EN IEC 61788-22-2:2021

SLOVENSKI STANDARD
01-februar-2022
Merjenje upornosti v normalnem stanju in merjenje kritičnega toka - Spoj "High-Tc
Josephson" (IEC 61788-22-2:2021)
Normal state resistance and critical current measurement - High-Tc Josephson junction
(IEC 61788-22-2:2021)
Supraleitfähigkeit - Teil 22-2: Messung des Normalleitungswiderstands und des
kritischen Stroms - HTS Josephson Kontakt (IEC 61788-22-2:2021)
Mesure de la résistance à l’état normal et du courant critique - Jonction Josephson à Tc
élevée (IEC 61788-22-2:2021)
Ta slovenski standard je istoveten z: EN IEC 61788-22-2:2021
ICS:
17.220.20 Merjenje električnih in Measurement of electrical
magnetnih veličin and magnetic quantities
29.050 Superprevodnost in prevodni Superconductivity and
materiali conducting materials
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD EN IEC 61788-22-2

NORME EUROPÉENNE
EUROPÄISCHE NORM
November 2021
ICS 29.050
English Version
Superconductivity - Part 22-2: Normal state resistance and
critical current measurement - High-T Josephson junction
c
(IEC 61788-22-2:2021)
Supraconductivité - Partie 22-2: Mesure de la résistance à Supraleitfähigkeit - Teil 22-2: Messung des
l'état normal et du courant critique - Jonction Josephson à Normalleitungswiderstands und des kritischen Stroms -
T élevée HTS Josephson Kontakt
c
(IEC 61788-22-2:2021)
(IEC 61788-22-2:2021)
This European Standard was approved by CENELEC on 2021-11-25. CENELEC members are bound to comply with the CEN/CENELEC
Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC
Management Centre or to any CENELEC member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CENELEC member into its own language and notified to the CEN-CENELEC Management Centre has the
same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic,
Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the
Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.

European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2021 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
Ref. No. EN IEC 61788-22-2:2021 E

European foreword
The text of document 90/484/FDIS, future edition 1 of IEC 61788-22-2, prepared by IEC/TC 90
“Superconductivity” was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as
The following dates are fixed:
• latest date by which the document has to be implemented at national (dop) 2022–08–25
level by publication of an identical national standard or by endorsement
• latest date by which the national standards conflicting with the (dow) 2024–11–25
document have to be withdrawn
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CENELEC shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national committee. A
complete listing of these bodies can be found on the CENELEC website.
Endorsement notice
The text of the International Standard IEC 61788-22-2:2021 was approved by CENELEC as a
European Standard without any modification.
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments)
applies.
NOTE 1 Where an International Publication has been modified by common modifications, indicated by (mod), the
relevant EN/HD applies.
NOTE 2 Up-to-date information on the latest versions of the European Standards listed in this annex is available
here: www.cenelec.eu.
Publication Year Title EN/HD Year
IEC 61788-22-1 - Superconductivity - Part 22–1: EN 61788-22-1 -
Superconducting electronic devices -
Generic specification for sensors and
detectors
IEC 60050-815 2015 International Electrotechnical Vocabulary - - -
Part 815: Superconductivity
IEC 60617 - Graphical symbols for diagrams - -

IEC 61788-22-2 ®
Edition 1.0 2021-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 22-2: Normal state resistance and critical current measurement –

High-T Josephson junction:
c
Supraconductivité –
Partie 22-2: Mesurage de la résistance à l’état normal et du courant critique –

Jonction Josephson à T élevée
c
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.050 ISBN 978-2-8322-1039-7

