SIST EN IEC 61788-7:2020

SLOVENSKI STANDARD
01-julij-2020
Nadomešča:
SIST EN 61788-7:2007
Superprevodnost - 7. del: Meritve elektronskih lastnosti - Površinska upornost
visokotemperaturnih superprevodnikov pri mikrovalovnih frekvencah (IEC 61788-
7:2020)
Superconductivity - Part 7: Electronic characteristic measurements - Surface resistance
of high-temperature superconductors at microwave frequencies (IEC 61788-7:2020)
Supraleitfähigkeit - Teil 7: Charakteristische elektronische Messungen -
Oberflächenwiderstand von Supraleitern bei Frequenzen im Mikrowellenbereich (IEC
61788-7:2020)
Supraconductivité - Partie 7: Mesures des caractéristiques électroniques - Résistance de
surface des supraconducteurs aux hyperfréquences (IEC 61788-7:2020)
Ta slovenski standard je istoveten z: EN IEC 61788-7:2020
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 61788-7

NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2020
ICS 29.050; 17.220.20 Supersedes EN 61788-7:2006 and all of its amendments
and corrigenda (if any)
English Version
Superconductivity - Part 7: Electronic characteristic
measurements - Surface resistance of high-temperature
superconductors at microwave frequencies
(IEC 61788-7:2020)
Supraconductivité - Partie 7: Mesurages des Supraleitfähigkeit - Teil 7: Messungen der elektronischen
caractéristiques électronique - Résistance de surface des Charakteristik - Oberflächenwiderstand von
supraconducteurs haute température critique aux Hochtemperatur-Supraleitern bei Frequenzen im
hyperfréquences Mikrowellenbereich
(IEC 61788-7:2020) (IEC 61788-7:2020)
This European Standard was approved by CENELEC on 2020-04-24. 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
© 2020 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
Ref. No. EN IEC 61788-7:2020 E

European foreword
The text of document 90/447/FDIS, future edition 3 of IEC 61788-7, 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) 2021-01-24
level by publication of an identical national standard or by endorsement
• latest date by which the national standards conflicting with the (dow) 2023-04-24
document have to be withdrawn
This document supersedes EN 61788-7:2006 and all of its amendments and corrigenda (if any).
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.

Endorsement notice
The text of the International Standard IEC 61788-7:2020 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 60050-815 - International Electrotechnical Vocabulary - - -
Part 815: Superconductivity
IEC 61788-7 ®
Edition 3.0 2020-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 7: Electronic characteristic measurements – Surface resistance of

high‑temperature superconductors at microwave frequencies

Supraconductivité –
Partie 7: Mesurages des caractéristiques électronique – Résistance de surface

des supraconducteurs haute température critique aux hyperfréquences

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.20; 29.050 ISBN 978-2-8322-7917-5

– 2 – IEC 61788-7:2020 © IEC 2020
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 8
2 Normative references . 8
3 Terms and definitions . 8
4 Requirements . 8
5 Apparatus . 9
5.1 Measurement system . 9
5.2 Measurement apparatus for R . 10
s
5.3 Dielectric rods . 12
6 Measurement procedure . 12
6.1 Specimen preparation . 12
6.2 Set-up . 13
6.3 Measurement of reference level . 13
6.4 Measurement of the frequency response of resonators . 14
6.5 Determination of surface resistance of the superconductor and ε′ and tan δ
of the standard sapphire rods. 16
7 Uncertainty of the test method . 17
7.1 Surface resistance . 17
7.2 Temperature . 18
7.3 Specimen and holder support structure . 18
7.4 Specimen protection . 19
7.5 Uncertainty of surface resistance measured by standard two-resonator
method . 19
8 Test report . 19
8.1 Identification of test specimen . 19
8.2 Report of R values . 19
s
8.3 Report of test conditions . 19
Annex A (informative) Additional information relating to Clauses 1 to 8 . 20
A.1 Scope . 20
A.1.1 General . 20
A.1.2 Cylindrical cavity method [10] [17] . 20
A.1.3 Parallel-plates resonator method [18] [19] . 20
A.1.4 Microstrip-line resonance method [20] [21] . 20
A.1.5 Dielectric resonator method [22] [23] [24] [25] . 20
A.1.6 Image-type dielectric resonator method [26] [27] . 21
A.1.7 Two-resonator method [28] [29] . 22
A.2 Requirements . 22
A.3 Theory and calculation equations . 22
A.4 Apparatus . 25
A.5 Dimensions of the standard sapphire rods . 26
A.6 Dimension of the closed type resonator . 28
A.7 Sapphire rod reproducibility . 30
A.8 Test results . 30
A.9 Reproducibility of measurement method . 31

