IEC 63185:2020

IEC 63185 ®
Edition 1.0 2020-12
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Measurement of the complex permittivity for low-loss dielectric substrates
balanced-type circular disk resonator method

Méthode au résonateur à disque circulaire de type symétrique pour mesurer la
permittivité complexe des substrats diélectriques à faible perte

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IEC 63185 ®
Edition 1.0 2020-12
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Measurement of the complex permittivity for low-loss dielectric substrates

balanced-type circular disk resonator method

Méthode au résonateur à disque circulaire de type symétrique pour mesurer la

permittivité complexe des substrats diélectriques à faible perte

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 33.120.30 ISBN 978-2-8322-9133-7

– 2 – IEC 63185:2020 © IEC 2020
CONTENTS
FOREWORD . 3
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 5
4 Measurement parameters . 6
5 Theory and calculation equations . 6
6 Measurement system . 8
7 Measurement procedure . 9
7.1 Preparation of measurement apparatus. 9
7.2 Adjustment of measurement conditions . 9
7.3 Calibration of a vector network analyzer . 9
7.4 Measurement of complex permittivity of test sample . 10
7.5 Periodic checkup of metal in resonator. 10
Annex A (informative) Example of measurement results and associated uncertainties
for complex permittivity . 11
Bibliography . 13

Figure 1 – Structure of a circular disk resonator . 7
Figure 2 – Relations between resonant frequency and relative permittivity . 8
Figure 3 – Schematic diagram of a vector network analyzer measurement system . 9
Figure 4 – Frequency response of |S | of balanced-type circular disk resonator . 10
Table A.1 – Parameters of the cavity and the sheet sample . 11
Table A.2 – The resonant frequencies and unloaded Q-factors . 11
Table A.3 – Measurement results of complex permittivity . 12

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT OF THE COMPLEX PERMITTIVITY
FOR LOW-LOSS DIELECTRIC SUBSTRATES
BALANCED-TYPE CIRCULAR DISK RESONATOR METHOD

FOREWORD
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rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 63185 has been prepared by subcommittee 46F: RF and microwave
passive components, of IEC technical committee 46: Cables, wires, waveguides, RF connectors,
RF and microwave passive components and accessories.
The text of this International Standard is based on the following documents:
FDIS Report on voting
46F/523/FDIS 46F/531/RVD
Full information on the voting for the approval of this International Standard can be found in the
report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.

– 4 – IEC 63185:2020 © IEC 2020
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this document using a colour printer.

MEASUREMENT OF THE COMPLEX PERMITTIVITY
FOR LOW-LOSS DIELECTRIC SUBSTRATES
BALANCED-TYPE CIRCULAR DISK RESONATOR METHOD

1 Scope
This document relates to a measurement method for complex permittivity of a dielectric
substrates at microwave and millimeter-wave frequencies. This method has been developed to
evaluate the dielectric properties of low-loss materials used in microwave and millimeter-wave
circuits and devices. It uses higher-order modes of a balanced-type circular disk resonator and
provides broadband measurements of dielectric substrates by using one resonator, where the
effect of excitation holes is taken into account accurately on the basis of the mode-matching
analysis.
In comparison with the conventional method described in IEC 62810 and IEC 61338-1-3, this
method has the following characteristics:
’ and loss tangent tanδ normal to dielectric plate
• the values of the relative permittivity ε
r
samples can be measured accurately and non-destructively;
• this method presents broadband measurements by using higher-order modes by one
resonator;
• this method is applicable for the measurements on the following condition:
– frequency: 10 GHz ≤ f ≤ 110 GHz;
– relative permittivity: 1 ≤ ε ’ ≤ 10;
r
–4 –2
– loss tangent: 10 ≤ tanδ ≤ 10 .
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 61338-1-3:1999, 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 62810:2015, Cylindrical cavity method to measure the complex permittivity of low-loss
dielectric rods
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp

