IEC 61788-16:2013
(Main)Superconductivity - Part 16: Electronic characteristic measurements - Power-dependent surface resistance of superconductors at microwave frequencies
Superconductivity - Part 16: Electronic characteristic measurements - Power-dependent surface resistance of superconductors at microwave frequencies
IEC 61788-16:2013 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. This method is the applicable for a frequency in the range of 10 GHz, for an input microwave power lower than 37 dBm (5 W). The aim is to report the surface resistance data at the measured frequency and that scaled to 10 GHz. Keyword: superconductivity
Supraconductivité - Partie 16: Mesures de caractéristiques électroniques - Résistance de surface des supraconducteurs aux hyperfréquences en fonction de la puissance
La CEI 61788-16:2013 décrit la méthode de mesure normale de la résistance de surface des supraconducteurs aux hyperfréquences en fonction de la puissance par la méthode du résonateur au saphir. La grandeur de mesure est la dépendance en fonction de la puissance de Rs à la fréquence de résonance. Cette méthode est applicable à des fréquences de l'ordre de 10 GHz pour une puissance d'entrée inférieure à 37 dBm (5 W). Il s'agit de consigner dans un rapport les données de résistance de surface à la fréquence mesurée et celles qui sont ramenées à une échelle de 10 GHz. Mot clé: supraconductivité
General Information
Standards Content (Sample)
IEC 61788-16 ®
Edition 1.0 2013-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
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
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IEC 61788-16 ®
Edition 1.0 2013-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
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
PRICE CODE
INTERNATIONALE
CODE PRIX V
ICS 17.220.20; 29.050 ISBN 978-2-83220-582-2
– 2 – 61788-16 © IEC:2013
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 TE mode . 11
6.2.3 Measurement of the frequency response of the TE 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 R values. 18
s
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
61788-16 © IEC:2013 – 3 –
Figure 3 – Sapphire resonator (open type) to measure the surface resistance of
superconductor films . 10
Figure 4 – Reflection scattering parameters (|S | and |S |) . 13
11 22
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 Q measurements using the conventional 3 dB
L
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 R on the maximum surface magnetic
s
flux density B [3] . 23
s max
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
– 4 – 61788-16 © IEC:2013
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 16: Electronic characteristic measurements –
Power-dependent surface resistance
of superconductors at microwave frequencies
FOREWORD
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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.
61788-16 © IEC:2013 – 5 –
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.
– 6 – 61788-16 © IEC:2013
INTRODUCTION
Since the discovery of high-T superconductors (HTS), extensive researches have been
c
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] .
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 R and the temperature dependence
s
of the R . Recent advances in HTS thin films with R , several orders of magnitude lower than
s s
normal metals has increased the need for a reliable characterization technique to measure this
property [5,6]. Among several methods to measure the R of superconductor materials at
s
microwave frequencies, the dielectric resonator method [7,8,9] has been useful due to that the
method enables to measure the R nondestructively and accurately. In particular, the sapphire
s
resonator is an excellent tool for measuring the R of HTS materials [10]. In 2002, the
s
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 R
s
but also the power dependence of R is needed to design the microwave components. Based on
s
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-T material.
c
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.
___________
Numbers in square brackets refer to the Bibliography.
61788-16 © IEC:2013 – 7 –
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 R at the resonant
s
frequency.
The following is the applicable measuring range of surface resistances for this method:
Frequency: f ~ 10 GHz
Input microwave power: P < 37 dBm (5 W)
in
The aim is to report the surface resistance data at the measured frequency and that scaled to
10 GHz using the R ∝ f relation for comparison.
s
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 Z for conductors including superconductors is defined as the ratio of
s
the electric field E to the magnetic field H , tangential to a conductor surface:
t t
Z = E /H = R + jX ,
s t t s s
where R is the surface resistance and X is the surface reactance.
s s
– 8 – 61788-16 © IEC:2013
4 Requirements
The surface resistance R of a superconductor film shall be measured by applying a microwave
s
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.
61788-16 © IEC:2013 – 9 –
Vector network
analyzer
Synthesized
sweeper
Thermometer
S-parameter
test set
Thermal sensor
Measurement apparatus
IEC 003/13
Cryocooler
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.