IEC 61788-7:2020 © IEC 2020 – 3 –
A.10 tan δ deviation effect of sapphire rods on surface resistance . 32
Annex B (informative) Evaluation of relative combined standard uncertainty for surface
resistance measurement . 34
B.1 Practical surface resistance measurement . 34
B.2 Determination of surface resistance of the superconductor . 35
B.3 Combined standard uncertainty . 36
B.3.1 General . 36
B.3.2 Calculation of c to c (12 GHz resonance at 20 K) . 36
2 5
B.3.3 Determination of u to u . 37
1 5
B.3.4 Combined relative standard uncertainty . 39
Bibliography . 41

Figure 1 – Schematic diagram of measurement system for temperature dependence of
R using a cryocooler . 9
s
Figure 2 – Typical measurement apparatus for R . 11
s
Figure 3 – Insertion attenuation, IA, resonant frequency, f , and half power bandwidth,
∆f, measured at T kelvin . 14
Figure 4 – Reflection scattering parameters (S and S ) . 16
11 22
Figure 5 – Term definitions in Table 4 . 18
Figure A.1 – Schematic configuration of several measurement methods for the surface
resistance . 21
Figure A.2 – Configuration of a cylindrical dielectric rod resonator short-circuited at
both ends by two parallel superconductor films deposited on dielectric substrates . 23
Figure A.3 – Computed results of the u-v and W-v relations for TE mode . 24
01p
Figure A.4 – Configuration of standard dielectric rods for measurement of R and tan δ . 25
s
Figure A.5 – Three types of dielectric resonators . 26
Figure A.6 – Mode chart to design TE resonator short-circuited at both ends by
parallel superconductor films [28] . 27
Figure A.7 – Mode chart to design TE resonator short-circuited at both ends by
parallel superconductor films [28] . 28
Figure A.8 – Mode chart for TE closed-type resonator [28] . 29
Figure A.9 – Mode chart for TE closed-type resonator [28] . 30
Figure A.10 – Temperature-dependent R of YBCO film with a thickness of 500 nm
s
and size of 25 mm square . 31
Figure A.11 – Temperature dependent R of YBCO film when R was measured three
s s
times. 32
Figure B.1 – Schematic diagram of TE and TE mode resonance . 34
011 013
Figure B.2 – Typical frequency characteristics of TE mode resonance . 35
Figure B.3 – Frequency characteristics of a resonator approximated by a Lorentz
distribution . 39

Table 1 – Typical dimensions of pairs of single-crystal sapphire rods for 12 GHz,
18 GHz and 22 GHz . 12
Table 2 – Dimensions of superconductor film for 12 GHz, 18 GHz, and 22 GHz . 13
Table 3 – Specifications for vector network analyzer . 17

– 4 – IEC 61788-7:2020 © IEC 2020
Table 4 – Specifications for sapphire rods . 17
Table A.1 – Standard deviation of the surface resistance calculated from the results of
Figure A.11 . 32
Table A.2 – Relationship between x, defined by Equation (A.12), and y, defined by
Equation (A.13) . 33

IEC 61788-7:2020 © IEC 2020 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 7: Electronic characteristic measurements –
Surface resistance of high-temperature
superconductors at microwave frequencies

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
co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and
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consensus of opinion on the relevant subjects since each technical committee has representation from all
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3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
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6) All users should ensure that they have the latest edition of this publication.
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other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications.
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.
International Standard IEC 61788-7 has been prepared by IEC technical committee 90:
Superconductivity.
This third edition cancels and replaces the second edition, published in 2006. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) informative Annex B, relative combined standard uncertainty for surface resistance
measurement has been added;
b) precision and accuracy statements have been converted to uncertainty;
c) reproducibility in surface resistant measurement has been added.

– 6 – IEC 61788-7:2020 © IEC 2020
The text of this International Standard is based on the following documents:
FDIS Report on voting
90/447/FDIS 90/452/RVD
Full information on the voting for the approval of this International Standard can be found in the
report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts of 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
maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. 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.