– 2 – IEC 61788-22-2:2021 © IEC 2021
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Symbols . 8
5 Principle of measurement method . 9
6 Apparatus . 9
6.1 General . 9
6.2 Cryogenic system . 9
6.3 Electrical measurement system . 10
6.4 Circuitry . 10
7 Estimation of normal state resistance (R ) and intrinsic critical current (I ) . 11
n ci
7.1 Calculation method . 11
7.2 Geometric mean criterion for hyperbolic function fitting . 12
8 Standard uncertainty . 12
8.1 General . 12
8.2 Type A uncertainty . 12
8.3 Type B uncertainty . 14
8.3.1 General . 14
8.3.2 Temperature . 14
8.3.3 Voltage measurement . 16
8.3.4 Current measurement . 16
8.4 Budget table . 17
8.5 Uncertainty requirement . 18
9 Test report . 18
9.1 Identification of test device . 18
9.2 R value . 18
n
9.3 I value . 18
ci
9.4 Standard uncertainty . 18
9.5 Atmospheric pressure . 18
9.6 Miscellaneous optional report . 18
Annex A (informative) Calculation technique and practical application to high-T
c
Josephson junctions . 20
A.1 General . 20
A.2 Hyperbolic function fitting method . 20
A.3 Geometric mean method . 21
A.4 Combined method . 22
A.5 Estimation of R , I , u and u . 23
n ci A,R A,I
A.5.1 General . 23
A.5.2 High-T Josephson junction (JL350) . 23
c
A.5.3 High-T Josephson junction (JL351) . 25
c
A.5.4 High-T Josephson junction (TUT) . 27
c
Annex B (informative) Practical application to low-T Josephson junctions . 30
c
IEC 61788-22-2:2021 © IEC 2021 – 3 –
B.1 General . 30
B.2 Estimation of R , I , u and u . 30
n ci A,R A,I
B.2.1 General . 30
B.2.2 Low-T Josephson junction (IU1) . 30
c
B.2.3 Low-T Josephson junction (IU2) . 31
c
B.2.4 Low-T Josephson junction (IU3) . 32
c
B.2.5 Low-T Josephson junction (IU4) . 34
c
Bibliography . 35

Figure 1 – Typical circuitry for voltage-current (U–I) characteristic curve measurement . 10
Figure 2 – Ideal U–I characteristic curve (red line) and hyperbolic function (RSJ) model
curve (dotted line) . 11
Figure 3 – Geometric mean criterion and RSJ model fitting for TUT-JJ05 at 75,8 K . 15
Figure 4 – Geometric mean criterion and RSJ model fitting for TUT-JJ05 at 76,3 K . 16
Figure A.1 – U–I curve based on resistively shunted junction (RSJ) model . 21
Figure A.2 – U–I curve affected by noise-rounding and self-heating . 21
Figure A.3 – Application of geometric mean method to ideal U–I in Figure A.1 . 22
Figure A.4 – Application of geometric mean method to U–I with noise-rounding and
self-heating effects in Figure A.2. 23
Figure A.5 – U–I curve of JL350 . 24
Figure A.6 – Application of geometric mean method to Figure A.5 . 24
Figure A.7 – Result of RSJ model fitting for JL350 . 25
Figure A.8 – U–I curve of JL351 . 26
Figure A.9 – Application of geometric mean method to Figure A.8 . 26
Figure A.10 – Result of RSJ model fitting for JL351 . 27
Figure A.11 – U–I curve of TUT with a small I . 28
m
Figure A.12 – Application of geometric mean method to TUT . 28
Figure A.13 – Application of adjusted geometrical mean method to TUT . 29
Figure A.14 – Result of RSJ model fitting for TUT . 29
Figure B.1 – Application of geometric mean method to IU1 . 31
Figure B.2 – Result of RSJ model fitting for IU1 . 31
Figure B.3 – Application of geometric mean method to IU2 . 32
Figure B.4 – Result of RSJ model fitting for IU2 . 32
Figure B.5 – Application of geometric mean method to IU3 . 33
Figure B.6 – Result of RSJ model fitting for IU3 . 33
Figure B.7 – Application of geometric mean method to IU4 . 34
Figure B.8 – Result of RSJ model fitting for IU4 . 34

Table 1 – Typical relative standard Type A uncertainty for high-T Josephson junctions . 14
c
Table 2 – Budget table for R . 17
n
Table 3 – Budget table for I . 17
ci
Table A.1 – R , I , u and u values of high-T Josephson junctions . 23
n ci A,R A,I c
Table B.1 – R , I , u and u values of low-T Josephson junctions . 30
n ci A,R A,I c
– 4 – IEC 61788-22-2:2021 © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 22-2: Normal state resistance and critical
current measurement – High-T Josephson junction
c
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
IEC 61788-22-2 has been prepared by IEC technical committee 90: Superconductivity. It is an
International Standard.
The text of this International Standard is based on the following documents:
FDIS Report on voting
90/484/FDIS 90/486/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.

