IEC 61338-1-5:2015

Waveguide type dielectric resonators - Part 1-5: General information and test conditions - Measurement method of conductivity at interface between conductor layer and dielectric substrate at microwave frequency

IEC 61338-1-5:2015 describes a measurement method for resistance and effective conductivity at the interface between conductor layer and dielectric substrate, which are called interface resistance and interface conductivity. This first edition cancels and replaces IEC PAS 61338-1-5 published in 2010. This edition includes the following significant technical changes with respect to the previous edition:
a) description of technical content related to patents (Japanese patent numbers JP3634966, JP3735501) in the Introduction;
b) changes to normative references;
c)addition to bibliography.

Résonateurs diélectriques à modes guidés - Partie 1-5: Informations générales et conditions d'essais - Méthode de mesure de la conductivité au niveau de l'interface entre une couche conductrice et un substrat diélectrique fonctionnant aux hyperfréquences

L'IEC 61338-1-5:2015 décrit une méthode de mesure de la résistance et de la conductivité efficace au niveau de l'interface entre la couche conductrice et le substrat diélectrique, appelées résistance d'interface et conductivité d'interface. Cette première édition annule et remplace l'IEC PAS 61338-1-5 parue en 2010. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente:
a) description de contenu technique lié à des brevets (brevets japonais numéro JP3634966 et JP3735501) dans l'Introduction;
b) modifications de références normatives;
c) ajout bibliographique.

General Information

• Status: Published
• Publication Date: 24-Jun-2015
• ICS: 31.140 - Piezoelectric devices
• Technical Committee: TC 49 - Piezoelectric, dielectric and electrostatic devices and associated materials for frequency control, selection and detection
• Drafting Committee: WG 10 - TC 49/WG 10
• Current Stage: PPUB - Publication issued
• Start Date: 30-Sep-2015
• Completion Date: 25-Jun-2015

Relations

• Replaces: IEC PAS 61338-1-5:2010 - Waveguide type dielectric resonators - Part 1-5: General information and test conditions - Measurement method of conductivity at interface between conductor layer and dielectric substrate at microwave frequency
• Effective Date: 05-Sep-2023

Standards Content (Sample)

IEC 61338-1-5 ®
Edition 1.0 2015-06
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Waveguide type dielectric resonators –
Part 1-5: General information and test conditions – Measurement method of
conductivity at interface between conductor layer and dielectric substrate at
microwave frequency
Résonateurs diélectriques à modes guidés –
Partie 1-5: Informations générales et conditions d'essais – Méthode de mesure
de la conductivité au niveau de l'interface entre une couche conductrice et un
substrat diélectrique fonctionnant aux hyperfréquences

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IEC 61338-1-5 ®
Edition 1.0 2015-06
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Waveguide type dielectric resonators –

Part 1-5: General information and test conditions – Measurement method of

conductivity at interface between conductor layer and dielectric substrate at

microwave frequency
Résonateurs diélectriques à modes guidés –

Partie 1-5: Informations générales et conditions d'essais – Méthode de mesure

de la conductivité au niveau de l'interface entre une couche conductrice et un

substrat diélectrique fonctionnant aux hyperfréquences

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 31.140 ISBN 978-2-8322-2721-3

– 2 – IEC 61338-1-5:2015 © IEC 2015
CONTENTS
FOREWORD . 3
INTRODUCTION . 5
1 Scope . 6
2 Normative references. 6
3 Measurement and related parameters . 6
4 Calculation equations for R and σ . 8
i i
5 Preparation of specimen . 12
6 Measurement equipment and apparatus . 12
6.1 Measurement equipment . 12
6.2 Measurement apparatus . 12
7 Measurement procedure . 13
7.1 Set-up of measurement equipment and apparatus . 13
7.2 Measurement of reference level . 13
7.3 Measurement procedure of Q . 13
u
7.4 Determination of σ and measurement uncertainty . 15
i
8 Example of measurement result . 15
Annex A (informative) Derivation of Equation (4) for R . 17
i
Annex B (informative) Calculation uncertainty of parameters in Figure 3 . 19
Bibliography . 20