IEC 61788-7:2020 © IEC 2020 – 7 –
INTRODUCTION
Since the discovery of some Perovskite-type Cu-containing oxides, extensive research and
development (R & D) work on high-temperature superconductors (HTS) has been, and is being,
done worldwide, and its application to high-field magnet machines, low-loss power transmission,
electronics and many other technologies is in progress.
In various fields of electronics, especially in telecommunication fields, microwave passive
devices such as filters using HTS are being developed and are undergoing on-site testing
[1] [2].
Superconductor materials for microwave resonators [3], filters [4], antennas [5] and delay
lines [6] have the advantage of very low loss characteristics. The parameters of superconductor
materials needed for the design of microwave low loss components are the surface resistance,
(R ) and the temperature dependence of the R . Knowledge of this parameter is of primary
s s
importance for the development of new materials on the supplier side and for the design of
superconductor microwave components on the customer side.
R of high quality HTS films is generally several orders of magnitude lower than that of normal
s
metals [7] [8] [9] [10], which has increased the need for a reliable characterization technique to
measure this property. Traditionally, the R of niobium or any other low-temperature
s
superconducting material was measured by first fabricating an entire three-dimensional
resonant cavity and then measuring its Q-value [11]. The R could be calculated by solving the
s
electro-magnetic field (EM) distribution inside the cavity. Another technique involves placing a
small sample inside a larger cavity. This technique has many forms but usually involves the
uncertainty introduced by extracting the loss contribution due to the HTS films from the
experimentally measured total loss of the cavity.
The best HTS samples are epitaxial films grown on flat crystalline substrates and no high-quality
films have been grown on any curved surface so far. What is needed is a technique that: can
use these small flat samples; requires no sample preparation; does not damage or change the
film; is highly repeatable; has great sensitivity (down to 1/1 000 the R of copper); has great
s
dynamic range (up to the R of copper); can reach high internal powers with only modest input
s
powers; and has broad temperature coverage (4,2 K to 150 K).
The dielectric resonator method is selected among several methods to determine the surface
resistance at microwave frequencies because it is considered to be the most popular and
practical at present. Especially, the sapphire resonator is an excellent tool for measuring
the R of HTS materials [12] [13] [14]
s
The test method given in this document can also be applied to other superconductor bulk plates
materials.
including low T
c
This document is intended to provide an appropriate and agreeable technical base for the time
being to engineers working in the fields of electronics and superconductivity technology.
The test method covered in this document is based on the VAMAS (Versailles Project on
Advanced Materials and Standards) pre-standardization work on the thin film properties of
superconductors.
___________
Numbers in square brackets refer to the bibliography.

– 8 – IEC 61788-7:2020 © IEC 2020
SUPERCONDUCTIVITY –
Part 7: Electronic characteristic measurements –
Surface resistance of high-temperature
superconductors at microwave frequencies

1 Scope
This part of IEC 61788 describes measurement of the surface resistance (R ) of
s
superconductors at microwave frequencies by the standard two-resonator method. The object
of measurement is the temperature dependence of R at the resonant frequency.
s
The applicable measurement range of R for this method is as follows:
s
– Frequency: 8 GHz < f < 30 GHz
– Measurement resolution: 0,01 mΩ at 10 GHz

The R data at the measured frequency, and that scaled to 10 GHz, assuming the f rule for
s
comparison, is reported.
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 60050-815, International Electrotechnical Vocabulary (IEV) – Part 815: Superconductivity
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-815 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
4 Requirements
The R of a superconductor film shall be measured by applying a microwave signal to a dielectric
s
resonator with the superconductor film specimen and then measuring the attenuation of the
resonator at each frequency. The frequency shall be swept around the resonant frequency as
the centre, and the attenuation–frequency characteristics shall be recorded to obtain
the Q- value, which corresponds to the loss.
The target relative combined standard uncertainty of this method is less than 20 % for the
measurement temperature range from 20 K to 80 K.