IEC 61788-22-2:2021 © IEC 2021 – 5 –
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/standardsdev/publications.
A list of all parts in the IEC 61788 series, published under the general title Superconductivity,
can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates that it
contains colours which are considered to be useful for the correct understanding of its
contents. Users should therefore print this document using a colour printer.

– 6 – IEC 61788-22-2:2021 © IEC 2021
INTRODUCTION
IEC 61788-22 (all parts) is a series of International Standards on superconductor electronic
devices. Superconductivity offers various possibilities of realizing sensors and detectors for a
variety of measurands. Several types of superconductor sensors and detectors have been
developed, using such features as superconducting energy gaps, sharp normal-
superconducting transition, nonlinear current-voltage characteristics, superconducting coherent
states and quantization of magnetic flux. Superconductors are influenced by interaction with
electromagnetic fields, photons, ions, etc. The superconductor sensors and detectors have
extremely high performance in resolution, time response and sensitivity, which cannot be
realized by any other sensors and detectors.
IEC 61788-22-1 lists various types of superconductor sensors and detectors. A key element of
some sensors and detectors is Josephson junction. The superconductor material types used for
Josephson junctions are divided into two categories: low-T superconductor (LTS) and high-T
c c
superconductor (HTS). This document (IEC 61788-22-2) defines a measurement method of
normal state resistance (R ) and intrinsic critical current (I ) of HTS Josephson junctions, which
n ci
are used for magnetic measurement with superconductor quantum interference device (SQUID),
detection of millimetre to terahertz band radiation and other applications.
The measurement method covered in this document is intended to give an appropriate and
agreeable technical base for those engineers working in the field of superconductor technology.
Although the mechanism of high-T superconductivity is under investigation, the occurrence of
c
the Josephson effect in such weak link structures as bicrystal, step-edge and ramp edge is
reliable, and characteristic parameters for conventional LTS Josephson junctions are valid also
for HTS Josephson junctions. The important parameters of HTS Josephson junctions for
designing superconductor devices are normal state resistance (R ) and critical current (I ),
n c
which are combined as I R product that is obtained experimentally. At this moment, most HTS
c n
Josephson junctions exhibit a non-hysteretic characteristic voltage-current (U–I) curve, which
is typical for superconductor/normal-conductor/superconductor (SNS) junctions. On U–I curves,
two types of distortions are often observed: noise-rounding and self-heating effects. Especially,
maximum current values without voltage drop on the U–I curves are often considerably reduced
because of the noise-rounding effect, and therefore it is difficult to estimate an intrinsic critical
current value. This document provides a method to obtain intrinsic values by selecting a data
set range to eliminate the distortions and by fitting a model function even when two effects are
present.
The critical current obtained by this standard method is therefore called intrinsic critical current
with the variable symbol of I , eliminating the noise-rounding effect on U–I curves. On the other
ci
hand, the normal state resistance is insensitive to the noise rounding and it is possible to avoid
the self-heating effect, so that the variable symbol R is used. The I R product is more
n ci n
essential for designing superconductor devices than the I R product. I values estimated by
c n ci
this document are usually higher than experimental I values.
c
Practical application of this document to HTS Josephson junctions is shown in Annex A. The
estimation method in this document is applied to SNS-type LTS Josephson junctions to check
universality in Annex B.
IEC 61788-22-2:2021 © IEC 2021 – 7 –
SUPERCONDUCTIVITY –
Part 22-2: Normal state resistance and critical
current measurement – High-T Josephson junction
c
1 Scope
This part of IEC 61788 is applicable to high-T Josephson junctions. It specifies terms,
c
definitions, symbols and the measurement and estimation method for normal state resistance
(R ) and intrinsic critical current (I ), based on a combination of selecting a data set from
n ci
measured U–I curves with a geometric mean criterion and fitting a hyperbolic function to that
data set.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 61788-22-1, Superconductivity – Part 22-1: Superconducting electronic devices – Generic
specification for sensors and detectors
IEC 60617, Graphical symbols for diagrams: available at http://std.iec.ch/iec60617
IEC 60050-815:2015, International Electrotechnical Vocabulary – Part 815: Superconductivity:
(available at http://www.electropedia.org/
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1
U–I characteristic curve
V–I characteristic curve
I–V characteristic curve
data set of voltage drop between two superconductors of a Josephson junction and current
applied to the junction
– 8 – IEC 61788-22-2:2021 © IEC 2021
3.2
normal state resistance
R
