IEC 62810:2015

IEC 62810 ®
Edition 1.0 2015-02
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Cylindrical cavity method to measure the complex permittivity of low-loss
dielectric rods
Mesure de la permittivité complexe des barreaux diélectriques à faibles pertes
par la méthode de la cavité cylindrique

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IEC 62810 ®
Edition 1.0 2015-02
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Cylindrical cavity method to measure the complex permittivity of low-loss

dielectric rods
Mesure de la permittivité complexe des barreaux diélectriques à faibles pertes

par la méthode de la cavité cylindrique

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 33.120.30 ISBN 978-2-8322-5194-2

– 2 – IEC 62810:2015 © IEC 2015

CONTENTS
FOREWORD . 3
1 Scope . 5
2 Normative references . 5
3 Measurement parameters . 5
4 Theory and calculation equations . 5
5 Measurement system . 12
6 Measurement procedure . 14
6.1 Preparation of measurement apparatus. 14
6.2 Measurement of reference level . 14
6.3 Measurement of cavity parameters: σ . 14
r
6.4 Measurement of complex permittivity of test sample: ε', tan d. 15
Annex A (informative) Example of measurement results and accuracy . 16
A.1 Measurement of ε' and tand values . 16
A.2 Measurement uncertainty of ε' and tand . 17
Bibliography . 19

Figure 1 – Structure of a cylindrical cavity resonator . 6
Figure 2 – Correction factor C for ε’. 7
Figure 3 – Correction factor C for tand with the different values of d . 9
2 1
Figure 4 – Schematic diagram of measurement systems . 13
Figure 5 – Resonance frequency f , insertion attenuation IA and half-power band
0 0
width f . 14
BW
Figure 6 – Frequency responses of the TM mode of cylindrical cavity . 15
Table 1 – Numerical values of correction factor C . 8
Table 2 – Numerical values of correction factor C . 10
Table 3 – Numerical values of correction factor C . 11
Table A.1 – The parameters of the cavity and the rod sample . 16
Table A.2 – The resonant frequencies and unloaded Q-factors . 16
Table A.3 – The approximate values and the relative conductivity value . 16
Table A.4 – Correction factors and the measurement results . 16
Table A.5 – The measurement uncertainty of ε’ . 17
Table A.6 – The measurement uncertainty of tand . 18

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
CYLINDRICAL CAVITY METHOD TO MEASURE
THE COMPLEX PERMITTIVITY OF LOW-LOSS DIELECTRIC RODS

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 62810 has been prepared by subcommittee 46F: R.F. and
microwave passive components, of IEC technical committee 46: Cables, wires, waveguides,
R.F. connectors, R.F. and microwave passive components and accessories.
This bilingual version (2017-12) corresponds to the monolingual English version, published in
2015-02.
The text of this standard is based on the following documents:
CDV Report on voting
46F/242/CDV 46F/260/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.
The French version of this standard has not been voted upon.

– 4 – IEC 62810:2015 © IEC 2015
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.
CYLINDRICAL CAVITY METHOD TO MEASURE
THE COMPLEX PERMITTIVITY OF LOW-LOSS DIELECTRIC RODS

1 Scope
This International Standard relates to a measurement method for complex permittivity of a
dielectric rod at microwave frequency. This method has been developed to evaluate the
dielectric properties of low-loss materials in coaxial cables and electronic devices used in
microwave systems. It uses the TM mode in a circular cylindrical cavity and presents
accurate measurement results of a dielectric rod sample, where the effect of sample insertion
holes is taken into account accurately on the basis of the rigorous electromagnetic analysis.
In comparison with the conventional method described in IEC 60556 [2] , this method has the
following characteristics:
• the values of the relative permittivity ε' and loss tangent tand of a dielectric rod sample
can be measured accurately and non-destructively;
• the measurement accuracy is within 1,0 % for ε' and within 20 % for tand;
• the effect of sample insertion holes is corrected using correction charts presented;
• this method is applicable for the measurements on the following condition:
– frequency: 1 GHz ≦f ≦10 GHz;
– relative permittivity: 1 ≦ε' ≦100;
–4 –1
– loss tangent: 10 ≦tand ≦10 .
2 Normative references
Void.
3 Measurement parameters
The measurement parameters are defined as follows:
ε = ε'-jε" (1)
r
tand = ε"/ε' (2)
where ε' and ε" are the real and imaginary parts of the complex relative permittivity ε .
r
4 Theory and calculation equations
A resonator structure used in these measurements is shown in Figure 1. A cavity, made with
copper, with diameter D and height H has sample insertion holes with diameter d and depth g
having ε' and tand is inserted into
oriented coaxially. A dielectric rod sample of diameter d
the holes.
___________
Figures in square brackets refer to the Bibliography.

