EN 61788-16:2013

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.RYUãLQVNDNYHQFDKSupraleitfähigkeit - Teil 16: Messung der elektronischen Eigenschaften - Leistungsabhängiger Oberflächenwiderstand bei MikrowellenfrequenzenSupraconductivité - Partie 16: Mesures de caractéristiques électroniques - Résistance de surface des supraconducteurs aux hyperfréquences en fonction de la puissanceSuperconductivity - Part 16: Electronic characteristic measurements - Power-dependent surface resistance of superconductors at microwave frequencies29.050Superprevodnost in prevodni materialiSuperconductivity and conducting materials17.220.20Measurement of electrical and magnetic quantitiesICS:Ta slovenski standard je istoveten z:EN 61788-16:2013SIST EN 61788-16:2013en01-julij-2013SIST EN 61788-16:2013SLOVENSKI
STANDARD
EUROPEAN STANDARD EN 61788-16 NORME EUROPÉENNE
EUROPÄISCHE NORM April 2013
CENELEC European Committee for Electrotechnical Standardization Comité Européen de Normalisation Electrotechnique Europäisches Komitee für Elektrotechnische Normung
Management Centre: Avenue Marnix 17, B - 1000 Brussels
© 2013 CENELEC -
All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 61788-16:2013 E
ICS 17.220.20; 29.050
English version
Superconductivity -
Part 16: Electronic characteristic measurements -
Power-dependent surface resistance of superconductors at microwave frequencies (IEC 61788-16:2013)
Supraconductivité -
Partie 16: Mesures de caractéristiques électroniques -
Résistance de surface des supraconducteurs aux hyperfréquences en fonction de la puissance (CEI 61788-16:2013)
Supraleitfähigkeit -
Teil 16: Messung der elektronischen Eigenschaften -
Leistungsabhängiger Oberflächenwiderstand bei Mikrowellenfrequenzen (IEC 61788-16:2013)
This European Standard was approved by CENELEC on 2013-02-20. 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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Foreword The text of document 90/309/FDIS, future edition 1 of IEC 61788-16, prepared by IEC TC 90, "Superconductivity" was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as EN 61788-16:2013.
The following dates are fixed: • latest date by which the document has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2013-11-20 • latest date by which the national standards conflicting with the document have to be withdrawn (dow) 2016-02-20
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such patent rights. Endorsement notice The text of the International Standard IEC 61788-16:2013 was approved by CENELEC as a European Standard without any modification. SIST EN 61788-16:2013

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Annex ZA
(normative)
Normative references to international publications with their corresponding European publications
The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
NOTE
When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD applies.
Publication Year Title EN/HD Year
IEC 60050 Series International electrotechnical vocabulary
- -
IEC 61788-15 - Superconductivity -
Part 15: Electronic characteristic measurements - Intrinsic surface impedance of superconductor films at microwave frequencies EN 61788-15 -
IEC 61788-16 Edition 1.0 2013-01 INTERNATIONAL STANDARD NORME INTERNATIONALE Superconductivity –
Part 16: Electronic characteristic measurements – Power-dependent surface resistance of superconductors at microwave frequencies
Supraconductivité –
Partie 16: Mesures de caractéristiques électroniques – Résistance de surface des supraconducteurs aux hyperfréquences en fonction de la puissance
INTERNATIONAL ELECTROTECHNICAL COMMISSION COMMISSION ELECTROTECHNIQUE INTERNATIONALE V ICS 17.220.20; 29.050 PRICE CODE CODE PRIX ISBN 978-2-83220-582-2
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CONTENTS FOREWORD . 4 INTRODUCTION . 6 1 Scope . 7 2 Normative references . 7 3 Terms and definitions . 7 4 Requirements . 8 5 Apparatus . 8 5.1 Measurement system . 8 5.1.1 Measurement system for the tan δ of the sapphire rod . 8 5.1.2 Measurement system for the power dependence of the surface resistance of superconductors at microwave frequencies . 9 5.2 Measurement apparatus . 10 5.2.1 Sapphire resonator . 10 5.2.2 Sapphire rod . 10 5.2.3 Superconductor films . 11 6 Measurement procedure . 11 6.1 Set-up . 11 6.2 Measurement of the tan δ of the sapphire rod . 11 6.2.1 General . 11 6.2.2 Measurement of the frequency response of the TE021 mode . 11 6.2.3 Measurement of the frequency response of the TE012 mode . 13 6.2.4 Determination of tan δ of the sapphire rod . 13 6.3 Power dependence measurement . 14 6.3.1 General . 14 6.3.2 Calibration of the incident microwave power to the resonator. 15 6.3.3 Measurement of the reference level . 15 6.3.4 Surface resistance measurement as a function of the incident microwave power . 15 6.3.5 Determination of the maximum surface magnetic flux density . 15 7 Uncertainty of the test method . 16 7.1 Surface resistance. 16 7.2 Temperature . 17 7.3 Specimen and holder support structure . 18 7.4 Specimen protection . 18 8 Test report . 18 8.1 Identification of the test specimen . 18 8.2 Report of power dependence of Rs values. 18 8.3 Report of test conditions . 18 Annex A (informative)
Additional information relating to Clauses 1 to 7 . 19 Annex B (informative)
Uncertainty considerations . 24 Bibliography . 29