Figure 1 – Surface resistance R , surface conductivity σ , interface resistance R , and
s s i
interface conductivity σ . . 7
i
Figure 2 – TE mode dielectric rod resonator to measure σ . . 8
01δ i
Figure 3 – Parameters chart of f , g, P and P for reference sapphire rod . 10
0 rod sub
Figure 4 – Parameters chart of f , g, P and P for reference (Zr,Sn)TiO rod . 11
0 rod sub 4
Figure 5 – Schematic diagram of measurement equipments . 12
Figure 6 – Schematic diagram of measurement apparatus for σ . . 13
i
Figure 7 – Frequency response for reference sapphire rod with two dielectric
substrates as shown in Figure 2. . 14
Figure 8 – Resonance frequency f , insertion attenuation IA and half-power band
0 0
width f . 15
BW
Table 1 – Specifications of reference rods . 9
Table 2 – ε’ and tanδ of reference rods measured by the method of IEC 61338-1-
rod rod
3 15
Table 3 – ε’ and tanδ of an LTCC test substrate measured by the method of
sub sub
IEC 62562 . 16
Table 4 – Measurement results of σ and σ of a copper layer in LTCC substrate . 16
i ri
Table B 1 – Parameters obtained by FEM and rigorous analysis of IEC 61338-1-3 for
the TE mode resonator . 19
Table B.2 – Calculated parameters f , g, P , P , R , σ and σ for the TE mode
0 rod sub i i ri 01δ
resonator . 19

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
WAVEGUIDE TYPE DIELECTRIC RESONATORS –

Part 1-5: General information and test conditions –
Measurement method of conductivity at interface between
conductor layer and dielectric substrate at microwave frequency

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
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
International Standard IEC 61338-1-5 has been prepared by IEC technical committee
49: Piezoelectric, dielectric and electrostatic devices and associated materials for frequency
control, selection and detection.
This first edition cancels and replaces IEC PAS 61338-1-5 published in 2010.
This edition includes the following significant technical changes with respect to the previous
edition:
a) description of technical content related to patents (Japanese patent numbers JP3634966,
JP3735501) in the Introduction;
b) changes to normative references;
c) addition to bibliography.
The text of this standard is based on the following documents:

– 4 – IEC 61338-1-5:2015 © IEC 2015
CDV Report on voting
49/1089/CDV 49/1103/RVC
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 parts in the IEC 61338 series, published under the general title Waveguide type
dielectric resonators, can be found on the IEC website.
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.
INTRODUCTION
IEC 61338 consists of the following parts, under the general title Waveguide type dielectric
resonators:
– Part 1: Generic specification
– Part 1-3: General information and test conditions − Measurement method of complex
relative permittivity for dielectric resonator materials at microwave frequency
– Part 1-4: General information and test conditions − Measurement method of complex
relative permittivity for dielectric resonator materials at millimeter-wave frequency
– Part 2: Guidelines for oscillator and filter applications
– Part 4: Sectional specification
– Part 4-1: Blank detail specification
The International Electrotechnical Commission (IEC) draws attention to the fact that it is
claimed that compliance with this document may involve the use of a patent concerning:
– The use of a TE mode dielectric rod resonator for the interface resistance and the
01δ
interface conductivity measurement, given in Clause 4;
– The use of a substrate/conductor/substrate layer structure, where a conductor is formed
between two dielectric substrates, for the interface resistance and interface conductivity
measurement, given in Clause 5.
IEC takes no position concerning the evidence, validity and scope of this patent right.
The holder of this patent right has assured the IEC that he/she is willing to negotiate licences
under reasonable and non-discriminatory terms and conditions with applicants throughout the
world. In this respect, the statement of the holder of this patent right is registered with IEC.
Information may be obtained from:
KYOCERA Corporation
6 Takeda Tobadono-cho, Fushimiku, Kyoto 612-8501, Japan
Attention is drawn to the possibility that some of the elements of this standard may be the
subject of patent rights other than those identified above. IEC shall not be held responsible for
identifying any or all such patent rights.
ISO (www.iso.org/patents) and IEC (http://patents.iec.ch) maintain on-line data bases of
patents relevant to their standards. Users are encouraged to consult the data bases for the
most up to date information concerning patents.