– 6 – IEC 62810:2015 © IEC 2015
The TM mode, where the electric field component in the cavity is parallel to the sample
rod, is used for the measurement. Taking account of the effect of sample insertion holes
calculated on the basis of the rigorous electromagnetic field analysis, ε' and tand are
determined from the measured values of the resonant frequency f and the unloaded Q-factor
Q . To avoid the tedious numerical calculation and make the measurements easy, the
u
following process is taken in this measurement:
Cylindrical cavity Dielectric rod (sample)
Sample insertion hole
Coaxial cable
with small loop
Ød
Ød
ØD
IEC
Figure 1 – Structure of a cylindrical cavity resonator
The following steps shall be taken:
1) At the first step, obtain approximate values ε and tand from the f and Q values by
p p 0 u
using the simple perturbation formulas, where the effect of sample insertion holes is
neglected. The subscript p denotes the calculated values using the following perturbation
formulas:
f − f  
1 D
0 1
 
ε = +1 (3)
p
 
α f d
1  1 
   
1 D 1 1
   
tand = − (4)
p
   
2αε d Q Q
p 1 u1 u0
   
where α = 1 J ( x ) = 1,855 .
1 01
is the Bessel function of order n of first kind and x = 2,405 is the first root of
J ( x)
n 01
J ( x) = 0 . f and Q are the resonant frequency and unloaded Q-factor measured for the
0 0 u0
and Q are ones measured for the cavity with a
cavity without a sample, respectively. f
1 u1
sample.
2) In the second step, obtain accurate values ε' and tand from ε and tand values by using
p p
the following equations with correction factors calculated based on the rigorous analysis:
ε ′ = C ε (5)
1 p
tand = C tand (6)
2 p
g H g
where correction factors C and C , due to the sample insertion holes and errors included
1 2
in the perturbation formulas, are calculated numerically by using the Ritz-Galerkin method
[3][5], as shown in Figure 2 and Figure 3, and the corresponding data are listed in detail in
Table 1, 2, and 3. The missing data of C and C can be obtained by interpolation or
1 2
extrapolation from the tables. The correction factors shown in these figures are calculated
for the cavity with D = 76,5 mm, H = 20,0 mm, d = 3,0 mm, and g = 10,0 mm, where the
resonant frequency is about 3 GHz. C is also used for a cavity having the same aspect
ratios as H/D, d /D and g/D.
It is found from the analysis for a cavity with insertion holes which constitute a cut-off TM
mode cylindrical waveguide that f converges to a constant value for g>10 mm and d = 3 mm.
0 2
Therefore, the correction factors shown in Figure 2 and Figure 3 are applicable to a dielectric
sample rod with d <3 mm and ε’ below the value calculated by the following equation for the
measured value of the resonant frequency:
 x c 
 
ε' ≤ (7)
 