Vector network
Synthesized sweeper
analyzer
Power sweep
TWT
amplifier
Attenuator
Resonator
Coupler Coupler
Cryostat
Power meter
Circulator Circulator
IEC 004/13
Figure 2 – Measurement system for the microwave power dependence
of the surface resistance
System interface
– 10 – 61788-16 © IEC:2013
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 R of superconductor films and tan δ of the sapphire rod [9]. In the sapphire
s
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 TM modes. The coupling loops shall be carefully checked for
mn0
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
Sapphire rod
films
Spring
Loop antenna
Copper base
IEC 005/13
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
–6
accuracy on R . A recommended sapphire rod is expected to have a tan δ less than 10 at 77 K.
s
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 of the
sapphire rods are described in 7.1.
61788-16 © IEC:2013 – 11 –
The diameter and height of the sapphire rod shall be carefully designed to ensure the TE ,
TE and TE modes do not couple to other TM, HE and EH modes, since coupling between
021 012
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
TE –mode resonant frequency of about 10 GHz.
Table 1 – Typical dimensions of the sapphire rod
Diameter Height
Resonance Frequency
d h
Mode GHz
mm mm
TE 10,6
TE 17,0 11,8 6,74
TE 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 R due to the radiation loss can
s
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 R should mean the effective surface resistance.
s
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 TE and TE modes of the same sapphire
021 012
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 TE mode
The temperature dependence of the resonant frequency f and unloaded quality factor Q for
0 u
TE resonance mode shall be measured as follows:
– 12 – 61788-16 © IEC:2013
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 TE 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 S as a function of frequency where S is the transmission scattering parameter.
21 21
Find the TE mode |S | resonance peak of this resonator at a frequency nearly equal to
021 21
the designed value of the resonant frequency f .
c) Narrow the frequency span on the display so that only the |S | resonance peak of TE
21 021
mode can be shown.
d) Collect both real and imaginary parts of the S , S and S as a function of frequency
21 11 22
(S (f), S (f) and S (f)) where S and S are reflection scattering parameters.
21 11 22 11 22
e) Resonant frequency f and loaded Q-value Q are obtained by fitting the experimentally
0 L
measured data S (f) to the Equation (1), where f and Q are fitting parameters.
21 0 L
S (f )
21 0
S (f ) = (1)
1+ jQ ∆(f )
L
where f is frequency and Δ(f) is defined as
f
∆(f ) = 1− (2)
f
This fitting technique is called the “Circle fit technique”, the details of which are described in
A.3.
f) The unloaded Q-value, Q , shall be extracted from the Q by the following Equation (3):
U L
(3)
Q = Q (1+ β + β )
U L 1 2
β and β are the coupling coefficients and defined as
where
1 2
1− | S |
β = (4)
| S | + | S |
11 22
1− | S |
β = (5)
| S | + | S |
11 22
where |S | and |S | are dips in the reflection scattering parameters at f as shown in Figure
11 22
4, and measured in linear units of power rather than relative dB.
61788-16 © IEC:2013 – 13 –
S
and
S
f
Frequency
IEC 006/13
Figure 4 – Reflection scattering parameters (|S | and |S |)
11 22
g) The f and Q measured for this TE mode are denoted as f and Q . By slowly
U 021 021 U021
changing the temperature of the cryocooler, the temperature dependence of f and Q
U021
shall be measured.
6.2.3 Measurement of the frequency response of the TE mode
The temperature dependence of the resonant frequency f and unloaded quality factor Q for
0 U
the TE resonance mode shall be measured similarly to the TE resonance mode. The
012 021
procedure is as follows:
a) After measuring the TE mode, cool down the specimen chamber below the critical
temperature again.
b) Measure S as a function of frequency. Find the TE mode |S | resonance peak of this
21 012 21
resonator at a frequency nearly equal to the designed value of the resonant frequency f .
c) Narrow the frequency span on the display so that only the |S | resonance peak of TE
21 012
mode can be shown.
d) Follow step 6.2.2 d) to g) to measure the temperature dependence of the resonant frequency
f and the unloaded Q value Q for this TE mode. They are denoted as f and Q .
0 U 012 012 U012
6.2.4 Determination of tan δ of the sapphire rod
Using the measured value of f , Q , f and Q , the surface resistance of the
021 U021 012 U012
superconductor films R and tan δ of the sapphire rod are given by the following simultaneous
s
equations:
1 A
R (f ) = − tanδ(f )
s 012 012
B Q
012 U012
(6)
1 A
R (f ) = − tanδ(f )
s 021 021
B Q
021 U021
where A , B , A and B are geometric factors of TE and TE , respectively, and
012 012 021 021 012 021
given by
W
A = 1+ (7)
ε'
λ 1+W
B = p , p = 1,2,⋅⋅⋅, (8)
2h
30π ε'
Reflection coefficient
– 14 – 61788-16 © IEC:2013
c
λ = (9)
f
2 2
J (u ) K (v )K (v ) −
K (v )
1 0 2 1
W = (10)
2 2
K (v ) J (u ) − J (u )J (u )
1 1 0 2
πd pλ
2 0
= -1 (11)
v
2h
λ
0
J (u) (v)
K
0 0
u = -v (12)
(u) (v)
J K
1 1
where,
λ is the free space resonant wavelength;
c is the velocity of light in a vacuum (c = 2,9979 × 10 m/s);
h is the height of the sapphire rod, and d is the diameter of the sapphire rod.