– 6 – IEC 61338-1-5:2015 © IEC 2015
WAVEGUIDE TYPE DIELECTRIC RESONATORS –

Part 1-5: General information and test conditions –
Measurement method of conductivity at interface between
conductor layer and dielectric substrate at microwave frequency

1 Scope
Microwave circuits are popularly formed on multi-layered organic or non-organic substrates. In
the microwave circuits, the attenuation of planar transmission lines such as striplines,
microstrip lines, and coplanar lines are determined by their conductor loss, dielectric loss and
radiation loss. Among them, the conductor loss is a major factor in the attenuation of the
planar transmission lines. A new measurement method is standardized in this document to
evaluate the conductivity of transmission line on or in the substrates such as the organic,
ceramic and LTCC (low temperature co-fired ceramics) substrates. This standard describes a
measurement method for resistance and effective conductivity at the interface between
conductor layer and dielectric substrate, which are called interface resistance and interface
conductivity.
This measurement method has the following characteristics:
– the interface resistance R is obtained by measuring the resonant frequency f and
i 0
unloaded quality factor Q of a TE mode dielectric rod resonator shown in Figure 2;
u 01δ
and the relative interface conductivity σ = σ / σ are calculated from
– the interface conductivity σ
i ri i 0
the measured R value, where σ = 5,8 × 10 S/m is the conductivity of standard copper;
i 0
– the measurement uncertainty of σ (Δσ ) is less than 5 %.
ri ri
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 61338-1-3: Waveguide type dielectric resonators − Part 1-3: General information and test
conditions – Measurement method of complex relative permittivity for dielectric resonator
materials at microwave frequency
IEC 62562: Cavity resonator method to measure the complex permittivity of low-loss dielectric
plates
3 Measurement and related parameters
The IEC 61338-1-3 described the measurement method for the surface resistance R and
s
effective conductivity σ on the surface of the conductor. The term σ is designated as σ in this
s
standard, and is called surface conductivity (Figure 1). This standard describes a
measurement method for resistance and effective conductivity at the interface between
conductor layer and dielectric substrate designated as R and σ respectively, and are called
i i
interface resistance and interface conductivity.

R and s (surface)
s s
Conductor layer
Dielectric substrate
R and s (interface)
i i
with ε′ and tan δ
sub sub
IEC
Figure 1 – Surface resistance R , surface conductivity σ ,
s s
interface resistance R , and interface conductivity σ .
i i
For the transmission line in the substrates, the electric current is concentrated at the interface
between conductor layer and dielectric substrate, because the skin depth δin the conductor is
the order of μm in thickness at the microwave frequencies. In microstrip lines, the current is
concentrated at the interface, rather than at the open face of the conductor. Furthermore, in
copper-clad organic substrates, the interface side of the copper foil has rugged structure to
hold the strong adhesive strength. In LTCC substrates, the interface between the conductor
and ceramics has a rough structure, depending on the co-firing process and the material
compositions. The conductor loss depends on the interface conditions. Therefore, the evaluation of
R and σ is important to design microwave circuit and to improve the conductor fabrication
i i
process.
The relationship between R and σ is given by
s s
πf µ
R = , s = s s (1)
s s rs 0
s
s
where
R is the surface resistance;
s
f is the resonance frequency;
μ is the permeability of the conductor;
σ  is the surface conductivity;
s
σ  is the relative surface conductivity.
rs
–7
Particularly, μ equals μ (μ = 4π × 10 H/m) for nonmagnetic conductors such as copper and
0 0
silver.
The relationship between R and σ is given by
i i
πf µ
R = , s = s s (2)
i i ri 0
s
i
where
R is the interface resistance;
i
σ is the interface conductivity;
i
σ is the relative interface conductivity.
ri
The skin depth δ is given by
– 8 – IEC 61338-1-5:2015 © IEC 2015
δ = (3)
πfµs
where
f is the frequency;
σ is the conductivity of the conductor.
To obtain high accuracy in this measurement method, the relative interface conductivity σ of
ri
the conductor is preferable to be higher than 5%, and the thickness of conductor to be three
times greater than skin depth δ. The measurement frequencies are limited to be 5 GHz and 13
GHz because of the reference dielectric rods used in this standard.
4 Calculation equations for R and σ
i i
Figure 2 shows the structure of a TE mode dielectric rod resonator for the R measurement.
01δ i
The resonator consists of a dielectric rod and a pair of dielectric substrates with a conductor
layer at one side. The dielectric rod has diameter d, height h, relative permittivity ε’ , and
rod
loss tangent tanδ . The pair of dielectric substrates have the same values of diameter d’,
rod
thickness t, relative permittivity ε’ , and loss tangent tanδ . To suppress the radiation loss,
sub sub
the diameter d’ shall be three times greater than d. The conductor layers on each dielectric
substrate are supposed to have the same value of R .
i
E
H
d ′
d Dielectric rod
with ε′ and tan δ
rod rod
Dielectric substrate
with ε′ and tan δ
sub sub
Conductor layer
IEC
Figure 2 – TE mode dielectric rod resonator to measure σ .
01δ i
In this structure, the conductive loss of the TE mode resonator is caused by the interface
01δ
resistance R . The value of 1/Q is given by a sum of power losses due to R , tanδ and
i u i rod
tanδ :
sub
1 R
i
= + P tanδ + P tanδ , (4)
rod rod sub sub
Q g
u
where
g is the geometric factor of the resonator (Ω);
P is the partial electric energy filling factor of the dielectric rod;
rod
P is the partial electric energy filling factor of the dielectric substrate.
sub
The equation for R is derived from Equation (4):
i
 