– 6 – IEC 63185:2020 © IEC 2020
4 Measurement parameters
The measurement parameters are defined as follows:
ε = ε ’ – jε ” (1)
r r r
tanδ =ε ”/ε ’ (2)
r r
where ε ’ and ε ” are the real and imaginary parts of the complex relative permittivity ε .
r r r
5 Theory and calculation equations
A resonator structure used in this method is shown in Figure 1. A thin circular conductor disk
with radius R is sandwiched between a pair of dielectric plate samples to be measured having
the same thickness t and dielectric properties ε ' and tanδ. Dielectric samples are sandwiched
r
by two parallel conductor plates. The thickness of the conductor disk is negligibly thin in the
analysis.
The resonator is excited and detected by coaxial lines through excitation holes having radius a
modes have the electric field in the center of the
and length M. Because only the TM
0m0
resonator, only those modes are selectively excited in the resonator, where the electric field
components in the resonator are normal to the plate samples for those modes.
ε ’ and tanδ normal to the dielectric plates are determined from the measured values of the
r
resonant frequencies f and the unloaded Q-factor Q for the TM mode by solving the
0 u 0m0
following resonant condition derived from the mode-matching analysis, where the exciting holes
are accurately taken into account:
detH(ε ’, f , t, R, a, M) = 0 (3)
r 0
tanδ = (1/Q – 1/Q )(1 + W /W ) (4)
u c 1 2
where
H is N × N matrix derived from the boundary conditions;
N is the number of terms of the series expansions for the mode-matching analysis;
Q is the Q-factor due to the conductor loss;
c
W and W are the electric energies stored in the dielectric region and the excitation hole
1 2
region, respectively.
W and W are calculated from the mode-matching analysis, and Q can be approximately by
1 2 c
0,5
Q = t/δ = t(πf μ σ) (5)
S
c 0 0
where
δ is the skin depth of the conductor;
S
σ is the conductivity;
is the permeability of free space.
μ
Figure 1 – Structure of a circular disk resonator
The maximum measurable frequency is limited by the following three cutoff frequencies:
Coax
a) cutoff frequency of coaxial lines used to excite the resonator f ;
c
Hole
b) cutoff frequency of excitation holes f ;
c
Rad
c) cutoff frequency for radial radiation through dielectric samples f .
c
Hole
f is calculated as a cutoff frequency for TM mode of a circular waveguide with radius a
c 01
and is given by
Hole
f = χ /2πa (6)
c 01
where
χ ≈ 2,404 8 is the first root of J (x) = 0;
01 0
J (x) is the Bessel function of order 0 of first kind;
c is the light velocity.
Rad
is determined by the sample thickness t and relative permittivity ε ’ and is given by
f
c r
Rad 0,5
f = c/4t(ε ’) (7)
c r
Figure 2 shows the relations between f and ε ’ for TM modes for R = 7,5 mm, a = 0,6 mm,
0 r 0m0
M = 5 mm, and t = 0,3 mm. Multiple resonances are appeared from 5 GHz to 110 GHz for
Rad
1 ≤ ε ’ ≤ 10 (5 to 11 modes). Radiation limit (f ) is also shown in the same figure.
r c
– 8 – IEC 63185:2020 © IEC 2020

Key
m is mode number of resonances in measurement
R 7,5 mm M 5 mm
a 0,6 mm t 0,3 mm
Figure 2 – Relations between resonant frequency and relative permittivity
The conductivity σ is measured by the two dielectric resonator method [5] .
Measurement uncertainties of ε ' and tanδ are evaluated by considering the uncertainty
r
propagations of the resonant frequency, Q-factor, dimensions of resonator and samples, and
conductivity of the resonator, and by estimating the effect of the error of the mode-matching
analysis [6].
6 Measurement system
Figure 3 shows a schematic diagram of a vector network analyzer measurement system for a
transmission-type resonator. A scalar network analyzer can also be used for measuring
equipment, because resonant frequencies and Q-factors can be derived from the frequency
dependence of the amplitude of the transmission, S . However, a vector network analyzer has
an advantage in precision of the measurement. Furthermore, resonant frequencies and
Q-factors are more accurate and less susceptible when they are derived from complex values
of measured S data by using the circle fitting on the complex plane of S [7].
21 21
___________
Figures in square brackets refer to the bibliography.

Figure 3 – Schematic diagram of a vector network analyzer measurement system
The structure of the resonator used in the complex permittivity measurements is shown in
Figure 1. A pair of dielectric plate samples to be measured, thin circular conductor disk, and
two parallel conductor plates constitutes a balanced-type circular disk resonator. The resonator
is excited by coaxial lines through excitation holes and under-coupled equally to the input and
output ports.
The resonant frequency f and the loaded Q-factor Q are derived from the frequency
0 l
dependence of S that is measured by using a vector network analyzer [7]. The unloaded
Q-factor Q is given by
u
LA0(dB)/20
Q = Q / (1-10 ) (8)
u l
Where LA (dB) is the insertion attenuation at f .
0 0
The coupling factor of electromagnetic wave signals shall be the same at input and output ports.
7 Measurement procedure
7.1 Preparation of measurement apparatus
Set up the measurement equipment and apparatus as shown in Figure 3. The cavity resonator
and dielectric samples shall be kept in a clean and dry state, as high humidity degrades
unloaded Q-factors.
7.2 Adjustment of measurement conditions
Set up the measurement conditions of a vector network analyzer. The interval between discrete
frequency points shall preferably be less than one tenth of the half width of the resonant
waveform. Intermediate frequency band width (IFBW), like as digital band pass filter condition
in vector network analyzer, is determined such that the noise floor is at least 20 dB lower than
the peak values.
7.3 Calibration of a vector network analyzer
A vector network analyzer shall be calibrated by using calibration kits.