n
normal resistance
resistance between two superconductors forming a Josephson junction in a normal-conducting
state
Note 1 to entry: In a Josephson bridge junction, a normal state resistance is also defined as the resistance at a
bias current that suppresses superconductivity well above critical current, when the self-heating effect is negligible.
Note 2 to entry: In a Josephson tunnel junction, a normal state resistance is also defined as the tunnelling resistance
at a bias voltage well above 2Δ/e, where Δ is the energy gap and e is the elementary electric charge, when the self-
heating effect is negligible.
3.3
intrinsic critical current
I
ci
maximum direct current that can be applied to a Josephson junction without causing a voltage
drop across the junction in the absence of noise-rounding on a U–I characteristic curve
Note 1 to entry: Critical current (I ) is the maximum direct current value that can be applied to a Josephson junction
c
experimentally so that it can be regarded as flowing without resistance (IEC 61788-22-1).
Note 2 to entry: The method described in this document estimates I , the value of which is usually higher than I .
ci c
3.4
geometric mean
square root of the product of dU/dI and U/I obtained from a U–I characteristic curve
3.5
noise-rounding effect
effect of noise on a U–I characteristic curve
Note 1 to entry: The U–I curve shape near I is rounded from an ideal shape by the noise-rounding effect. Because
ci
of this, an I value is lower than the I value.
c ci
3.6
self-heating effect
effect of power dissipation due to transport current applied to a Josephson junction on a U–I
characteristic curve
Note 1 to entry: The current generates heat, and a U–I curve shape in a high current region well above I deviates
ci
upward above a straight line corresponding to R .
n
4 Symbols
U voltage drop across two superconductors connected by a weak link
NOTE "V" can also be used.
I current flowing through two superconductors connected by a weak link
R normal state resistance
n
I experimental critical current
c
I intrinsic critical current estimated by this document
ci
u type A standard uncertainty of R
A,R n
u type A standard uncertainty of I
A,I ci
u type B standard uncertainty of R
B,R n
IEC 61788-22-2:2021 © IEC 2021 – 9 –
u type B standard uncertainty of I
B,I ci
5 Principle of measurement method
On U–I curves, two types of distortions are often observed: noise-rounding and self-heating.
When the noise-rounding effect is negligible, the I value is the maximum current applied to
ci
the junction without resistance. When the self-heating effect and the nonlinear property due to
superconductivity are negligible, the R value of the junction corresponds to a value of U/I at a
n
current much higher than the critical current of the junction. Since a high probe current may
cause damage to the junction, the determination of R may need to be based on a range of the
n
U–I characteristic curve obtained for moderate currents. The moderate currents are also
effective in avoiding the self-heating effect. Here, a nonlinear least-squares fitting method with
and I . Even when these two
the hyperbolic function is practical to determine the values of R
n ci
types of the distortions exist, the combination of the geometric mean criterion and the hyperbolic
function fitting gives proper R and I values.
n ci
The R and I values of a HTS Josephson junction are determined by selecting a data set from
n ci
the whole data set of a U–I characteristic curve with the geometric mean criterion, and then by
fitting the hyperbolic function model (or resistively-shunted junction (RSJ) model) [1] to that
selected data set. This is called the combined method. The geometric mean criterion and the
hyperbolic function fitting method are described in Clause 7.
6 Apparatus
6.1 General
The apparatus required for this measurement method includes a cryogenic system and an
electrical measurement system.
6.2 Cryogenic system
An open cryostat with liquid nitrogen shall be used to cool Josephson junctions. The cryostat
shall have an open structure so that the pressure of the bath is equal to atmospheric pressure.
The atmospheric pressure on earth is normally between 950 hPa and 1 050 hPa, corresponding
to a temperature range from 76,8 K to 77,7 K. Measurement during abnormal weather
conditions shall be avoided. An atmospheric pressure value from a weather report source near
the measurement site or measured locally shall be reported. The cryostat should be equipped
with a magnetic shield with an attenuation factor of over 100 (−40 dB) and a RF shield with
1 000 (−60 dB) at 100 kHz. A specimen probe, which may consist of a junction or junctions, a
specimen holder and a support structure, shall be cooled from room temperature to liquid
nitrogen temperature over a time period of at least three minutes.
It is well known that I depends on flux trapping that occurs during cooling process from a
c
normal-conducting state to a superconducting state. Therefore, the cooling process from a
temperature above T to a base temperature of the liquid nitrogen bath and the R and I
c n ci
estimation shall be repeated at least 10 times, and the R and I values obtained from the U–I
n ci
data set showing the highest I value shall be reported.
ci
___________
Numbers in square brackets refer to the Bibliography.

