IEC 61189-2-721:2015

IEC 61189-2-721 ®
Edition 1.0 2015-04
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Test methods for electrical materials, printed boards and other interconnection
structures and assemblies –
Part 2-721: Test methods for materials for interconnection structures –
Measurement of relative permittivity and loss tangent for copper clad laminate
at microwave frequency using split post dielectric resonator

Méthodes d'essai pour les matériaux électriques, les cartes imprimées et autres
structures d'interconnexion et ensembles –
Partie 2-721: Méthodes d'essai des matériaux pour structures d'interconnexion –
Mesure de la permittivité relative et de la tangente de perte pour les stratifiés
recouverts de cuivre en hyperfréquences à l'aide d'un résonateur diélectrique
en anneaux fendus
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IEC 61189-2-721 ®
Edition 1.0 2015-04
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Test methods for electrical materials, printed boards and other interconnection

structures and assemblies –
Part 2-721: Test methods for materials for interconnection structures –

Measurement of relative permittivity and loss tangent for copper clad laminate

at microwave frequency using split post dielectric resonator

Méthodes d'essai pour les matériaux électriques, les cartes imprimées et autres

structures d'interconnexion et ensembles –

Partie 2-721: Méthodes d'essai des matériaux pour structures d'interconnexion –

Mesure de la permittivité relative et de la tangente de perte pour les stratifiés

recouverts de cuivre en hyperfréquences à l'aide d'un résonateur diélectrique

en anneaux fendus
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 31.180 ISBN 978-2-8322-2648-3

– 2 – IEC 61189-2-721:2015 © IEC 2015
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Test specimens . 6
2.1 Specimen size . 6
2.2 Preparation . 7
2.3 Marking . 7
2.4 Thickness . 7
3 Equipment/apparatus . 7
3.1 General . 7
3.2 Vector network analyzer (VNA) . 8
3.3 SPDR test fixture . 8
3.3.1 General . 8
3.3.2 Parameters . 8
3.3.3 Frequency . 8
3.4 Verify unit . 9
3.5 Micrometer . 9
3.6 Circulating oven . 9
3.7 Test chamber . 9
4 Procedure . 9
4.1 Preconditioning . 9
4.2 Testing of relative permittivity and loss tangent at room temperature . 9
4.2.1 Test conditions . 9
4.2.2 Preparation . 9
4.2.3 Fixture . 10
4.2.4 Connection to VNA . 10
4.2.5 VNA parameter . 10
4.2.6 Frequency and Q-factor without specimen . 10
4.2.7 Micrometer . 10
4.2.8 Setting the specimen . 10
4.2.9 Frequency and Q-factor with specimen . 10
4.2.10 Comparison . 10
4.2.11 Calculation . 11
4.2.12 Change the specimen . 12
4.2.13 Change in test frequency . 12
4.3 Testing of relative permittivity and loss tangent at variable temperatures . 12
4.3.1 Test conditions . 12
4.3.2 Preparation . 12
4.3.3 Fixture . 12
4.3.4 Connection to VNA . 12
4.3.5 VNA parameter . 12
4.3.6 Temperature in the chamber . 12
4.3.7 Frequency and Q-factor without specimen . 12
4.3.8 Micrometer . 12
4.3.9 Setting of the specimen . 13
4.3.10 Frequency and Q-factor with specimen . 13
4.3.11 Calculation . 13

4.3.12 Options . 13
4.3.13 Thermal coefficient . 13
4.3.14 Change in test frequency . 14
5 Report . 14
5.1 At room temperature . 14
5.2 At variable temperature . 14
6 Additional information . 14
6.1 Accuracy . 14
6.2 Maintenance . 14
6.3 Matters to be attended . 15
6.4 Additional information concerning fixtures and results . 15
6.5 Additional information on K (ε ,h) and p . 15
ε r es
Annex A (informative) Example of test fixture and test result . 16
A.1 Example of test fixture . 16
A.2 Example of test result . 16
Annex B (informative) Additional information on K (ε ,h) and p . 19
ε r es
Bibliography . 22