 
R = g − P tanδ − P tanδ (5)
i rod rod sub sub
 
Q
u
 
t
h
The value σ is calculated from this R value by Equation (2).
i i
The derivation of Equation (4) is given in Annex A, together with definitions of the parameters
g, P and P . These parameters for the TE mode resonator can be calculated by using
rod sub 01δ
the FEM or the mode matching method. However, the calculation requires complicated and
tedious works. To make the treatment simple and easy, this standard recommends to use the
graphical charts that are prepared for the parameters of reference dielectric rod resonators; a
sapphire single crystal and a (Zr,Sn)TiO ceramic (Table 1). The axis of sapphire rod should
be parallel to the c-axis within 0,3 degree. The (Zr,Sn)TiO ceramic rod is provided from the
Japan fine ceramics center. The parameters f , g, P and P for the reference rods were
0 rod sub
calculated by an FEM analyzed in cylindrical coordinate and are shown in Figures 3 and 4
graphically. The calculation uncertainty on the parameters is shown in Annex B.
To calculate the R in Equation (5), the complex permittivity values of the dielectric rod and the
i
substrate are necessary to be given in advance. IEC 61338-1-3 shall be used to measure the
values of ε’ and tanδ . IEC 62562 shall be used to measure the values of ε’ and tanδ .
rod rod sub sub
Table 1 – Specifications of reference rods
Reference rod f ε’  tanδ  diameter d height h
0 rod rod
GHz mm mm
-6
Sapphire single crystal 13
9,4 ± 0.1 13 × 10 10,00 ± 0,05 5,00 ± 0,05
-4
(Zr,Sn)TiO ceramics 5
39 ± 1 <10 × 10 14,00 ± 0,05 6,46 ± 0,05
NOTE 1 The reference dielectric rod of (Zr,Sn)TiO is provided by JFCC (Japan fine ceramics center ) as ER-
ZST.
———————
Japan fine ceramics center is an example of a suitable commercial supplier. This information is given for the
convenience of users of this document and does not constitute an endorsement by IEC of this supplier.