πd f
 2 0 
where c is the velocity of light in a vacuum (c = 2,9 979 × 108 m/s).
1,2
1,0 0,5
76,5 76,5
1,1
1,5
76,5
1,0
2,0
76,5
0,9
2,5
76,5
0,8
d 3,0
=
0,7
D 76,5
0,6
2 3 4 5 6 2 3 4 5 6
1 10 100
ε
p
IEC
Assumptions
D 76,5 mm d 3,0 mm
H 20,0 mm g 10,0 mm
Figure 2 – Correction factor C for ε’
Factor C
– 8 – IEC 62810:2015 © IEC 2015
Table 1 – Numerical values of correction factor C
d (mm)
ε
p
0, 5 1, 0 1, 5 2, 0 2, 5 3, 0
1 1, 000 1, 000 1, 000 1, 000 1, 000 1, 000
1, 5 1, 023 1, 022 1, 021 1, 019 1, 016 1, 010
2 1, 035 1, 034 1, 033 1, 030 1, 024 1, 013
3 1, 047 1, 047 1, 046 1, 041 1, 032 1, 012
4 1, 054 1, 055 1, 053 1, 047 1, 035 1, 007
5 1, 058 1, 060 1, 059 1, 051 1, 037 1, 001
6 1, 061 1, 064 1, 063 1, 054 1, 037 0, 995
7 1, 064 1, 068 1, 066 1, 056 1, 037 0, 988
8 1, 066 1, 071 1, 069 1, 058 1, 036 0, 981
9 1, 068 1, 073 1, 071 1, 059 1, 035 0, 975
10 1, 070 1, 076 1, 073 1, 060 1, 033 0, 968
15 1, 077 1, 085 1, 080 1, 061 1, 024 0, 936
20 1, 082 1, 091 1, 084 1, 060 1, 013 0, 907
30 1, 090 1, 101 1, 088 1, 052 0, 992 0, 859
40 1, 097 1, 107 1, 088 1, 043 0, 971 0, 820
50 1, 102 1, 112 1, 086 1, 032 0, 953 0, 789
60 1, 107 1, 115 1, 082 1, 021 0, 938 0, 764
70 1, 112 1, 117 1, 077 1, 011 0, 924 0, 743
80 1, 116 1, 118 1, 071 1, 001 0, 912 0, 726
90 1, 119 1, 118 1, 065 0, 991 0, 903 0, 712
100 1, 123 1, 117 1, 058 0, 982 0, 894 0, 700

1,4
σ = 1,0
d 2,0 r
=
D 76,5
σ = 0,9
r
1,3
1,2
tand =
p
-5
6×10
-4
1×10
1,1
-4
2×10
-4
4×10
1,0
-3
1×10
-2
1×10
-1
1×10
0,9
2 3 4 5 6 7 2 3 4 5 6 7
1 10 100
ε
p
IEC
a) Dielectric sample rod with d = 2,0 mm
Factor C
1,4
σ = 1,0
d r
2,5
=
D 76,5
σ = 0,9
r
1,3
1,2
tand =
p
-5
6×10
1,1
-4
1×10
-4
2×10
-4
4×10
1,0
-3
1×10
-2
1×10
-1
1×10
0,9
2 3 4 5 6 7 2 3 4 5 6 7
1 10 100
ε
p
IEC
b) Dielectric sample rod with d = 2,5 mm
Assumptions
D 76,5 mm d 3,0 mm
H 20,0 mm g 10,0 mm
Figure 3 – Correction factor C for tand with the different values of d
2 1
Factor C
– 10 – IEC 62810:2015 © IEC 2015
Table 2 – Numerical values of correction factor C
(Dielectric sample rod with d = 2,0 mm)
σ =0,9
r
tand
p
ε
p
-5 -4 -4 -4 -3 -2 -1
6×10 1×10 2×10 4×10 1×10 1×10 1×10
1 1, 045 1, 058 1, 057 1, 057 1, 057 1, 056 1, 056
1, 5 1, 081 1, 070 1, 055 1, 048 1, 043 1, 040 1, 040
2 1, 099 1, 077 1, 055 1, 044 1, 037 1, 033 1, 033
3 1, 119 1, 085 1, 055 1, 041 1, 032 1, 026 1, 026
4 1, 130 1, 090 1, 056 1, 040 1, 030 1, 024 1, 023
5 1, 137 1, 093 1, 057 1, 039 1, 029 1, 022 1, 021
6 1, 143 1, 096 1, 058 1, 039 1, 028 1, 021 1, 020
7 1, 147 1, 098 1, 059 1, 039 1, 028 1, 020 1, 020
8 1, 151 1, 100 1, 060 1, 039 1, 027 1, 020 1, 019
9 1, 154 1, 102 1, 060 1, 039 1, 027 1, 019 1, 019
10 1, 157 1, 103 1, 061 1, 039 1, 027 1, 019 1, 018
15 1, 167 1, 108 1, 062 1, 039 1, 025 1, 017 1, 016
20 1, 173 1, 111 1, 063 1, 038 1, 024 1, 015 1, 014
30 1, 179 1, 113 1, 062 1, 036 1, 021 1, 012 1, 011
40 1, 181 1, 114 1, 061 1, 034 1, 019 1, 009 1, 008
50 1, 180 1, 113 1, 060 1, 033 1, 018 1, 008 1, 007
60 1, 177 1, 111 1, 059 1, 033 1, 018 1, 009 1, 008
70 1, 172 1, 109 1, 059 1, 034 1, 019 1, 011 1, 010
80 1, 165 1, 106 1, 060 1, 036 1, 022 1, 014 1, 013
90 1, 158 1, 104 1, 061 1, 040 1, 027 1, 019 1, 018
100 1, 150 1, 102 1, 063 1, 044 1, 032 1, 025 1, 025