IEC 61788-7:2020 © IEC 2020 – 9 –
It is the responsibility of the user of this document to establish appropriate safety and health
practices and to determine the applicability of regulatory limitations prior to use.
Hazards exist in this type of measurement. The use of a cryogenic system is essential to cool
the superconductors to allow transition into the superconducting state. Direct contact of skin
with cold apparatus components can cause immediate freezing, as can direct contact with a
spilled cryogen. The use of an RF generator is also essential to measure high-frequency
properties of materials. If its power is too high, direct contact to human bodies can cause an
immediate burn.
5 Apparatus
5.1 Measurement system
Figure 1 shows a schematic diagram of the system required for the microwave measurement.
The system consists of a network analyzer system for transmission measurement, a
measurement apparatus, and a thermometer for monitoring the measuring temperature.
An incident power generated from a suitable microwave source such as a synthesized sweeper
is applied to the dielectric resonator fixed in the measurement apparatus. The transmission
characteristics are shown on the display of the network analyzer. The measurement apparatus
is fixed in a temperature-controlled cryocooler.
Vector network analyzer
Figure 1 – Schematic diagram of measurement system
for temperature dependence of R using a cryocooler
s
For the measurement of R for superconductor films, a vector network analyzer is recommended.
s
A vector network analyzer has better measurement accuracy than a scalar network analyser
due to its wide dynamic range. The performance requirements of the vector network analyzer
are specified in 7.1.
– 10 – IEC 61788-7:2020 © IEC 2020
5.2 Measurement apparatus for R
s
Figure 2 shows a schematic of a typical measurement apparatus (closed type resonator) for
the R of HTS films deposited on a substrate with a flat surface. The upper HTS film is pressed
s
down by a spring, which is made of phosphor bronze. The plate type spring should be used for
the improvement of measurement uncertainty. This type of spring reduces the friction between
the spring and the other part of the apparatus, and allows the smooth movement of
superconductor films due to the thermal expansion of the dielectric rod. In order to minimize
the measurement uncertainty, the sapphire rod and the copper ring shall be arranged coaxially.
Two semi-rigid cables for measuring transmission characteristics of the resonator shall be
attached on both sides of the resonator in an axial symmetrical position (φ = 0 and π, where φ
is the rotational angle around the central axis of the sapphire rod). Each of the two semi-rigid
cables shall have a small loop at the ends. The plane of the loop shall be set parallel to that of
the superconductor films in order to suppress the unwanted Transverse Magnetic Wave Modes
modes). The coupling loops shall be carefully checked for cracks in the spot weld joint
(TM
mn0
that may have developed upon repeated thermal cycling. These cables can move right and left
to adjust the insertion attenuation (IA). In this adjustment, coupling of unwanted cavity modes
to the interested dielectric resonance mode shall be suppressed. Unwanted, parasitic coupling
to the other modes reduces the high Q-value of the Transverse Electro-Magnetic Mode
(TE mode) resonator. For suppressing the parasitic coupling, special attention shall be paid to
designing high-Q resonators. Two other types of resonators along with the closed type shown
in Figure 2 can be used. They are explained in A.4.

IEC 61788-7:2020 © IEC 2020 – 11 –

Figure 2 – Typical measurement apparatus for R
s
A reference line made of a semi-rigid cable shall be used to measure the full transmission power
level, i.e. the reference level. This cable has a length equal to the sum of the two cables of the
measurement apparatus. Semi-rigid cable with an outer diameter of 1,20 mm is recommended.