– 10 – IEC 61338-1-5:2015 © IEC 2015
13,8 0,004 6
t = 0,0 mm
t = 0,0 mm
13,6
0,004 4
0,1
13,4
0,1 0,004 2
0,2
13,2
0,3
0,004 0
0,2
13,0
0,4
12,8 0,003 8
0,5
0,3
0,6
12,6
0,003 6
0,4
12,4
0,003 4
0,5
12,2
0,6
0,003 2
12,0
11,8
0,003 0
0 2 4 6 8 10 0 2 4 6 8 10
ε′ ε′
sub sub
0,985 0,018
t = 0,0 mm
0,1
0,016
t = 0,6 mm
0,2
0,980
0,014
0,3
0,975 0,012
0,4
0,010
0,5
0,970
0,5 0,008
0,965 0,006
0,4
0,6
0,004
0,960
0,3
0,002
0,2
0,1
0,955 0,000
0 2 4 6 8 10 0 2 4 6 8 10
ε′ ε′
sub sub
IEC
The calculation conditions are the following:
ε’ = 9,4, d = 10,00 mm and h = 5,00 mm.
rod
Figure 3 – Parameters chart of f , g, P and P for reference sapphire rod
0 rod sub
P  f  (GHz)
rod 0
P
sub
1/g  (1/Ω)
5,1 0,010 0
t = 0,0 mm
t = 0,0 mm
5,0
0,009 5
0,1
0,1
4,9 0,009 0
0,2
0,2
0,3
4,8 0,008 5
0,3
0,4
0,4
4,7 0,008 0
0,5
0,5
0,6
4,6 0,007 5
0,6
4,5 0,007 0
0 2 4 6 8 10 0 2 4 6 8 10
ε′ ε′
sub sub
0,997 5
0,002 0
t = 0,6 mm
t = 0,0 mm
0,997 0
0,1
0,001 6
0,2
0,996 5
0,3
0,001 2
0,996 0 0,5
0,4
0,995 5
0,000 8
0,5
0,4
0,995 0
0,000 4
0,3
0,994 5
0,2
0,1
0,994 0 0,000 0
0 2 4 6 8 10
0 2 4 6 8 10
ε′ ε′
sub sub
IEC
The calculation conditions are the following:
ε’ = 39, d = 14,00 mm and h = 6,46 mm.
rod
Figure 4 – Parameters chart of f , g, P and P for reference (Zr,Sn)TiO rod
0 rod sub 4
P
rod
f  (GHz)
P
sub
1/g  (1/Ω)
– 12 – IEC 61338-1-5:2015 © IEC 2015
5 Preparation of specimen
Two test specimens of dielectric substrates with a conductor at one side are prepared for the
σ measurement. The thickness of the conductor t shall be three times greater than the skin
i c
depth δ. The values of δ is 0,9 µm for copper and 1,7 µm for tungsten at 5 GHz. The diameter
d’ of dielectric substrate shall be three times greater than the diameter d of the reference
dielectric rod. Dielectric substrates with any shape larger than the diameter 3×d is used in
practical measurement. Bending of specimen causes measurement error of σ. A
i
substrate/conductor/substrate layer structure, where a conductor is formed between two
dielectric substrates, is effective to avoid the bending of specimen.
6 Measurement equipment and apparatus
6.1 Measurement equipment
Figure 5 shows a schematic diagram of two measurement systems. For the measurement of
Q of the resonator to evaluate σ , only the information on the amplitude of transmitted power
u i
is needed, that is, the information on the phase of the transmitted power is not required.
Therefore, a scalar network analyzer can be used for the measurement shown in Figure 5(a).
However, a vector network analyzer shown in Figure 5(b) has better measurement accuracy
than a scalar network analyzer due to its wide dynamic range.
Scalar
network
Sweeper
Vector
analyser
network
analyser
Detector
Measurement
Power
Detector Measurement
appartus
splitter
appartus
Reference line Reference line
IEC IEC
Figure 5a) Scalar network analyzer system Figure 5b) Vector network analyzer system
Figure 5 – Schematic diagram of measurement equipments
6.2 Measurement apparatus
Figure 6 shows a measurement apparatus for σ. The reference dielectric rod is placed
i
between the dielectric sides of two substrates with a conductor at one side. Two substrates
are set to be parallel to each other.
Each of the two semi-rigid coaxial cables have a small loop at the top. The semi-rigid cable
with the outer diameter of 1,2 mm is recommended. The two loops have the same diameter
and the length shall be less than the quarter wavelength of measurement frequency. In
practice, the loop with a diameter from 1 mm to 2 mm is preferable for the measurement
around 10 GHz. The plane of the loop is set parallel to the dielectric substrates to suppress
the excitation of the unwanted TM mode. The cables can move right and left to adjust the
insertion attenuation IA at f to be around 30 dB (as shown in Figure 8). The IA value is
0 0 0
recommended to be between 20 dB and 30 dB, in order to decrease the field disturbance due
to the coupling loop and to decrease the noise influence on the resonance curve of the
network analyzer.
A reference line made of a semi-rigid cable, shown in Figure 6, is used to measure the full
transmission power level, i.e., the reference level as shown in Figure 8. This cable has a
length equal to the sum of the two cables with a loop.
Reference line
A
Loop
Soldering
A
Dielectric Reference
Conductor
substrate rod
Coaxial cable
with loop
Connector
XY stage XY stage
Z stage
IEC
Figure 6 – Schematic diagram of measurement apparatus for σ .
i
7 Measurement procedure
7.1 Set-up of measurement equipment and apparatus
Set up the measurement equipment and apparatus as shown in Figures 5 and 6. Relative
humidity shall be less than 60 %, because high humidity degrades Q .
u
7.2 Measurement of reference level
Measure the reference transmission level, shown in Figure 8, over the entire measurement
frequency range.
7.3 Measurement procedure of Q
u
Place the reference dielectric rod between the dielectric sides of two substrates. Adjust the
distance between the reference rod and each of the loops of the semi-rigid cables to be equal.
Find the TE mode resonance peak of the resonator on the display of the network analyzer,
01δ
by reading the approximate f value of the TE mode resonance from Figures 3 or 4 for
0 01δ
each reference rod. This peak can be identified as the one which shifts downward in
frequency when the upper substrate is slowly separated from the top of the reference
dielectric rod. Figure 7 shows an example of frequency response for a resonator.