σ =1,0
r
tand
p
ε
p
-5 -4 -4 -4 -3 -2 -1
6×10 1×10 2×10 4×10 1×10 1×10 1×10
1 0, 932 0, 990 1, 023 1, 040 1, 050 1, 056 1, 056
1, 5 1, 004 1, 024 1, 032 1, 036 1, 038 1, 040 1, 040
2 1, 040 1, 042 1, 037 1, 035 1, 033 1, 033 1, 032
3 1, 077 1, 060 1, 043 1, 034 1, 029 1, 026 1, 026
4 1, 097 1, 070 1, 046 1, 035 1, 028 1, 023 1, 023
5 1, 110 1, 077 1, 049 1, 035 1, 027 1, 022 1, 021
6 1, 118 1, 081 1, 051 1, 036 1, 026 1, 021 1, 020
7 1, 125 1, 085 1, 052 1, 036 1, 026 1, 020 1, 020
8 1, 131 1, 088 1, 053 1, 036 1, 026 1, 020 1, 019
9 1, 135 1, 090 1, 054 1, 037 1, 026 1, 019 1, 019
10 1, 139 1, 092 1, 055 1, 037 1, 026 1, 019 1, 018
15 1, 152 1, 099 1, 058 1, 037 1, 024 1, 017 1, 016
20 1, 159 1, 103 1, 058 1, 036 1, 023 1, 015 1, 014
30 1, 167 1, 106 1, 058 1, 034 1, 020 1, 012 1, 011
40 1, 170 1, 107 1, 057 1, 033 1, 018 1, 009 1, 008
50 1, 169 1, 106 1, 056 1, 032 1, 017 1, 008 1, 007
60 1, 166 1, 104 1, 056 1, 032 1, 017 1, 008 1, 008
70 1, 162 1, 103 1, 056 1, 033 1, 019 1, 010 1, 010
80 1, 156 1, 101 1, 057 1, 035 1, 022 1, 014 1, 013
90 1, 150 1, 099 1, 059 1, 038 1, 026 1, 019 1, 018
100 1, 142 1, 097 1, 061 1, 043 1, 032 1, 025 1, 025

Table 3 – Numerical values of correction factor C
(Dielectric sample rod with d = 2,5 mm)
σ =0,9
r
tand
p
ε
p
-5 -4 -4 -4 -3 -2 -1
6×10 1×10 2×10 4×10 1×10 1×10 1×10
1 1, 042 1, 049 1, 049 1, 048 1, 048 1, 048 1, 048
1, 5 1, 077 1, 063 1, 048 1, 040 1, 036 1, 033 1, 033
2 1, 095 1, 070 1, 048 1, 037 1, 030 1, 026 1, 026
3 1, 113 1, 078 1, 048 1, 033 1, 024 1, 019 1, 018
4 1, 123 1, 081 1, 048 1, 031 1, 021 1, 015 1, 014
5 1, 129 1, 084 1, 048 1, 030 1, 019 1, 012 1, 012
6 1, 133 1, 086 1, 047 1, 028 1, 017 1, 010 1, 009
7 1, 136 1, 087 1, 047 1, 027 1, 015 1, 008 1, 008
8 1, 139 1, 087 1, 047 1, 026 1, 014 1, 007 1, 006
9 1, 141 1, 088 1, 046 1, 025 1, 013 1, 005 1, 004
10 1, 142 1, 088 1, 046 1, 024 1, 011 1, 004 1, 003
15 1, 146 1, 088 1, 043 1, 020 1, 006 0, 998 0, 997
20 1, 148 1, 088 1, 040 1, 017 1, 002 0, 994 0, 993
30 1, 150 1, 088 1, 039 1, 014 0, 999 0, 991 0, 990
40 1, 150 1, 089 1, 041 1, 016 1, 002 0, 993 0, 992
50 1, 152 1, 094 1, 047 1, 023 1, 009 1, 001 1, 000
60 1, 154 1, 100 1, 056 1, 034 1, 021 1, 013 1, 012
70 1, 157 1, 108 1, 068 1, 048 1, 036 1, 029 1, 028
80 1, 161 1, 118 1, 083 1, 065 1, 055 1, 048 1, 048
90 1, 165 1, 130 1, 100 1, 084 1, 075 1, 070 1, 069
100 1, 170 1, 142 1, 118 1, 106 1, 098 1, 094 1, 094