Figure 1 – Measurement system for tan δ of the sapphire rod . 9 Figure 2 – Measurement system for the microwave power dependence of the surface resistance . 9 SIST EN 61788-16:2013

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Figure 3 – Sapphire resonator (open type) to measure the surface resistance of superconductor films . 10 Figure 4 – Reflection scattering parameters (|S11| and |S22|) . 13 Figure 5 – Term definitions in Table 3 . 17 Figure A.1 – Three types of sapphire rod resonators . 19 Figure A.2 – Mode chart for a sapphire resonator (see IEC 61788-15) . 20 Figure A.3 – Loaded quality factor QL measurements using the conventional 3 dB method and the circle fit method . 21 Figure A.4 – Temperature dependence of tan δ of a sapphire rod measured using the two-resonance mode dielectric resonator method [3] . 22 Figure A.5 – Dependence of the surface resistance Rs on the maximum surface magnetic flux density Bs max [3] . 23
Table 1 – Typical dimensions of the sapphire rod . 11 Table 2 – Specifications of the vector network analyzer . 16 Table 3 – Specifications of the sapphire rods . 17 Table B.1 – Output signals from two nominally identical extensometers . 25 Table B.2 – Mean values of two output signals . 25 Table B.3 – Experimental standard deviations of two output signals . 25 Table B.4 – Standard uncertainties of two output signals . 26 Table B.5 – Coefficient of Variations of two output signals . 26
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INTERNATIONAL ELECTROTECHNICAL COMMISSION ____________
SUPERCONDUCTIVITY –
Part 16: Electronic characteristic measurements –
Power-dependent surface resistance
of 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 in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work. International, governmental and non-governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations. 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user. 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications. Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter. 5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any services carried out by independent certification bodies. 6) All users should ensure that they have the latest edition of this publication. 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or 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 61788-16 has been prepared by IEC technical committee 90: Superconductivity. The text of this standard is based on the following documents: FDIS Report on voting 90/309/FDIS 90/318/RVD
Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table. This publication has been drafted in accordance with the ISO/IEC Directives, Part 2. A list of all the parts in the IEC 61788 series, published under the general title Superconductivity, can be found on the IEC website. SIST EN 61788-16:2013

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The committee has decided that the contents of this publication will remain unchanged until the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to the specific publication. At this date, the publication 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.
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INTRODUCTION Since the discovery of high-Tc superconductors (HTS), extensive researches have been performed worldwide for electronic applications and large-scale applications. In the fields of electronics, especially in telecommunications, microwave passive devices such as filters using HTS are being developed and testing is underway on sites [1,2,3,4]1. Superconductor materials for microwave resonators, filters, antennas and delay lines have the advantage of ultra-low loss characteristics. Knowledge of this parameter is vital for the development of new materials on the supplier side and the design of superconductor microwave components on the customer side. The parameters of superconductor materials needed to design microwave components are the surface resistance Rs and the temperature dependence of the Rs. Recent advances in HTS thin films with Rs, several orders of magnitude lower than normal metals has increased the need for a reliable characterization technique to measure this property [5,6]. Among several methods to measure the Rs of superconductor materials at microwave frequencies, the dielectric resonator method [7,8,9] has been useful due to that the method enables to measure the Rs nondestructively and accurately. In particular, the sapphire resonator is an excellent tool for measuring the Rs of HTS materials [10]. In 2002, the International Electrotechnical Commission (IEC) published the dielectric resonator method as a measurement standard [11]. The test method given in this standard enables measurement of the power-dependent surface resistance of superconductors at microwave frequencies. For high power microwave device applications such as those of transmitting devices, not only the temperature dependence of Rs but also the power dependence of Rs is needed to design the microwave components. Based on the measured power dependence, the RF current density dependence of the surface resistance can be evaluated. The simulation software to design the device gives the RF current distribution in the device. The results of the power dependence measurement can be directly compared with the simulation and allow the power handling capability of the device to be evaluated.