Figure 1 – Scheme of SPDR test fixture . 6
Figure 2 – Component diagram of test system . 8
Figure 3 – Scheme of the change of resonance frequency with or without the
specimen . 10
Figure A.1 – Test fixture . 16
Figure A.2 – Relative permittivity versus frequency (laminate of Dk 3,8 and thickness
0,51 mm) . 17
Figure A.3 – Loss tangent versus frequency (laminate of Dk 3,8 and thickness
0,51 mm) . 17
Figure A.4 – Curve of relative permittivity and loss tangent at variable temperatures
(laminate of Dk 3,8 and thickness 0,51 mm) . 18
Figure B.1 – K (ε ,h) versus relative permittivity at different sample thicknesses . 19
ε r
Figure B.2 – Distribution of the electric field of the split dielectric resonator (side view
of the dielectric resonators) . 20
Figure B.3 – Distribution of the electric field of the split dielectric resonator (top view
between the dielectric resonators) . 21
Figure B.4 – p versus relative permittivity at different sample thicknesses . 21
es
Table 1 – Specimen dimensions . 7
Table 2 – SPDR test fixture’s parameter . 9
Table B.1 – Results of measurements of different materials using a 10 GHz SPDR. 20

– 4 – IEC 61189-2-721:2015 © IEC 2015
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
TEST METHODS FOR ELECTRICAL MATERIALS, PRINTED BOARDS AND
OTHER INTERCONNECTION STRUCTURES AND ASSEMBLIES –

Part 2-721: Test methods for materials for interconnection structures –
Measurement of relative permittivity and loss tangent for copper clad
laminate at microwave frequency using split post dielectric resonator

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
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61189-2-721 has been prepared by IEC technical committee 91:
Electronics assembly technology.
The text of this standard is based on the following documents:
FDIS Report on voting
91/1246/FDIS 91/1258/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.

A list of all parts in the IEC 61189 series, published under the general title Test methods for
electrical materials, printed boards and other interconnection structures and assemblies, can
be found on the IEC website.
Future standards in this series will carry the new general title as cited above. Titles of existing
standards in this series will be updated at the time of the next edition.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC website 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 – IEC 61189-2-721:2015 © IEC 2015
TEST METHODS FOR ELECTRICAL MATERIALS, PRINTED BOARDS AND
OTHER INTERCONNECTION STRUCTURES AND ASSEMBLIES –

Part 2-721: Test methods for materials for interconnection structures –
Measurement of relative permittivity and loss tangent for copper clad
laminate at microwave frequency using split post dielectric resonator

1 Scope
This part of IEC 61189 outlines a way to determine the relative permittivity (ε ) and loss
r
δ) (also called dielectric constant (Dk) and dissipation factor (Df)) of copper clad
tangent (tan
laminates at microwave frequencies (from 1,1 GHz to 20 GHz) using a split post dielectric
resonator (SPDR).
This part of IEC 61189 is applicable to copper clad laminates and dielectric base materials.
2 Test specimens
2.1 Specimen size
The size of the specimen shall be larger than the internal diameter D of the metal enclosures,
and the maximum thickness of the specimen shall be smaller than the distance h between
g
the metal enclosures of the fixture. (See Figure 1.)
Z
Support
D
Dielectric resonators
Coupling loop
Sample
d
r
Metal enclosure
IEC
Key
h distance between the metal enclosures of the fixture;
g
D internal diameter of the metal enclosures;
L internal height of the metal enclosures;
d diameter of the dielectric resonator;
r
h thickness of the dielectric resonator.
r
Figure 1 – Scheme of SPDR test fixture
h
g
h
r
L
Three specimens for the test at room temperature and one specimen for the test at variable
temperatures are required for each SPDR test fixture for this test. Table 1 shows the
supported specimen dimensions.
Table 1 – Specimen dimensions
SPDR test fixture’s nominal
Supported specimen sizes Maximum thickness of specimens
frequency
GHz mm mm
1,1 150 × 150 6,0
3 3,0
80 × 80
5 to 6 2,0
80 × 80
9 to 10 80 × 80 0,9
13 to 16 50 × 35 0,6
18 to 20 0,5
15 × 15
If applicable, a specimen size different from those given in Table 1 can be used. For example,
specimen size “130 mm × 130 mm” can be used for 1,1 GHz.
2.2 Preparation
Copper clad laminates shall have all copper cladding removed by etching, and shall be
thoroughly cleaned.
2.3 Marking
Mark each specimen in the upper left corner with an engraving pencil or other suitable method.
2.4 Thickness
Within the limits of the test fixture, the thicker the specimen is, the less error occurs in the
measurements. Thin specimen can be stacked up to a minimum of 0,4 mm to improve
measurement accuracy.
NOTE Air gaps between the sample and fixture do not affect the measurement.
3 Equipment/apparatus
3.1 General
The component diagram of the test system is shown in Figure 2.