– 10 – IEC 61788-22-2:2021 © IEC 2021
6.3 Electrical measurement system
A measurement system for U–I characteristic curve data sets should consist of a waveform
generator, a data acquisition system, differential amplifiers and other necessary instruments
such as filters. A four terminal method shall be applied to measure voltage and current. The
digital values of voltage and current shall be stored on the data acquisition system with an
analogue-to-digital converter (ADC) having a resolution better than eight bits. The U–I data sets
are transferred to a computer for estimating R and I . Other equivalent measurement systems
n ci
may also be used.
When a waveform generator is used, a current bias with a constant sweep rate shall be applied
to the junction and corresponding voltage drop is measured. The current bias shall be
triangularly swept from a minus value to a positive value or vice versa while the voltage is
recorded. The time for the ramp from −I to +I shall be longer than 10 ms, where I is the
m m m
maximum current. A sweep frequency (f ) lower than 50 Hz ensures quasi-DC measurement, in
s
which the effects of stray capacitance and junction capacitance are negligible. The data
sampling number per second shall be between 100 × f and 200 × f to obtain enough data
s s
points. The U–I data in the first quadrant and the absolute value data in the third quadrant shall
and I estimation described in Clause 7.
be used for the R
n ci
Differential amplifiers should be used to separate the grounds of the cryostat and the data
acquisition system. The input resistance of differential amplifiers should be higher than 100 kΩ.
The input resistance of the data acquisition system should be set at a high value, for example
1 MΩ. Low pass filters with a cutoff frequency of less than approximately 1 MHz should be used.
≈ 5 × I to avoid any damage to the
The data measurement range should be approximately I
m ci
junction and to obtain enough data points. The origin offset shall be minimized before the data
acquisition.
6.4 Circuitry
An example of the equivalent circuit for the U–I characteristic curve measurement is shown in
Figure 1. The Josephson junction indicated by IEC 60617-S01926:2017-10 and the surrounding
wiring are in a superconducting state. The normal-superconducting boundaries indicated by
IEC 60617-S01925:2017-10 distinguish the superconducting circuit and the normal-conducting
one. The waveform generator, shunt resistor and data acquisition system may be placed at
room temperature. The waveform generator and the digital oscilloscope may be replaced by
equivalent instruments.
Figure 1 – Typical circuitry for voltage-current (U–I) characteristic curve measurement