The test method given in this standard can be also applied to other superconductor bulk plates including low-Tc material. This standard is intended to give an appropriate and agreeable technical base for the time being to those engineers working in the fields of electronics and superconductivity technology. The test method covered in this standard is based on the VAMAS (Versailles Project on Advanced Materials and Standards) pre-standardization work on the thin film properties of superconductors.
___________ 1
Numbers in square brackets refer to the Bibliography. SIST EN 61788-16:2013

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SUPERCONDUCTIVITY –
Part 16: Electronic characteristic measurements –
Power-dependent surface resistance
of superconductors at microwave frequencies
1 Scope This part of IEC 61788 involves describing the standard measurement method of power-dependent surface resistance of superconductors at microwave frequencies by the sapphire resonator method. The measuring item is the power dependence of Rs at the resonant frequency.
The following is the applicable measuring range of surface resistances for this method: Frequency: f ~ 10 GHz Input microwave power: Pin < 37 dBm (5 W) The aim is to report the surface resistance data at the measured frequency and that scaled to 10 GHz using the Rs ∝ f2 relation for comparison. 2 Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. IEC 60050 (all parts), International Electrotechnical Vocabulary (available at: ) IEC 61788-15, Superconductivity – Part 15: Electronic characteristic measurements – Intrinsic surface impedance of superconductor films at microwave frequencies 3 Terms and definitions For the purposes of this document, the definitions given in IEC 60050-815, one of which is repeated here for convenience, apply. 3.1
surface impedance impedance of a material for a high frequency electromagnetic wave which is constrained to the surface of the material in the case of metals and superconductors Note 1 to entry: The surface impedance governs the thermal losses of superconducting RF cavities. Note 2 to entry: In general, surface impedance Zs for conductors including superconductors is defined as the ratio of the electric field Et to the magnetic field Ht, tangential to a conductor surface: Zs = Et /Ht = Rs + jXs, where Rs is the surface resistance and Xs is the surface reactance. SIST EN 61788-16:2013

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4 Requirements The surface resistance Rs of a superconductor film shall be measured by applying a microwave signal to a sapphire resonator with the superconductor film specimen and then measuring the insertion attenuation of the resonator at each frequency. The frequency shall be swept around the resonant frequency as the center and the insertion 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 the coefficient of variation (standard deviation divided by the average of the surface resistance determinations), which is less than 20 % for a measurement temperature range from 30 K to 80 K. It is the responsibility of the user of this standard to consult and establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use. Hazards exist in such measurement. The use of a cryogenic system is essential to cool the superconductors and 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 the high-frequency properties of materials. If its power is excessive, direct contact to human bodies could cause immediate burns. 5 Apparatus
5.1 Measurement system 5.1.1 Measurement system for the tan δ of the sapphire rod Figure 1 shows a schematic diagram of the system required for the tan δ measurement. The system consists of a network analyzer system for transmission measurements, a measurement apparatus in which a sapphire resonator with superconductor films is fixed, and a thermometer for monitoring the measuring temperature.
The incident power generated from a suitable microwave source such as a synthesized sweeper is applied to the sapphire 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. To measure the tan δ of the sapphire rod, a vector network analyzer is recommended, since its measurement accuracy is superior to a scalar network analyzer due to its wide dynamic range.
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Cryocooler Thermal sensor Measurement apparatus Vector network analyzer Thermometer Synthesized sweeper S-parameter test set System interface IEC
003/13
Figure 1 – Measurement system for tan δ of the sapphire rod 5.1.2 Measurement system for the power dependence of the surface resistance of superconductors at microwave frequencies Figure 2 shows the measurement system for the power dependence of the surface resistance of superconductors using a sapphire resonator. A travelling wave tube (TWT) power amplifier with a maximum output power of around 40 dBm is inserted at the input into the resonator. The maximum input power into the resonator is around 37 dBm in this measurement system shown in Figure 2. The typical maximum input power of a network analyzer is in the order of 0 dBm, so a measurement circuit shall be designed to avoid direct exposure of high powered microwaves to the network analyzer, and also by using a circulator and an attenuator, significant reflection from the sapphire resonator should not affect the TWT amplifier.