– 8 – IEC 61189-2-721:2015 © IEC 2015
Room temperature test
Variable temperature test
VNA
VNA
Environmental test chamber
SPDR test fixture
Sample
SPDR test fixture
Sample
IEC
Figure 2 – Component diagram of test system
3.2 Vector network analyzer (VNA)
The following values are required:
a) The frequency range of VNA shall be 500 MHz to 20 GHz.
b) The dynamic range of VNA shall be more than 60 dB.
3.3 SPDR test fixture
3.3.1 General
Figure 1 shows the scheme of SPDR test fixture.
3.3.2 Parameters
Table 2 shows the typical relationship between the SPDR test fixture’s nominal frequency and
h and D.
g
3.3.3 Frequency
For different test frequencies, use a corresponding SPDR test fixture of nominal frequency.

Table 2 – SPDR test fixture’s parameter
SPDR test fixture’s nominal frequency D h
g
GHz mm mm
1,1 120 6,0
3 50 3,0
5 to 6 30 2,0
9 to 10 22 0,9
13 to 16 15 0,6
18 to 20 10 0,5
3.4 Verify unit
The verify unit includes the following:
a) Standard reference sample, for example, single-crystal quartz or equivalent sample.
b) A calibration assembly of VNA.
3.5 Micrometer
Micrometer with 0,001 mm resolution (or better).
3.6 Circulating oven
+5
Circulating oven with stabilized temperature at 105 °C.
−2
3.7 Test chamber
For the environmental test chamber for variable temperature testing the following
requirements apply:
a) Temperature ranges: –125 °C to +110 °C, other temperature range is as agreed between
user and supplier.
b) Temperature accuracy-set point to actual: ±1 °C.
4 Procedure
4.1 Preconditioning
All specimens shall be conditioned at (23 ± 2) °C and (50 ± 5) % RH for at least 24 h prior to
testing. However, if a specimen has recently been etched or exposed to excessive moisture, it
+5
should be dried in an air-circulating oven for 2 h at 105 °C and then conditioned at the
−2
condition as mentioned above.
4.2 Testing of relative permittivity and loss tangent at room temperature
4.2.1 Test conditions
The ambient test temperature should be (23 ± 2) °C. The variation should not exceed 1 °C
during the test.
4.2.2 Preparation
Allow at least 30 min for the VNA to warm up and stabilize.