IEC 61788-22-2:2021 © IEC 2021 – 11 –
The data acquisition system records the voltage (U ) between two electrodes of the Josephson
y
junction and the voltage (U ) across the shunt resistor of resistance R . The current values
x s
should be obtained by dividing the U values by R . The R should be more than 1 000 times
x s s
smaller than the input resistance of the oscilloscope or the differential amplifier. The tolerance
of the shunt resistor should be better than ±0,05 %. When the oscilloscope is set at X-Y mode,
U–I characteristic curves can be seen on-screen to check the extent of the noise-rounding and
self-heating effects, and the origin offset. U–I curve data sets with considerably large effects of
noise-rounding and self-heating cannot be used to estimate R and I . In this case, the
n ci
measurement apparatus or the junction structure shall be improved.
7 Estimation of normal state resistance (R ) and intrinsic critical current (I )
n ci
7.1 Calculation method
The R and I values shall be estimated by optimizing the variables R and I with the least-
n ci n ci
squares fitting method so that the hyperbolic function expressed by Formula (1) [1] fits best to
a U–I characteristic data set as shown in Figure 2 after selecting a data set range in accordance
with the geometric mean criterion mentioned in 7.2.
U=RI− I for I> I , U=0 for I< I
(1)
n ci ci ci
Figure 2 – Ideal U–I characteristic curve (red line) and
hyperbolic function (RSJ) model curve (dotted line)
In order to avoid the effects of the noise-rounding and self-heating, a data set range for fitting
shall be determined by the geometric mean criterion, taking into account three curves of dU/dI,
0,5
U/I and (dU/dI × U/I) plotted against I. The appropriate data set range shall be such that the
0,5
geometric mean curve (dU/dI·U/I) against I has a plateau within 5 % deviation and dU/dI
decreases monotonously. The geometric mean of R is expressed by Formula (2).
n
R ddU I× UI , (2)
( ) ( )
n
where
=
– 12 – IEC 61788-22-2:2021 © IEC 2021
ddU I IR I− I (3)
n ci
and
UI (R I)× I− I , (4)
n ci
thus
(ddU I)×=(UI) R
. (5)
n
The dU/dI and U/I values can be calculated by using a measured U–I data set. By selecting a
data set appropriate for the least-squares fitting from the whole U–I characteristic curve, the
effects of noise-rounding and self-heating are minimized.
The hyperbolic function nonlinear fitting method shall be applied to a data set selected by the
geometric mean method. The convergence condition of fitting routine should be that the R and
n
I parameters are stationary at a digit position that corresponds to the rightmost digit of
ci
standard uncertainty values (standard deviation values) with two significant figures (see
Table A.1 and Table B.1). For practical calculation, software packages with a function of
and I and corresponding standard
nonlinear least-squares fitting can be used to estimate R
n ci
deviation of these mean quantities. The software packages make no meaningful difference in
estimation results. Actual estimation examples are found in 8.3.2 and Annex A.
7.2 Geometric mean criterion for hyperbolic function fitting
A data set range appropriate for the hyperbolic function fitting method shall be such that the
0,5
geometric mean curve (dU/dI·U/I) against I has a plateau within 5 % deviation and dU/dI
decreases monotonously as I increases.
8 Standard uncertainty
8.1 General
Type A uncertainty, which is the evaluation of a component of measurement uncertainty by a
statistical analysis, is estimated by the standard deviations of R and I when Formula (1) is
n ci
fitted to the U–I characteristic data set selected by the geometric mean criterion [2] [3]. The
Type A uncertainty of this document is estimated by using the typical U–I curve of JL350 in
Annex A. Type B uncertainty, which is the evaluation of uncertainty by means other than the
statistical analysis, includes uncertainty arising from variation in temperature and measurement
of voltage and current [2] [3].
The total standard uncertainty of this measurement method is the sum of the Type A uncertainty
and Type B uncertainty according to the propagation law. Actual application of this document
requires the Type A uncertainty estimation from experimental data only. Taking into account
the Type B uncertainty values tabulated in Table 2 and Table 3, the Type A uncertainty values
shall be kept less than the values in 8.5.
8.2 Type A uncertainty
The mean quantities R and I and their standard deviation values of u and u are obtained
n ci A,R A,I
by minimizing the sum of
=
=
IEC 61788-22-2:2021 © IEC 2021 – 13 –
m
22
J= U−−RI I , (6)
j n j ci
∑ ( )


j=1
where, I and U (j = 1, …, m) are the data set selected by the geometrical mean criterion.
j j
For uncertainty estimation, the sensitivity matrix X is expressed by Formula (7):
 