σ =1,0
r
tand
p
ε
p
-5 -4 -4 -4 -3 -2 -1
6×10 1×10 2×10 4×10 1×10 1×10 1×10
1 0, 970 1, 006 1, 027 1, 037 1, 044 1, 048 1, 048
1, 5 1, 027 1, 033 1, 033 1, 033 1, 033 1, 033 1, 033
2 1, 056 1, 046 1, 036 1, 031 1, 028 1, 026 1, 026
3 1, 085 1, 060 1, 039 1, 029 1, 022 1, 019 1, 018
4 1, 100 1, 068 1, 041 1, 028 1, 020 1, 015 1, 014
5 1, 109 1, 072 1, 042 1, 027 1, 018 1, 012 1, 012
6 1, 115 1, 075 1, 042 1, 026 1, 016 1, 010 1, 009
7 1, 120 1, 077 1, 042 1, 025 1, 014 1, 008 1, 008
8 1, 123 1, 078 1, 042 1, 024 1, 013 1, 007 1, 006
9 1, 126 1, 079 1, 042 1, 023 1, 012 1, 005 1, 004
10 1, 128 1, 080 1, 041 1, 022 1, 011 1, 004 1, 003
15 1, 134 1, 081 1, 039 1, 018 1, 006 0, 998 0, 997
20 1, 137 1, 081 1, 037 1, 015 1, 002 0, 994 0, 993
30 1, 139 1, 081 1, 035 1, 012 0, 999 0, 990 0, 990
40 1, 141 1, 083 1, 038 1, 015 1, 001 0, 993 0, 992
50 1, 143 1, 088 1, 044 1, 022 1, 009 1, 001 1, 000
60 1, 146 1, 095 1, 054 1, 033 1, 021 1, 013 1, 012
70 1, 150 1, 104 1, 066 1, 047 1, 036 1, 029 1, 028
80 1, 154 1, 114 1, 081 1, 064 1, 054 1, 048 1, 048
90 1, 159 1, 126 1, 098 1, 084 1, 075 1, 070 1, 069
100 1, 165 1, 139 1, 116 1, 105 1, 098 1, 094 1, 094

– 12 – IEC 62810:2015 © IEC 2015
The value of relative conductivity σ is determined from the measured unloaded Q-factor Q
r u0
at f for the TM mode by the following equation:
0 010
 D 
 
2π1+ 
 
d 2H
 
σ0  
(8)
σ = Q
 
r u0
λ x
0 01
 
 
 
where λ = c/f is the wave length, and the skin depth d at f is defined as follows:
0 0 s0 0
d = (9)
σ 0
π f µ σ
0 0 0
where µ is the permeability of vacuum and σ = 5,8 × 10 S/m is the conductivity of standard
0 0
copper.
Measurement uncertainties of ε' and tand, u(ε') and u(tand), are estimated as the mean square
uncertainty and given respectively by
2 2 2 2 2
 ′   ′   ′  ′  ′ 
∂ ε ∂ ε ∂ ε  ∂ ε  ∂ ε
2 2 2 2 2 2
(10)
′          
u(ε ) = u( f ) + u( f ) + u(d ) + u(D) + u(C )
0 1 1 1
         