In the equations, f = f and p = 2 for TE mode, and f = f and p = 1 for TE mode,
0 012 012 0 021 021
respectively.
2 2
The value u is given by the transcendental Equation (12) using the value of v , where J (u) is
n
the Bessel function of the first kind and K (v) is the modified Bessel function of the second kind,
n
respectively. For any value of v, the m-th solution u exists between u and u , where
0m 1m
J (u ) = 0 and J (u ) = 0. m = 1 for TE mode and m = 2 for TE mode.
0 0m 1 1m 012 021
In Equation (8), both R and tan δ are frequency-dependent and the scaling relations R ∝ f as
s s
explained by the two-fluid model, and tan δ ∝ f an assumed relation for low-loss dielectrics, can
be applied.
R (f ) = R (f )×(f / f ) (13)
s 021 s 012 021 012
tan δ(f ) = tan δ(f )×(f / f ) (14)
021 012 021 012
In Equations (7) and (8), ε‘ is the relative permittivity of the sapphire rod and given by
λ
0 2 2
( ) (15)
ε' = + +1
u v
πd
2 2
using the values of v and u .
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. TE is suitable for this
measurement because of the strong resonance peak. The experimental procedure for the power
dependence measurements is as follows.
61788-16 © IEC:2013 – 15 –
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, P , was
in
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
|S | ≅ 3 dB. Cool down the specimen chamber to below the critical temperature.
b) Measure S as a function of frequency. Find the TE mode |S | resonance peak of this
21 21
resonator at a frequency nearly equal to the designed value of the resonant frequency f .
c) Narrow the frequency span on the display so that only the |S | resonance peak of TE
mode can be shown. Measure the insertion attenuation, a , which is the attenuation (in dB)
ins
from the reference level to the |S | at the resonant frequency f of the TE mode.
21 0 011
d) Collect both real and imaginary parts of the S and S as a function of frequency (S (f)
21 11 21
and S (f))
e) Follow the step 6.2.2 e) to measure the resonant frequency f and the loaded Q value Q for
0 L
mode. They are denoted as f and Q .
this TE
011 011 L011
f) Extract the unloaded Q value, Q , from the Q by the following equation:
U011 L011
Q
−a / 20
L011
ins
Q = ,A = 10 (16)
U011 t
1 - A
t
g) The surface resistances of the superconductor films are obtained by the following equation:
A
R (f ) = − tanδ(f ) (17)
s 011 011
B Q
011 U011
where A and B are geometric factors of TE mode, and obtained by equations (7) to
011 011 011
(15) setting f = f , p = 1, and m = 1. The tan δ(f ) should be the scaled value at f of
0 011 011 011
the value determined in 6.2.4 which corresponds to f ,
tanδ(f ) = tanδ(f )×(f / f ) (18)
011 012 011 012
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
– 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 P is evaluated from the incident power to the resonator
P and S parameters as follows:
in
2 2
P = P (1− | S | − | S | ) (19)
0 in 11 21
The surface magnetic flux density of the superconducting films can be calculated by the
analytical equation. The maximum surface magnetic flux density B is given by the following
s max
equation [14]:
−1/ 2
2
d / 2
2πR 2u 240π ε ′tanδ h
s 2
B = 0,581865 J ( ρ)ρdρ 1+ W + (20)
s max 1
∫
P d R λ
0 s 0
where d, J , u, W, ε’, h and λ are the same as defined in Equations (7) to (15), and λ is the
d
1 0
penetration depth of the superconductor films. The λ can be directly measured according to
d
IEC 61788-15. When the directly measured λ data is not available, a typical reported value for
d
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
–2
uncertainty of 10 .
Table 2 – Specifications of the vector network analyzer
Dynamic range of S 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 –
Flatness
Surface roughness
Perpendicularity
c-axis of
Cylinder axis
crystal
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
cyli
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