIS junctions with precisely quantized zero crossing steps,
they suffer serious limitations. Several steps with different
number N are possible for a given level of a small bias current
and microwave excitation. Consequently, spontaneous jumps
between steps due to system noise can occur, resulting in the
instability of the output voltage. At the same time, it was impossible to quickly provide the setting of the Josephson output
voltage which was highly desirable for the calibration, for example, of digital-to-analog and analog-to-digital converters.
A big effort has been made in the last decades to overcome
these limitations, with the development of new arrays where
it was possible to control the junction voltage by means of bias
signals, making them capable of generating ac voltage, with
two widely different approaches: programmable Josephson
voltage standard (PJVS) [17] and ac Josephson voltage standard (ACJVS) [18]. The new arrays consist of thousands of
Superconductor-Normal Layer-Superconductor (SNS) junctions or stacks with single valued non-hysteretic IVCs. The
typical materials used for manufacturing SNS JJs are NbNbxSi1-x-Nb [19].
In order to be driven by the same bias current and irradiation signal for the first constant voltage step (n=1), the
junctions should have very small spread of Rn and the characteristic frequency fc ≥ f. In this case the quantized voltage Vj will
appear at each junction of the array biased to the first step (n =
1) obtaining the series combined sum equal to (2) [20]. Moreover, for the stable and immune to noise exploitation of the
ac standards, voltage steps with current margins larger than
2 mA are highly desirable. Taking into account the most used
irradiation frequencies approximately equal to 20 GHz and
70 GHz, the normal resistances of the junctions should be adjusted to small values (tens or several of milliohms).
PJVS consists of many thousands of junctions, arranged
in individually biased sub arrays in binary progression
(1,2,4,8...). Junction bias currents are used to activate/deactivate array sections, and combining sections, it is possible
to source binary programmed voltages in a way very similar to the technique used in semiconductor digital-to-analog
converters. Presently, PJVS are the most successful attempt
to extend metrological applications of Josephson standards

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Instrumentation & Measurement Magazine 23-2

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