– 10 – IEC 63185:2020 © IEC 2020
7.4 Measurement of complex permittivity of test sample
Constitute a balanced-type circular disk resonator by the pair of test samples. Figure 4 shows
the frequency dependence of |S |. Resonant frequencies of TM to TM modes are
21 010 050
indicated by the downward arrows. Measure the resonant frequency and unloaded Q-factor of
each mode and calculate the complex permittivity at each resonant frequency of test samples
by using Equations (3) and (4).
The alignment between the conductor disk and excitation holes is critical to measurement
results, but it is possible to find a misalignment by detecting resonances of unwanted modes
between adjacent TM modes. In the frequency response of |S |, resonant peaks for
0m0 21
unwanted modes shall be at least 15 dB lower than those for adjacent TM modes.
0m0
Figure 4 – Frequency response of |S | of balanced-type circular disk resonator
7.5 Periodic checkup of metal in resonator
Since the conductivity of the conductor plates and circular disk degrades due to oxidation of
the metals and scratches on the surfaces, the quality of the metals of the resonator shall be
checked periodically. It can be checked by measuring the conductivity by using the two dielectric
resonator method [5]. Instead, it can be checked by measuring the same low-loss sample
periodically. By checking the reproducibility of the measurement results of loss tangent of the
specified verification sample, it is possible to find the surface characteristic change in the metals
of the resonator.
Annex A
(informative)
Example of measurement results and associated
uncertainties for complex permittivity
The measurement results and associated uncertainties for the complex permittivity of cyclic
olefin polymer (COP) sheet sample are obtained as followed. Hereafter, measurement
uncertainty of each quantity is expressed by its expanded uncertainty with a coverage factor of
k = 2.
a) The parameters such as R, a, and M of the cavity and t of the COP sample used in the
measurements are shown in Table A.1.
Table A.1 – Parameters of the cavity and the sheet sample
R (mm) a (mm) M (mm) t (mm)
7,482 5 0,60 ± 0,03 5,00 ± 0,25 0,376 ± 0,001

b) The resonant frequency f and unloaded Q-factor Q of the TM to TM modes in the
0 u 010 080
cavity with the COP sample are measured and shown in Table A.2. Uncertainty evaluations
of the resonant frequency and Q-factor are performed by considering the uncertainty
propagation of the uncertainty of S , measurement repeatability, and the effect of frequency
resolution determined by the interval between discrete frequency points. Monte-Carlo
calculations are performed to evaluate the uncertainties of these resonant properties [7].
Table A.2 – The resonant frequencies and unloaded Q-factors
Mode f (GHz) Q
0 u
TM 15,716 62 ± 0,000 70 602 ± 36
TM 28,915 72 ± 0,000 78 707 ± 32
TM 42,077 54 ± 0,000 82 793 ± 32
TM 55,234 90 ± 0,000 88 860 ± 30
TM 68,364 ± 0,012 910 ± 190
TM 81,430 ± 0,012 930 ± 180
TM 94,397 ± 0,012 940 ± 160
TM 107,185 ± 0,012 910 ± 140
c) To express the leakage field through sample in a radial direction (fringing field), the effective
radius R + ΔR is introduced in the analysis where the cylindrical magnetic wall is assumed
[1]. When t is much smaller than a wavelength, ΔR is approximated by (2ln2/π)d [5]. Because
the introduction of the effective radius is the approximate analytical method for
compensating the fringing field, the uncertainty of R is conservatively estimated:
u(R) = ΔR/√3, by assuming that the radius follows a uniform distribution ranging from
R to R + 2ΔR.
d) The conductivity of the metal of the resonator is measured by the two dielectric resonator
method at 10 GHz, and the result is σ = 5,63 ± 0,18 × 10 S/m.

– 12 – IEC 63185:2020 © IEC 2020
e) The measurement results of the complex permittivity of the COP sample are calculated by
deriving Equations (3) and (4). Associated uncertainties are evaluated by considering the
uncertainty propagations of f , Q , t, R, a, M and σ. The effect of the finiteness of the number
0 u
of terms used in the mode-matching analysis (relative convergence error) is also considered
in the uncertainty evaluation [8] of the complex permittivity. The results are shown
in Table A.3.
Table A.3 – Measurement results of complex permittivity
-4
Mode ε '
tanδ (10 )
r
TM 2,35 ± 0,12 2,39 ± 0,68
TM 2,35 ± 0,12 3,66 ± 0,47
TM 2,35 ± 0,12 3,92 ± 0,38
TM 2,35 ± 0,12 4,03 ± 0,32
TM 2,35 ± 0,13 4,2 ± 1,2
TM 2,36 ± 0,13 4,5 ± 1,0
TM 2,37 ± 0,13 4,87 ± 0,93
TM 2,38 ± 0,13 5,55 ± 0,86
Bibliography
[1] KAWABATA, H HASUIKE, K
...