– 10 – IEC 61189-2-721:2015 © IEC 2015
4.2.3 Fixture
Select an SPDR test fixture in accordance with the test frequency. The specimen size and
thickness shall comply with the requirements specified in Table 1. For example, if the test
frequency is 10 GHz, a SPDR test fixture with 10 GHz nominal frequency should be selected.
The supported specimen size is 80 mm × 80 mm and the maximum thickness of specimens is
no more than 0,9 mm.
4.2.4 Connection to VNA
Connect the SPDR test fixture to the VNA. The test fixture shall be kept horizontal.
4.2.5 VNA parameter
Set the VNA parameters according to the manufacturer's instructions and the nominal
frequency of the SPDR fixture.
4.2.6 Frequency and Q-factor without specimen
Measure the resonance frequency (f ) and Q-factor (Q ) values of the empty resonator.
0 0
4.2.7 Micrometer
Utilize a micrometer to measure the thickness of the specimen and record as h.
4.2.8 Setting the specimen
Insert the specimen into the test fixture. The side with marking is face up and the edge of this
side has to be aligned with the fixture edge.
4.2.9 Frequency and Q-factor with specimen
Measure the resonance frequency (f ) and Q-factor (Q ) of the resonator containing the
s s
specimen.
4.2.10 Comparison
The scheme of the change of resonance frequency with or without the specimen is shown in
Figure 3.
Empty resonator
Resonator containing
the specimen
f f
S 0
Resonance frequency
IEC
Figure 3 – Scheme of the change of resonance frequency
with or without the specimen
Resonance amplitude
4.2.11 Calculation
4.2.11.1 General
Calculation of relative permittivity and loss tangent at room temperature.
Relative permittivity and loss tangent at room temperature shall be calculated as follows. It is
recommended to use the computer software provided by the equipment supplier for
calculation.
4.2.11.2 Relative permittivity
The relative permittivity (ε ) shall be calculated according to Equation (1).
r
f − f
0 s
ε = 1+ (1)
r
hf K (ε ,h)
0 ε r
where
ε is relative permittivity;
r
h is the thickness of the specimen under test, in mm;
f is the resonant frequency of the empty SPDR;
f is the resonant frequency of the resonator with the dielectric specimen;
s
K (ε h) is a function of ε and h. For a fixed resonant cavity, its physical parameters (size,
ε r, r
dielectric resonators ε ) should have been identified. K (ε h) is pre-computed and
r ε r,
tabulated by electromagnetic field simulation with the strict Rayleigh-Ritz method.
Put the empty SPDR frequency (f ), the resonant frequency with dielectric
specimen (f ) and the thickness of the specimen (h) under test into Equation (1).
s
Enter a similar arbitrary value of the relative permittivity of the sample, and use a
successive approximation algorithm. After several iterations, end the calculation
when the relative error of the last two calculated relative permittivities is less than
0,1 %. The last calculated data is taken as the relative permittivity of the specimen.
Some additional information is shown in Annex B.
4.2.11.3 Loss tangent
The loss tangent shall be calculated according to Equation (2).
−1 −1 −1
(Q − Q − Q )
S DR C
tanδ = (2)
p
es
where
tanδ is the loss tangent;
is the unloaded Q-factor of a resonant fixture containing the specimen;
Q
s
Q is the Q-factor depending on metal losses for the resonant fixture containing the
c
specimen;
Q is the Q-factor depending on dielectric losses in the dielectric posts for the fixture
DR
containing the specimen;
p is the electromagnetic energy filling factor of the specimen. After identifying the
es
physical parameters of the resonant cavity, the electromagnetic energy filling factor
p can be determined by electromagnetic field simulation. For a fixed resonant
es
cavity, p is a constant value. Some additional information is showed in Annex B.
es
– 12 – IEC 61189-2-721:2015 © IEC 2015
4.2.12 Change the specimen
Measure the two remaining specimens by repeating steps 4.2.6 through 4.2.11.
4.2.13 Change in test frequency
If another test frequency is selected, change the SPDR test fixture in accordance with the test
frequency. Then repeat steps 4.2.3 through 4.2.12.
4.3 Testing of relative permittivity and loss tangent at variable temperatures
4.3.1 Test conditions
The ambient test temperature should be (23 ± 2) °C. The variation should not exceed 1 °C
during the test.
4.3.2 Preparation
Allow at least 30 min for the VNA to warm up.
4.3.3 Fixture
Select an SPDR test fixture in accordance with the test frequency. The specimen size and
thickness shall comply with the requirements specified in Table 1. For example, if the test
frequency is 10 GHz, an SPDR test fixture with 10 GHz nominal frequency should be selected.
The supported specimen size is 80 mm × 80 mm and the maximum thickness of the specimen
is no more than 0,9 mm.
4.3.4 Connection to VNA
Connect the SPDR test fixture to the VNA. The test fixture shall be kept in a horizontal
position in the test chamber.
4.3.5 VNA parameter
Set the VNA parameters according to the manufacturer's instructions and the nominal
frequency of the SPDR fixture.
4.3.6 Temperature in the chamber
Adjust the test temperature of the test chamber. After reaching the set temperature (T), hold it
for at least 15 min.
4.3.7 Frequency and Q-factor without specimen
Measure the resonance frequency f (T) and Q-factor Q (T) of the empty resonator.
0 0
The resonance peak should be between –40 dB and –45 dB; adjust the position of the
coupling loops to achieve this whilst ensuring their position is symmetrical.
When measuring the Q-factor, the frequency span of the VNA should be adjusted such that it
is between 110 % and 200 % of the full width at half maximum of the resonant curve.
4.3.8 Micrometer
Use a micrometer to measure the thickness of the specimen, and record as h.