  
∂∂UU
   
∂∂RI
n  ci
 
j=1 j=1
 
(7)
X= 
 
 
  
∂∂UU
 
  
∂∂RI
 
n  ci
jm= jm=
 
where
∂U
II− (8)
j ci
∂R
n
and
∂U RI
n ci
= (9)
∂I
ci
II−
j ci
Therefore, the uncertainty matrix of the parameter is expressed by Formula (10):
 
−1 u R uR , I
( ) ( )
n n ci
T 2
U XX×σˆ   (10)
( )
uR , I u I
 ( ) ( )
n ci ci
 
where
J
σˆ =
(11)
m−1
For typical Type A uncertainty estimation, the U–I data set with the largest relative standard
uncertainty (standard deviation divided by average) values is selected from the HTS junctions
in Annex A. The data of the junction TUT in Table 1 are excluded, since the sinusoidal current
scan does not meet this document. The largest relative uncertainty values are 0,029 % for R
n
and 0,33 % for I for the junction JL350, and the corresponding standard deviation values are
ci
0,003 8 Ω and 0,21 µA in Table 1.
= =
=
– 14 – IEC 61788-22-2:2021 © IEC 2021
Table 1 – Typical relative standard Type A uncertainty
for high-T Josephson junctions
c
Estimation by combined method
R u Relative I u Relative
n A,R ci A,I
Junction (type) standard standard
uncertainty uncertainty
Ω Ω % µA µA %
JL350 (YBCO step-edge) 12,934 0 0,003 8 0,029 63,33 0,21 0,33
JL351 (YBCO step-edge) 9,304 2 0,001 8 0,019 32,651 0,045 0,14
TUT (YBCO step-edge) 0,810 0 0,005 0 0,62 358,2 3,5 0,98

8.3 Type B uncertainty
8.3.1 General
The Type B uncertainty of the measurement of R and I in this document is expressed by
n ci
Formula (12) and Formula (13):
22 2
∂∂RR ∂R
  
2 22 2
nn n
u= ×uu+×+×u
(12)
B,R  TU  I
∂∂TU ∂I
  
and
22 2
∂∂II ∂I
     
2 ci 22ci ci 2
u= ×uu+×+×u
(13)
B,I TU I
     
∂∂TU ∂I
     
where
∂R /∂T is a sensitivity of R to a variation of temperature T;
n n
∂R /∂U is a sensitivity of R to a variation of voltage U;
n n
∂R /∂I is a sensitivity of R to a variation of current I;
n n
u , u and u are the standard deviation values for the measurement of temperature, voltage
T U I
and current, respectively.
The notation for I is the same as that for R .
ci n
8.3.2 Temperature
U–I curve measurement shall be carried out in a liquid nitrogen bath. The temperature variation
between 76,8 K and 77,7 K is expected from the variation of atmospheric pressure on earth.
The ∂R /∂T was approximated by obtaining R values at T and T by applying this document to
n n 1 2
experimental U–I curves, and then calculating [R (T ) − R (T )] / [T − T ]. The same method
n 2 n 1 2 1
was applied to I . U–I curves of a bicrystal YBCO junction tagged as "TUT-JJ05" were
ci
measured at 75,8 K and 76,3 K. The data set range determined with the geometric mean
criterion and the U–I curves with the hyperbolic function fitting results (RSJ model) are shown
in Figure 3 and Figure 4 for 75,8 K and 76,3 K, respectively.

IEC 61788-22-2:2021 © IEC 2021 – 15 –
For 75,8 K a data set between 35 µA and 107 µA indicated by the arrow was selected for
hyperbolic function fitting as shown in Figure 3 (a). The least-squares fitting with Formula (1)
gives R = 1,540 0 (0,001 8) Ω and I = 29,16 (0,13) μA a
...