– 14 – IEC 61338-1-5:2015 © IEC 2015
Narrow the frequency span, so that only the resonance peak of TE mode can be shown on
01δ
the display as shown in Figure 8. By changing the distance between the reference dielectric
rod and the loops of the semi-rigid cables, adjust IA to be around 30 dB from the reference
level.
Measure f , the half-power band-width f and IA . The loaded quality factor Q and the
0 BW 0 L
unloaded quality factor Q of this resonance mode are given by
u
f
Q = (6)
L
f
BW
Q − IA (dB) / 20
L
Q = , A = 10 (7)
u t
1− A
t
–20
TE
01δ
–40
–60
–80
10 11 12 13 14 15
Frequency  (GHz)
IEC
Figure 7 – Frequency response for reference sapphire rod with two
dielectric substrates as shown in Figure 2.
Insertion attenuation  (dB)
Reference level
f
f
BW
Frequency  (GHz)
IEC
Figure 8 – Resonance frequency f , insertion attenuation IA
0 0
and half-power band width f
BW
7.4 Determination of σ and measurement uncertainty
i
Repeat the measurement of Q several times. Then, calculate R from the mean value of Q
u i u
using Equation (5). The values g, P and P are given from Figures 3 and 4 using the ε’
rod sud sub
and thickness t of the test substrate. The values σ and σ are given from R using Equation (2).
i ri i
Measurement uncertainty of σ , Δσ , estimated as the mean square errors is given by
i i
2 2 2 2
(∆s ) = (∆s ) + (∆s ) + (∆s ) (8)
i i i i
,Qu ,tanδrod ,tanδsub
where
Δσ  is the uncertainty of σ due to standard deviations of Q ;
i,Qu i u
Δσ  is the uncertainty of σ due to standard deviations of tanδ ;
i,tanδrod i rod
Δσ  is the uncertainty of σ due to standard deviations of tanδ .
i,tanδsub i sub
8 Example of measurement result
Table 2 shows the values of ε’ and tanδ for the reference rods measured by the dielectric rod
rod rod
resonator method (IEC 61338-1-3). Table 3 shows the values of ε’ and tanδ of a LTCC test
sub sub
substrate measured by the cavity resonator method (IEC 62562). A copper layer was co-fired in
this substrate and the σ and σ were measured. The results are shown in Table 4.
i ri
Table 2 – ε’ and tanδ of reference rods measured by
rod rod
the method of IEC 61338-1-3
Reference D h f Q ε’ tanδ
0 u rod rod
-4
Rod mm mm GHz (10 )
Sapphire 10,000 5,004 13,524 6 413 9,435 0,13