4.3.9 Setting of the specimen
The environmental test chamber shall be returned to room temperature. Insert the specimen
into the test fixture. The side with marking is face up and the edge of this side has to be
aligned with the fixture edge.
4.3.10 Frequency and Q-factor with specimen
Repeat step 4.3.6. Measure the resonance frequency f (T) and Q-factor Q (T) of the resonator
s s
with the specimen at temperature T.
When measuring the Q-factor, the frequency span of the VNA should be adjusted such that it
is between 110 % and 200 % of the full width at half maximum of the resonant curve.
4.3.11 Calculation
Follow step 4.2.11 and calculate the value of the relative permittivity Dk(T) and the loss
tangent Df(T) at temperature T.
4.3.12 Options
If another test temperature is selected, repeat steps 4.3.6 through 4.3.11.
4.3.13 Thermal coefficient
4.3.13.1 General
Thermal coefficient of relative permittivity and thermal coefficient of loss tangent.
4.3.13.2 Relative permittivity
The thermal coefficient of the relative permittivity ε (brief for TCε ) is the change rate of the
r r
–6
relative permittivity per temperature change. The unit of TCε is 10 /°C. Generally, the
r
relative permittivity of a specimen at its base temperature T of 23 °C is used as the base
ref
relative permittivity Dk(T ). For temperature T, TCε shall be calculated according to Equation
ref r
(3).
Dk(T ) − Dk(T )
ref
TCε = (3)
r
( ) ( )
T − T × Dk T
ref ref
where
–6
TCε is the thermal coefficient of ε , 10 /°C;
r r
T is the test temperature, in °C;
T is the base temperature, in °C;
ref
Dk(T) is the relative permittivity at temperature T
;
Dk(T ) is the relative permittivity at temperature T .
ref ref
4.3.13.3 Loss tangent
The Thermal coefficient of tanδ (TC tanδ) is the change rate of the loss tangent per
–6
temperature (every increase or decrease 1 °C). The unit of TC tanδ is 10 /°C. Generally, the
loss tangent of the specimen at base temperature T of 23 °C is used as the base loss
ref
tangent Df(T ). For temperature T, TC tanδ is calculated according to Equation (4).
ref
Df (T ) − Df (T )
ref
TC tanδ =
(4)
(T − T )× Df (T )
ref ref
– 14 – IEC 61189-2-721:2015 © IEC 2015
where
TC tanδ is thermal coefficient of tanδ, in ppm/°C;
T is the test temperature, in °C;
T is the base temperature, in °C;
ref
Df(T) is the loss tangent at temperature T;
Df(T ) is the loss tangent at temperature T .
ref ref
4.3.14 Change in test frequency
If another test frequency is selected, change the SPDR test fixture in accordance with the test
frequency. Then repeat steps 4.3.3 through 4.3.13.
5 Report
5.1 At room temperature
For room temperature tests, report the following:
a) test environment (temperature, humidity);
b) test frequency;
c) the values and the average values of the relative permittivity and loss tangent at test
frequency;
d) the preconditioning of the specimen;
e) any anomalies in the test or variations from this test method.
5.2 At variable temperature
For variable temperature tests, report the following:
a) test temperature (T) and base temperature (T );;
ref
b) test frequency;
c) Dk(T)and Df(T)at test temperature (T);
d) TCε and TC tanδ;
r
e) Dk(T ) and Df(T );
ref ref
f) if more than one test temperature is necessary, report the curve diagram of the relative
permittivity and loss tangent in accordance with the temperature variation;
g) the preconditioning of the specimen;
h) any anomalies in the test or variations from this test method.
6 Additional information
6.1 Accuracy
Accuracy of measurements of a sample of thickness h.
Permittivity measurement: ∆ε/ε = ±(0,0015+∆h/h).
−5
Loss tangent: ∆tanδ = ±2 × 10 or ±0,03 tanδ whichever is higher.
6.2 Maintenance
Clean the test heads, standard materials and fixtures regularly.