Synthesized sweeper Power sweep TWT amplifier Circulator Coupler Attenuator Power meter Cryostat Resonator Coupler Circulator Vector network analyzer IEC
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Figure 2 – Measurement system for the microwave power dependence of the surface resistance SIST EN 61788-16:2013

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Incident microwave power to the resonator is calibrated using a power meter before the measurement (dotted line in Figure 2). The incident power of the microwave is swept by changing the input power of the TWT amplifier. 5.2 Measurement apparatus 5.2.1 Sapphire resonator Figure 3 shows a schematic diagram of a typical sapphire resonator (open type resonator) used to measure Rs of superconductor films and tan δ of the sapphire rod [9]. In the sapphire resonator, a sapphire rod was sandwiched between two superconducting films. The upper superconductor film is pressed down by a spring, which is made of phosphor bronze. The use of a plate type spring is recommended to improve measurement accuracy. This type of spring reduces the friction between the spring and the rest of the apparatus, and facilitates the movement of superconductor films during the thermal expansion of the sapphire rod. Two semi-rigid cables for measuring transmission characteristics of the resonator shall be attached on both sides of the resonator in axially symmetrical positions (φ = 0 and π, where φ is the rotational angle around the central axis of the sapphire rod). A semi-rigid cable with an outer diameter of 3,50 mm is recommended. Each of the two semi-rigid cables shall have a small loop at the end. The plane of the loop shall be set parallel to that of the superconductor films in order to suppress the unwanted TMmn0 modes. The coupling loops shall be carefully checked for cracks in the spot weld joint 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 modes to the interested resonance mode shall be suppressed. Unwanted coupling to the other modes reduces the high Q value of the TE mode resonator. To suppress the unwanted coupling, special attention shall be paid to designing high Q resonators. Two other types of resonators usable along with the open type shown in Figure 3 are explained in A.1. A reference line made of a semi-rigid cable shall be used to measure the full transmission power level, i.e. the reference level. The cable length equals to the sum of the two cables of the measurement apparatus. To minimize the measurement error, two superconductor films shall be set in parallel. To ensure that the two superconductor films remain in tight contact with the ends of the sapphire rod, without any air gap, the surface of the two films and both ends of the rod shall be cleaned carefully.
Superconductor films Sapphire rod Spring Copper base Loop antenna IEC
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Figure 3 – Sapphire resonator (open type) to measure the surface resistance of superconductor films 5.2.2 Sapphire rod A high-quality sapphire rod with low tan δ is required to achieve the requisite measurement accuracy on Rs. A recommended sapphire rod is expected to have a tan δ less than 10–6 at 77 K. To minimize the measurement error in Rs of the superconductor films, both ends of the sapphire rods shall be polished parallel to each other and perpendicular to the axis. Specifications of the sapphire rods are described in 7.1. SIST EN 61788-16:2013

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The diameter and height of the sapphire rod shall be carefully designed to ensure the TE011, TE021 and TE012 modes do not couple to other TM, HE and EH modes, since coupling between TE mode and other modes causes the unloaded Q to deteriorate. The design guideline for the sapphire rod is described in A.2. Table 1 shows typical dimensions of the sapphire rod for a TE011–mode resonant frequency of about 10 GHz.
Table 1 – Typical dimensions of the sapphire rod Resonance Mode
Frequency GHz Diameter Height d
mm h
mm TE011 10,6 11,8 6,74 TE021 17,0 TE012 17,0
5.2.3 Superconductor films The diameter of the superconductor films shall be about three times larger than that of the sapphire rods. In this configuration, the increased uncertainty of Rs due to the radiation loss can be considered negligible, given the target relative combined standard uncertainty of 20%.
The film thickness shall be more than three times larger than the London penetration depth value at each temperature. If the film thickness is less than three times the London penetration depth, the measured Rs should mean the effective surface resistance. 6 Measurement procedure 6.1 Set-up All the components of the sapphire resonator, such as the sapphire rod, superconductor films, and so on, shall be kept in a clean and dry state such as in a dry box or desiccator, as high humidity may degrade the unloaded Q-value.