±0,001 ±0,001 ±0,002 ±52 ±0,004 ±0,01
(Zr,Sn)TiO 14,000 6,465 4,9966 3 612 39,27 0,90
±0,001 ±0,001 ±0,0004 ±21 ±0,01 ±0,02

Insertion attenuation  (dB)
IA = 30 dB
3 dB
– 16 – IEC 61338-1-5:2015 © IEC 2015
Table 3 – ε’ and tanδ of an LTCC test substrate measured by
sub sub
the method of IEC 62562
d’ t f  Q  ε’ tanδ
0 u sub sub
-4
mm mm GHz (10 )
50 0,965 10,287 3 313 4,76 7,18
±0,08 ±0,003 ±22 ±0,04 ±0,05
Table 4 – Measurement results of σ and σ of a copper layer in LTCC substrate
i ri
Reference
f Q  σ  σ
0 u i ri
rod GHz 10 S/m %
Sapphire 12,426 6 725 3,68 63,5
±0,002 ±5 ±0,05 ±0,9
(Zr,Sn)TiO 4,6626 3 738 3,83 66,0
±0,0003 ±20 ±0,10 ±1,8
NOTE The calculation conditions are ε’ = 4,76, d’ = 45 mm and t = 0,415 mm.
sub
Annex A
(informative)
Derivation of Equation (4) for R
i
The unloaded quality factor Q is defined by
u
P
d
= (A.1)
Q ω W
u 0
where
P is the power dissipated in the resonator per second;
d
ω is 2π × f ;
0 0
W is the energy stored in the resonator.
In the TE dielectric rod resonator (Figure 2), P and W are given by
01δ d
P = P + ω W tanδ + ω W tanδ (A.2)
d ci 0 rod rod 0 sub sub
W = W +W +W (A.3)
rod sub air
where
P is the conductive energy loss at the interface between the conductor and
ci
the dielectric substrate;
W is the electric energy stored in the dielectric rod;
rod
W is the electric energy stored in the dielectric substrate;
sub
W is the electric energy stored in the air region;
air
ω W tanδ is the dielectric energy loss in the dielectric rod;
0 rod rod
ω W tanδ is the dielectric energy loss in the dielectric substrate.
0 sub sub
Equation (3) is obtained from Equation (A.1), (A.2) and (A.3), using the parameters, g, P
rod
and P defined as follows:
sub
1 2
H ds
t
∫∫
1 P
ci 2
(A.4)
= =
g ωWR ωW
si
ε ε' E dv
0 rod
∫∫∫
W
Vrod
rod 2
(A.5)
P = =
rod
W W
1 2
ε ε' E dv
0 sub
∫∫∫
W Vsub
sub
(A.6)
P = =
sub
W W
– 18 – IEC 61338-1-5:2015 © IEC 2015
1  2 2 2 
(A.7)
W = ε ε' E dv + ε' E dv + E dv
0 rod sub
 
∫∫∫ ∫∫∫ ∫∫∫
Vrod Vsub Vair
 
where
is the surface integration of the tangential magnetic field at the interface
H ds
t
∫∫
between the conductor and the dielectric substrate.