6.3 Matters to be attended
To prevent damage to the test fixture because of the variable temperature tests, verify the
test system regularly with a standard reference sample. For example, single-crystal quartz is
used as the standard reference sample of thickness 0,4 mm. The deviation of the relative
permittivity measurement between the test result and the nominal value of the standard
reference sample shall be less than ±0,7 %, while the deviation of the loss tangent shall be
−5
less than ±2 × 10 .
6.4 Additional information concerning fixtures and results
An example of a test fixture and test result is shown in Annex A.
6.5 Additional information on K (ε ,h) and p
ε r es
Some additional information on K (ε ,h) and p is shown in Annex B.
ε r es
– 16 – IEC 61189-2-721:2015 © IEC 2015
Annex A
(informative)
Example of test fixture and test result
A.1 Example of test fixture
Figure A.1 shows a picture of an SPDR fixture at 5 GHz. Utilize a 3,5 mm female-to-female
adapter to connect the coaxial cable and the SPDR test fixture.
An SPDR fixture has a coupling loop on both ends to adjust the coupling coefficient. The
maximum thickness of the specimen of this fixture is 2 mm.
Coupling loop
Marking
Coupling loop
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Figure A.1 – Test fixture
A.2 Example of test result
Figure A.2 and Figure A.3 show the typical measurement of relative permittivity and loss
ε
tangent at microwave frequencies (from 1,1 GHz to 19 GHz) for a copper clad laminate of
r
3,8. Figure A.4 shows the curve diagram of relative permittivity and loss tangent at variable
temperatures (from −125 °C to 110 °C) for a copper clad laminate of ε 3,8.
r
4,0
DK 3,8
3,9
3,8
3,7
3,6
3,5
0 2 4 6 8 10 12 14 16 18 20
Frequency,  GHz
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Figure A.2 – Relative permittivity versus frequency
(laminate of Dk 3,8 and thickness 0,51 mm)
0,010
Df
0,009
0,008
0,007
0 2 4 6 8 10 12 14 16 18 20
Frequency,  GHz
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Figure A.3 – Loss tangent versus frequency
(laminate of Dk 3,8 and thickness 0,51 mm)
Loss tangent
Relative permittivity
– 18 – IEC 61189-2-721:2015 © IEC 2015
3,92 0,014
0,012
3,88
0,010
3,84
0,008
0,006
3,80
0,004
Dk
3,76
0,002
Df
3,72 0,000
−150 −100 −50 0 50 100 150
Temperature,  °C
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Figure A.4 – Curve of relative permittivity and loss tangent
at variable temperatures (laminate of Dk 3,8 and thickness 0,51 mm)
Relative permittivity
Loss tangent
Annex B
(informative)
Additional information on K (ε ,h) and p
ε r es
By definition K (ε ,h) function values are specified for a given resonant fixture and with fixed
ε r
values ε and h as follows:
r
f − f
0 s
K (ε ,h) = (B.1)
ε r
(ε −1)hf
r 0
The function K (ε ,h) is computed and tabulated for every specific SPDR. Exact resonant
ε r
frequencies and the resulting values of K (ε ,h) are computed for a number of ε and h and
ε r r
tabulated. Interpolation has been used to compute K (ε ,h) for any other values of ε and h.
ε r r
The initial value of K (ε ,h) in the permittivity evaluation using Equation (1) is taken to be the
ε r
same as its corresponding value for a given h and ε = 1. Subsequent values of K (ε ,h) are
r ε r
found for the subsequent dielectric constant values obtained in the iterative procedure.
Because K (ε ,h) is a slowly varying function of ε and h, the iterations using Equation (1)
ε r r
converge rapidly. Figure B.1 shows K (ε ,h) versus relative permittivity at different sample
ε r
thicknesses for a 10 GHz SPDR.
12,6
h = 0,1 mm
12,5
h = 0,3 mm
12,4
h = 0,5 mm
12,3
h = 0,7 mm
h = 0,9 mm
12,2
12,1
2 4 6 8 10 12 14
ε
r
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Figure B.1 – K (ε ,h) versus relative permittivity at
ε r
different sample thicknesses
By definition the p value is specified for a given resonant fixture and with fixed values ε′
es r
and h as follows:
′ ′
p = hε K (ε ,h) (B.2)
es r 1 r
K (ε ,h)
ε r
– 20 – IEC 61189-2-721:2015 © IEC 2015
where
ε′ is the relative permittivity;
r
h is the thickness of the specimen, mm;
K (ε′ ,h) is a function of ε′ and h.
1 r r
The Rayleigh-Ritz method permits to compute the p value for a given resonant structure.
es
ε′ .
These parameters have been computed for a number of h and
r
For a 10 GHz SPDR with resonant structure D = 16,5 mm, L = 9 mm, d = 8 mm, h = 1 mm, h