– 12 – IEC 61788-7:2020 © IEC 2020
In order to minimize the measurement uncertainty, two superconductor films shall be set to be
parallel to each other. To ensure that the two superconductor films remain in tight contact with
the ends of the sapphire rod, without any air gap, both of the surfaces of the films and the ends
of the rod shall be cleaned carefully.
5.3 Dielectric rods
Two dielectric rods with the same relative permittivity, ε′, and loss factor, tan δ, preferably cut
from one cylindrical dielectric rod, are required. These two rods, standard dielectric rods, shall
have the same diameter but different heights: one shall have height three times longer than the
other.
It is preferable to use dielectric rods with low tan δ to achieve the requisite measurement
uncertainty on R . Recommended dielectric rods are single-crystal sapphire rods with tan δ less
s
-7
than 2 × 10 at 77 K. Specifications on the sapphire rods are described in 7.1. In order to
minimize the measurement error in R of the superconductor films, both ends of the sapphire
s
rods shall be polished parallel to each other and perpendicular to the axis. Specifications for
the sapphire rods are given in Clause 7.
The diameter and the heights of the standard sapphire rods shall be carefully designed so that
the TE and TE modes do not couple to other TM, HE and EH modes, since the coupling
011 013
between TE mode and other modes causes the degradation of unloaded Q. A design guideline
for the standard sapphire rods is described in Clause A.5. Table 1 shows typical examples of
dimensions of the standard sapphire rods for 12 GHz, 18 GHz, and 22 GHz resonance. In the R
s
measurement at 22 GHz, the required film diameter can be set to 20 mm, and the measured Q
L
is small, therefore the effect of the dielectric loss of sapphire rod can be reduced.
Table 1 – Typical dimensions of pairs of single-crystal
sapphire rods for 12 GHz, 18 GHz and 22 GHz
Frequency Diameter, d Height, h
GHz mm mm
Short rod (TE resonator) 11,40 ± 0,05 5,70 ± 0,05
Long rod (TE resonator) 11,40 ± 0,05 17,10 ± 0,05
Short rod (TE resonator) 7,60 ± 0,05 3,80 ± 0,05
Long rod (TE resonator) 7,60 ± 0,05 11,40 ± 0,05
Short rod (TE resonator) 6,20 ± 0,05 3,10 ± 0,05
Long rod (TE resonator) 6,20 ± 0,05 9,30 ± 0,05
6 Measurement procedure
6.1 Specimen preparation
From uncertainty estimation, the film diameter shall be about three times larger than that of the
sapphire rods. In this configuration, the increase in uncertainty of R due to the different
s
radiation losses between TE and TE mode can be considered negligible, given the target
011 013
relative combined standard uncertainty of 20 %. The film thickness shall be about two times
larger than the magnetic-field penetration depth value at the maximum temperature in the
measurement temperature range. If the film thickness is much less than two times the magnetic-
field penetration depth, the measured R should mean the effective surface resistance.
s
IEC 61788-7:2020 © IEC 2020 – 13 –
Table 2 shows dimensions of the superconductor films recommended for the standard sapphire
rods of 12 GHz, 18 GHz, and 22 GHz.
Table 2 – Dimensions of superconductor film for 12 GHz, 18 GHz, and 22 GHz
c-cut single-crystal sapphire rod Superconductor film
Frequency Diameter, d Diameter, d′ Thickness
GHz mm mm μm
12 11,40 ± 0,05 > 35 ≅ 05,
18 7,60 ± 0,05 > 25
≅ 05,
22 6,20 ± 0,05 > 20
≅ 05,
In case of using closed type resonators, the dimensions of the superconductor films shall also
be designed taking into account the dimension of the copper cylinder between the
superconductor films. A design guideline for the dimension of the copper cylinder of the closed
type resonator is described in Clause A.6.
6.2 Set-up
Set up the measurement equipment as shown in Figure 1. All of the measurement apparatus,
standard sapphire rods, and superconductor films shall be kept in a clean and dry state as high
humidity may degrade the unloaded Q-value. The specimen and the measurement apparatus
shall be fixed in a temperature-controlled cryocooler. The specimen chamber shall be totally
evacuated. The temperatures of the superconductor films and standard sapphire rods shall be
measured by a diode thermometer, or a thermocouple. The temperatures of the upper and lower
superconductor films and standard sapphire rods shall not differ by more than 0,5 K. This can
be achieved by covering the measurement apparatus with aluminium foil or filling the specimen
chamber with helium gas.
6.3 Measurement of reference level
The level of full transmission power (reference level) shall be measured first. Fix the output
power of the synthesized sweeper below 10 mW because the measurement uncertainty
depends on the measuring signal level. Connect the reference line of semi-rigid cable between
the input and output connectors. Then, measure the transmission power level over the entire
measurement frequency and temperature range. The reference level can change several
decibels when temperature of the apparatus is changed from room temperature to the lowest
measurement temperature. Therefore, the temperature dependence of the reference level must
be taken into account.
– 14 – IEC 61788-7:2020 © IEC 2020