The sapphire resonator shall be fixed in a specimen chamber inside the temperature-controlled cryocooler. The specimen chamber shall be generally evacuated. The temperatures of the superconductor films and sapphire rod shall be measured by a diode thermometer, or a thermocouple. The temperatures of the upper and lower superconductor films, and the sapphire rod must be kept as close as possible. This can be achieved by covering the sapphire resonator with aluminum foil, or filling the specimen chamber with helium gas. 6.2 Measurement of the tan δ of the sapphire rod 6.2.1 General To measure the surface resistance of the superconductor films precisely using a sapphire resonator, the tan δ of the sapphire rod shall be known. The two-resonance mode dielectric resonator method [12,13], which uses the TE021 and TE012 modes of the same sapphire resonator shall be adopted to measure the tan δ of the sapphire rod. The measurement procedure of the tan δ is as follows: 6.2.2 Measurement of the frequency response of the TE021 mode
The temperature dependence of the resonant frequency f0 and unloaded quality factor Qu for TE021 resonance mode shall be measured as follows: SIST EN 61788-16:2013

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a) Connect the measurement system as shown in Figure 1. Fix the distance between the sapphire rod and each of the loops of the semi-rigid cables to be equal, so that this transmission-type resonator can be under-coupled equally to both loops. The coupling shall be adjusted to be weak enough not to excite unwanted resonance modes such as TM, HE and EH modes but strong enough to be able to excite TE021 mode. The input power to the resonator shall be below 10 dBm (typically 0 dBm). Confirm that the insertion attenuation of this mode is larger than 20 dB from the reference level. Evacuate and cool down the specimen chamber to below the critical temperature. b) Measure S21 as a function of frequency where S21 is the transmission scattering parameter. Find the TE021 mode |S21| resonance peak of this resonator at a frequency nearly equal to the designed value of the resonant frequency f0.
c) Narrow the frequency span on the display so that only the |S21| resonance peak of TE021 mode can be shown. d) Collect both real and imaginary parts of the S21 , S11 and S22 as a function of frequency (S21(f), S11(f) and S22(f)) where S11 and S22 are reflection scattering parameters. e) Resonant frequency f0 and loaded Q-value QL are obtained by fitting the experimentally measured data S21(f) to the Equation (1), where f0 and QL are fitting parameters.
)f(Q)f(S)f(S∆Lj102121+= (1) where f is frequency and û(f) is defined as
2201ff)f(−=∆
(2)
This fitting technique is called the “Circle fit technique”, the details of which are described in A.3.
f) The unloaded Q-value, QU, shall be extracted from the QL by the following Equation (3):
)1(21LUββ++=QQ (3) where β1 and β2 are the coupling coefficients and defined as
|S||S||S|22111111+−=β (4)
|S||S||S|22112221+−=β (5)
where |S11| and |S22| are dips in the reflection scattering parameters at f0 as shown in Figure 4, and measured in linear units of power rather than relative dB.
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Reflection coefficient f0 S11 and S22 Frequency 0 IEC
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Figure 4 – Reflection scattering parameters (|S11| and |S22|) g) The f0 and QU measured for this TE021 mode are denoted as f021 and QU021. By slowly changing the temperature of the cryocooler, the temperature dependence of f021 and QU021 shall be measured. 6.2.3 Measurement of the frequency response of the TE012 mode The temperature dependence of the resonant frequency f0 and unloaded quality factor QU for the TE012 resonance mode shall be measured similarly to the TE021 resonance mode. The procedure is as follows: a) After measuring the TE021 mode, cool down the specimen chamber below the critical temperature again. b) Measure S21 as a function of frequency. Find the TE012 mode |S21| resonance peak of this resonator at a frequency nearly equal to the designed value of the resonant frequency f0.