r r g
= 1 mm and a relative permittivity of a dielectric resonator = 38, the distribution of the electric
field component E in the split dielectric resonator operating at a nominal frequency (without
sample) of 10 GHz is shown in Figure B.2 and Figure B.3.
Figure B.4 shows p versus relative permittivity at different sample thicknesses.
es
For a 10 GHz SPDR with different samples, the parameters are shown in Table B.1.
Table B.1 – Results of measurements of
different materials using a 10 GHz SPDR
Thickness
Material
Dk Df p K (ε h) Q Q
es ε r, c DR
mm
–4 5
2,05 0,000 3 0,3 8,3 × 10 12,477 > 10 16 000 PTFE
–3 5
3,0 0,003 0 0,3 12,412 16 000 Low-Dk FR4
1,2 × 10 > 10
–3 5
3,8 0,009 0 0,3 3 × 10 12,364 > 10 16 000 Low-loss FR4
–3 5
4,5 0,015 0 0,3 4,2 × 10 12,332 > 10 16 000 Halogen-free FR4

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Figure B.2 – Distribution of the electric field of the split dielectric resonator
(side view of the dielectric resonators)

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Figure B.3 – Distribution of the electric field of the split dielectric resonator
(top view between the dielectric resonators)
h = 0,8 mm
0,1
h = 0,4 mm
0,01
h = 0,2 mm
h = 0,1 mm
-3
-4
0 20 40 60 80 100
Relative permittivity
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Figure B.4 – p versus relative permittivity at different sample thicknesses
es
p
es
– 22 – IEC 61189-2-721:2015 © IEC 2015
Bibliography
[1] Nishikawa, T.; Wakino, K.; Tanaka, H.; Ishikawa, Y., "Dielectric Resonator Method for
Nondestructive Measurement of Comp
...