Figure 3 – Insertion attenuation, IA, resonant frequency, f ,
and half power bandwidth, ∆f, measured at T kelvin
6.4 Measurement of the frequency response of resonators
The temperature dependence of the R can be obtained through the measurements of resonant
s
frequency, f , and unloaded quality factor, Q , for TE and TE resonators, which shall be
0 u 011 013
measured as follows.
a) Connect the measurement apparatus between the input and output connectors (Figure 1).
Insert the standard short sapphire rod near the centre of the lower superconductor film and
fix the distance between the rod and each of the loops of the semi-rigid cables to be equal
to each other, so that this transmission-type resonator can be under-coupled equally to both
loops. Put down the upper superconductor film gently to touch the top face of the rod. Be
careful not to damage the surface of the superconductor films by excessive pressure.
Evacuate and cool down the specimen chamber below the critical temperature.
b) Find the TE mode resonance peak of this resonator at a frequency nearly equal to the
.
designed value of f
c) Narrow the frequency span on the display so that only the resonance peak of TE mode
can be shown (Figure 3). Confirm that the insertion attenuation, IA, of this mode is larger
than 20 dB from the reference level, which depends strongly on the temperature.
d) Measure the temperature dependence of f and the half power band width ∆f. The loaded
Q-value, Q , of the TE resonator is given by
L 011
f
Q = (1)
L
Δf
e) The unloaded Q-value, Q , shall be extracted from the Q by at least one of the two following
u L
techniques.
1) One technique for extracting the unloaded Q-value involves measuring the insertion
attenuation IA. Q is given by
u
Q
−IA dB /20
L [ ]
QA, 10
ut (2)
1 − A
t
==
IEC 61788-7:2020 © IEC 2020 – 15 –
The IA of each temperature is determined as follows. In the R measurement system
s
shown in Figure 2, a semi-rigid cable is connected instead of the measurement
apparatus, and the measurement system is short-circuited to determine the reference
level. Measure the reference level at each temperature and use it to determine IA at
each temperature.
This technique of using insertion attenuation assumes that the coupling on both sides of
the resonator is identical. The coupling loops are difficult to fabricate, the orientation of
the loop is difficult to control, and any movement of the sapphire rod during measurement
is not known. These assembly-dependent effects are also temperature dependent. This
potential asymmetry in coupling can result in large errors in calculating the coupling
factor if the coupling is strong (IA <~ 10 dB). If the coupling is weak enough (IA > 20 dB),
asymmetry in the coupling becomes less important.
2) Another technique for extracting the unloaded Q-value involves measuring the reflection
scattering parameters at the resonant frequency of both sides of the resonator.
QQ ()1+ ββ+
u L 12
(3)
1− ||S
β = (4)
| SS||+ |
11 22
1− ||S
β = (5)
| SS||+ |
11 22
In Equations (4) and (5), S and S are the reflection scattering parameters as shown
11 22
β and β are the
in Figure 4, and are measured in linear units of power, not relative dB.
1 2
coupling coefficients.
This technique of using the reflection scattering parameters has two advantages. It does
not require the additional step of calibration of the reference level and it gives a
measurement of the coupling values for both sides of the resonator. This also has two
disadvantages. It only works for a narrow band resonance (which is fortunately the case)
and is limited by the dynamic range of the network analyzer in measuring the reflection
coefficients [15] [16].
A combination of the two techniques is useful for a "double" check.
f) The f and Q measured for this short rod are denoted as f and Q for TE mode
0 u 01 u1 011
resonance. By slowly changing the temperature of the cryocooler the temperature
dependence of f and Q shall be measured.

01 u1
g) After the temperature dependence measurement of f and Q is finished, the measurement
01 u1
apparatus shall be heated up to room temperature.
h) Then, replace the TE resonator in the apparatus with the TE resonator at room
011 013
temperature, cool down the apparatus to a temperature lower than the critical temperature,
and measure the temperature dependence of f and Q of its TE resonance mode,
0 u 013
denoted as f and Q , in a similar way to the TE resonator case. When the length of
03 u3 011
the sapphire rod of the TE resonator is precisely three times longer than that of the TE
013 011
of the TE resonator must coincide with f of the TE resonator. If
resonator, the f
03 013 01 011
carefully designed, the difference between f and f is usually very small (<~ 0,25 %). We
01 03
can consider that the f in equation (9) can be replaced by f or f
.
0 01 03
=
– 16 – IEC 61788-7:2020 © IEC 2020

Figure 4 – Reflection scattering parameters (S and S )
11 22
6.5 Determination of surface resistance of the superconductor and ε′ and tan δ of the
standard sapphire rods
Calculate the temperature dependence of the R of the superconductor films, and ε′ and tan δ
s
of the standard sapphire rods using the temperature dependence of Q and Q . Q and Q

u1 u3 u1 u3
can be calculated using equations (1) and (2). If the measured temperatures for Q appear to
u3
be slightly different from those for Q , interpolation can be used for preparing adjusted
u1
temperature values for the former at the same temperatures for the later. Equations (6) to (12)
are established in the open type cavity, but when the superconductor film size is three times
larger than sapphire rod diameter, these equations can be used for closed type cavity.

′ 
30π ×3 2h εW+ 1 1
R − (6)


s

31−+1 WQ Q
( )
u1 u3
λ0

λ
ε' = + +1 (7)
uv
( )

πd

W
1+

′
ε
tan δ = − (8)


(3 −1) QQ
u3 u1
wh
...