c) Narrow the frequency span on the display so that only the |S21| resonance peak of TE012 mode can be shown. d) Follow step 6.2.2 d) to g) to measure the temperature dependence of the resonant frequency f0 and the unloaded Q value QU for this TE012 mode. They are denoted as f012 and QU012. 6.2.4 Determination of tan δ of the sapphire rod Using the measured value of f021, QU021, f012 and QU012, the surface resistance of the superconductor films Rs and tan / of the sapphire rod are given by the following simultaneous equations:
−=−=)(1)()(1)(021021U021021021s012012U012012012sftanQABfRftanQABfRδδ (6) where A012, B012, A021 and B021 are geometric factors of TE012 and TE021, respectively, and given by
'WAε+=1 (7)
,,,p,'WhpB⋅⋅⋅=π+=2130122302ελ (8) SIST EN 61788-16:2013

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00cf=λ (9)
)u(J)u(J)u(J)v(K)v(K)v(K)v(K)u(JW202121202121−−= (10)
π1202022-hp
d =λλv (11)
(v)K(v)K-v=(u)J(u)J1010u (12) where, λ0 is the free space resonant wavelength; c is the velocity of light in a vacuum (c = 2,9979 ×=108 m/s);
h is the height of the sapphire rod, and d is the diameter of the sapphire rod. In the equations, f0 = f012 and p = 2 for TE012 mode, and f0 = f021 and p = 1 for TE021 mode, respectively.
The value u2 is given by the transcendental Equation (12) using the value of v2, where Jn(u) is the Bessel function of the first kind and Kn(v) is the modified Bessel function of the second kind, respectively. For any value of v, the m-th solution u exists between u0m and u1m, where J0(u0m) = 0 and J1(u1m) = 0. m = 1 for TE012 mode and m = 2 for TE021 mode. In Equation (8), both Rs and tan δ are frequency-dependent and the scaling relations Rs ∝ f2 as explained by the two-fluid model, and tan δ ∝ f an assumed relation for low-loss dielectrics, can be applied.
2012021012s021s)f/f()f(R)f(R×= (13)
)f/f()f(tan)f(tan012021012021×=δδ (14) In Equations (7) and (8), ε‘ is the relative permittivity of the sapphire rod and given by
()12202+v+ud ='πλε
(15) using the values of v 2 and u 2. 6.3 Power dependence measurement 6.3.1 General Once the tan δ of the sapphire rod has been measured, the surface resistance and its power dependence can be evaluated using the single resonance mode. TE011 is suitable for this measurement because of the strong resonance peak. The experimental procedure for the power dependence measurements is as follows. SIST EN 61788-16:2013

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6.3.2 Calibration of the incident microwave power to the resonator The incident microwave power to the resonator shall be calibrated using a power meter before the measurement (dotted line in Figure 2). The incident power to the resonator, Pin, was determined as the measured power at the input of the resonator.
6.3.3 Measurement of the reference level The level of full transmission power (reference level) shall be measured first. Connect the reference line of the semi-rigid cable between the input and output connectors. Subsequently, measure the transmission power level over the entire measurement frequency and temperature range. The reference level can change several decibels when the temperature of the apparatus changes from room temperature to the lowest measurement temperature. Therefore, the temperature dependence of the reference level must be taken into account. 6.3.4 Surface resistance measurement as a function of the incident microwave power
a) Connect the measurement system as shown in Figure 2. Fix the distance between the sapphire rod and the loops of the semi-rigid cables using a strong coupling, so that high microwave power can be introduced into the resonator. A suitable coupling strength is |S11| ≅=3 dB. Cool down the specimen chamber to below the critical temperature. b) Measure S21 as a function of frequency. Find the TE011 mode |S21| resonance peak of this resonator at a frequency nearly equal to the designed value of the resonant frequency f0.
c) Narrow the frequency span on the display so that only the |S21| resonance peak of TE011 mode can be shown. Measure the insertion attenuation, ains, which is the attenuation (in dB) from the reference level to the |S21| at the resonant frequency f0 of the TE011 mode.
d) Collect both real and imaginary parts of the S21 and S11 as a function of frequency (S21(f) and S11(f)) e) Follow the step 6.2.2 e) to measure the resonant frequency f0 and the loaded Q value QL for this TE011 mode. They are denoted as f011 and QL011. f) Extract the unloaded Q value, QU011, from the QL011 by the following equation:
20ttL011U011ins10 - 1/aA,AQQ−== (16) g) The surface resistances of the superconductor films are obtained by the following equation:
−=)(1)(011011U011011011sftanQABfRδ (17)
where A011and B011 are geometric factors of TE011 mode, and obtained by equations (7) to (15) setting f0 = f011, p = 1, and m = 1. The tan δ(f011) should be the scaled value at f011 of the value determined in 6.2.4 which corresponds to f012,
)f/f()f(tan)f(tan012011012011×=δδ (18) h) The incident power of the microwave was swept by changing the input power of the TWT amplifier with the specimen chamber maintained at a constant temperature. Repeat steps c) to g) for each incident microwave power. i) Change the temperature of the specimen chamber and repeat steps c) to h) for each temperature.