Annex B
(informative)
Calculation uncertainty of parameters in Figure 3
The parameters f , g, P and P in Figures 3 and 4 were calculated by using a FEM
0 rod sub
analyzed in cylindrical coordinate. The resonator structure for t = 0,0 mm in Figure 2
corresponds to the TE mode dielectric resonator short-circuited at the both ends, described
in IEC 61338-1-3. So, the comparison of the calculated parameters for t = 0,0 mm by the FEM
and by the rigorous analysis in IEC 61338-1-3 gives the calculation uncertainty of the FEM.
Table B.1 shows calculated results for the TE mode sapphire resonator with the values of
ε’ = 9,4, d = 10,0 mm and h = 5,0 mm. The difference between the two methods is negligibly
rod
small for the calculation of R and σ .
i i
The parameters in Figure 3 were calculated for the reference sapphire rod with ε’ = 9,4.
rod
The actual sapphire rod usually has the ε’ in the range from 9,35 to 9,45. Table B.2 shows
rod
the calculated parameters for the sapphire rods with ε’ = 9,4 and 9,3. It shows that this
rod
difference of 0,1 on ε’ results in the calculation difference of 0,06 % on σ . This value is
rod ri
negligibly small, compared with the measurement uncertainties of σ given in Table 4.
ri
Table B 1 – Parameters obtained by FEM and rigorous analysis
of IEC 61338-1-3 for the TE mode resonator
Parameter FEM IEC 61338-1-3 Difference
f (GHz) 13,5566 13,5545 0,0021
1/g (1/Ω ) 0,004432 0,004436 -0,000004
P 0,98319 0,98321 -0,00002
rod
NOTE The calculation conditions are ε’ = 9,4, d = 10,0 mm, and h = 5,0 mm.
rod
Table B.2 – Calculated parameters f , g, P , P , R , σ and σ for
0 rod sub i i ri
the TE mode resonator
01δ
Parameter ε’ = 9,4 ε’ = 9,3 Difference
rod rod
f (GHz) 12,2452 12,3089 -0,0637
1/ g (1/Ω ) 0,003584 0,003570 0,000014
P  0,9707 0,9703 0,0004
rod
P  0,00569 0,00575 -0,00006
sub
R (mΩ)
41,60 41,73 -0,13
i
σ (10 S/m) 2,794 2,790 0,004
i
σ (%) 48,17 48,11 0,06
ri
NOTE The calculation conditions are ε’ = 6,0, tanδ = 0,001, t = 0,5 mm, and Qu = 6 000.
sub sub
– 20 – IEC 61338-1-5:2015 © IEC 2015
Bibliography
[1] A. Nakayama, Y. Terashi, H. Uchimura, and A. Fukuura, “Conductivity measurements
at the interface between the sintered conductor and dielectric substrate at microwave
frequencies,” Microwave Theory and Techniques, IEEE Transactions on, Vol. 50, No. 7,
pp. 1665-1674, July, 2002.
[2] Y. Kobayashi, “Microwave characterization of copper-clad dielectric laminate
substrates,” IEICE Trans. Electronics, Vol.E90-C, No.12, pp. 2178-2184, Dec, 2007.

____________
– 22 – IEC 61338-1-5:2015 © IEC 2015
SOMMAIRE
AVANT-PROPOS . 23
INTRODUCTION . 25
1 Domaine d’application. 26
2 Références normatives . 26
3 Mesure et paramètres associés . 26
4 Equations de calcul pour R et σ . 28
i i
5 Préparation des spécimens . 32
6 Equipements et appareillage de mesure . 32
6.1 Equipements de mesure . 32
6.2 Appareillage de mesure . 32
7 Procédure de mesure . 33
7.1 Montage de l'équipement et de l'appareillage de mesure . 33
7.2 Mesure du niveau de référence . 33
7.3 Procédure de mesure de Q . 33
u
7.4 Détermination de σ et incertitude de mesure . 35
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8 Exemple de résultat de mesure . 35
Annexe A (informative) Dérivation de l'Equation (4) pour R . 37
i
Annexe B (informative) Incertitude de calcul des paramètres de la Figure 3 . 39
Bibliographie . 40

Figure 1 – Résistance de surface R , conductivité de surface σ , résistance d'interface
s s
R et conductivité d'interface σ . . 27
i i
Figure 2 – Résonateur en barreau diélectrique en mode TE pour la mesure de σ . 28
01δ i
Figure 3 – Représentation des paramètres f , g, P et P pour un barreau de
0 rod sub
saphir de référence . 30
Figure 4 – Représentation des paramètres f , g, P et P pour un barreau
0 rod sub
(Zr,Sn)TiO de référence . 31
Figure 5 – Représentation schématique d'équipements de mesure . 32
Figure 6 – Représentation schématique d'un appareillage de mesure pour σ . 33
i
Figure 7 – Réponse en fréquence pour un barreau de saphir de référence avec deux
substrats diélectriques comme représenté sur la
...