6.3.5 Determination of the maximum surface magnetic flux density
The measured incident microwave power dependence of the surface resistance itself does not directly show the power handling capability of the superconductor films. The latter shall be measured in terms of the maximum surface magnetic flux density without causing its properties to deteriorate. High surface magnetic flux density, i.e., RF current induces the pair breaking of SIST EN 61788-16:2013

– 16 – 61788-16 © IEC:2013
the Cooper pair and increases the surface resistance. Also weak coupling between the grain boundaries or d-wave symmetry of the superconductor is considered to increase the surface resistance. From the measured incident power dependence of the surface resistance, the maximum surface magnetic flux density shall be calculated as follows [14,15]. The dissipated power in the resonator P0 is evaluated from the incident power to the resonator Pin and S parameters as follows:
)|S||S|(PP221211in01−−= (19) The surface magnetic flux density of the superconducting films can be calculated by the analytical equation. The maximum surface magnetic flux density Bs max is given by the following equation [14]:
2/130s22/0210smax s2401)2(2581865,0−′π++π=∫λδερρρhRtanWdduJPRBd (20) where d, J1, u, W, ε’, h and λ0 are the same as defined in Equations (7) to (15), and λd is the penetration depth of the superconductor films. The λd can be directly measured according to IEC 61788-15. When the directly measured λd data is not available, a typical reported value for the same material should be used.
7 Uncertainty of the test method 7.1 Surface resistance A vector network analyzer as specified in Table 2 shall be used to record the frequency dependence of attenuation. The resulting record shall allow the determination of Q to a relative uncertainty of 10–2. Table 2 – Specifications of the vector network analyzer Dynamic range of S21 above 60 dB Frequency resolution below 1 Hz Attenuation uncertainty below 0,1 dB Input power limitation below 10 dBm
The specifications of the sapphire rod are shown in Table 3. Term definitions in Table 3 are shown in Figure 5.
61788-16 © IEC:2013 – 17 –
Cylinder axis c-axis of crystal Perpendicularity Flatness Surface roughness IEC
007/13
Figure 5 – Term definitions in Table 3 Table 3 – Specifications of the sapphire rods Tolerance in diameter ±0,05 mm Tolerance in height ±0,05 mm
Flatness below 0,005 mm Surface roughness top and bottom surface: root mean square height below 10 nm cylindrical surface: root mean square height below 0,001 mm Perpendicularity within 0,1° Axis
parallel to c-axis within 0,3°
7.2 Temperature The measurement apparatus is cooled down to the specified temperature by any means during testing. An easy choice would be to immerse the apparatus into a liquid cryogen. This technique is quick and simple and yields a known and stable temperature. Unfortunately, most HTS materials are damaged by the condensation of moisture that occurs when removing the sample from the cryogen. In addition, uncertainties generated by the presence of a gas/liquid mixture within the cavity, and the inability to measure Rs as a function of temperature support the use of other cooling methods. These limitations can be circumvented by the immersion of a vacuum can into a liquid cryogen. If the vacuum can is backfilled with gas, then rapid cooling and uniform temperatures occur. If heaters are attached to the apparatus, then the temperature-dependent properties of the HTS material can be measured. A third and equally good choice is the use of a cryocooler. In this case, the resonator is under vacuum and cooled by conduction through the metallic package. Care must be taken to avoid temperature gradients with the apparatus.
A cryostat shall be provided with the necessary environment for measuring Rs and the specimen shall be measured while in a stable and isothermal state. The specimen temperature is assumed to be the same as that of the sample holder. The holder temperature shall be reported to an accuracy of ±2 K, measured using an appropriate temperature sensor.
The difference between the specimen and holder temperatures shall be minimized by using shields with good thermal conductivity. For power dependence measurement, heating of the loop antenna by elevated microwave power level may affect the measurements. To minimize the heating effects, the distance between the sapphire rod and the loops of the semi-rigid cables should be short enough to realize a strong coupling an
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