∂ f ∂ f ∂d ∂D ∂C
 0   1   1     1 
2 2 2
 ∂ tand   ∂ tand   ∂ tand 
2 2 2 2
     
u(tand ) = u(ε ) + u(d ) + u(D) +
P 1
     
∂ε ∂d ∂D
 P   1   
2 2 2
 tand   tand   tand 
∂ ∂ ∂
2 2 2
(11)
     
u(Q ) + u(Q ) + u(C )
u0 u1 2
     
∂Q ∂Q ∂C
u0 u1  2 
   
where u(f ), u(f ), u(d ), u(D), and u(C ) are the standard uncertainties of f , f , d , D, and C ,
0 1 1 1 0 1 1 1
respectively. Also, u(tand) is mainly attributed to measurement uncertainty of ε , d , D, Q ,
p 1 u0
Q , and C . u(ε ), u(d ), u(D), u(Q ), u(Q ), and u(C ) are the standard uncertainties of
u1 2 p 1 u0 u1 2
them, respectively.
5 Measurement system
Figure 4 shows a schematic diagram of two equipment systems required for microwave
measurement. For the measurement of dielectric properties, only the information on the
amplitude of transmitted power is needed, that is, the information on the phase of the
transmitted power is not required. Therefore, a scalar network analyser can be used for the
measurement shown in Figure 4a. However, a vector network analyser, as shown in
Figure 4b, has an advantage in precision of the measurement.

Scalar
Sweeper
network Vector
analyser network
analyser
Detector
Measurement
Power Measurement
Detector
apparatus
splitter apparatus
Reference line
Reference line
IEC
IEC
a) Scalar network analyzer system b) Vector network analyzer system
Figure 4 – Schematic diagram of measurement systems
The structure of the TM mode cylindrical cavity resonator used in the complex permittivity
measurement is shown in Figure 1. The cavity has D = 76,5 mm, H = 20,0 mm, d = 3,0 mm,
and g = 10,0 mm for the measurement around 3 GHz. A sample with diameter d 1 2
coaxially inserted into the holes and excited magnetically by a pair of semi-rigid coaxial
cables with a small loop at the top. The transmission-type resonator is constituted and under-
coupled equally to the input and output loops with setting S = S .
11 22
The resonant frequency f , half-power band width f , and the insertion attenuation IA (dB)
0 BW 0
are measured using a network analyser by means of the swept-frequency method, as
at f
shown in Figure 5. The value of Q is given by
u
f
Q
L 0
Q = Q =
u L
IA (dB) 20
f
1− 10 BW
,  (12)
1) At the first step, obtain approximate values ε and tand from the f and Q values by
p p 0 u
using the simple perturbation formulas, where the effect of sample insertion holes is
neglected. The subscript p denotes the calculated values using the following perturbation
formulas:
f − f  
1 D
0 1
 
ε = +1 (13)
p
 
α f d
1  1 
 
1  D  1 1
   
tand = − (14)
p
   
2αε d Q Q
p 1 u1 u0
   
where α = 1/J (x ) = 1,855. J (x) is the Bessel function of order n of first kind and
1 01 n
x = 2,405 is the first root of J (x) = 0. f and Q are the resonant frequency and
01 0 0 u0
unloaded Q-factor measured for the cavity without a sample, respectively. f and Q are
1 u1
ones measured for the cavity with a sample.
2) In the second step, obtain accurate values ε' and tand from ε and tand values by using
p p
the following equations with correction factors calculated based on the rigorous analysis:
′
ε = C ε (15)
1 p
tand = C tand (16)
2 p
– 14 – IEC 62810:2015 © IEC 2015
where correction factors C and C due to the sample insertion holes and errors included
1 2
in the perturbation formulas are calculated numerically by using the Ritz-Galerkin method
[3][5], as shown in Figure 2 and Figure 3, and the corresponding data are listed in detail in
Table 1, 2, and 3. The missing data of C and C can be obtained by interpolation or
1 2
extrapolation from the tables. The correction factors shown in these figures are calculated
for the cavity with D = 76,5 mm, H = 20,0 mm, d = 3,0 mm, and g = 10,0 mm, where the
resonant frequency is about 3 GHz. C is also used for a cavity having the same aspect
ratios as H/D, d /D and g/D.
It is found from the analysis for a cavity with insertion holes which constitute a cut-off TM
mode cylindrical waveguide that f converges to a constant value for g>10 mm and d = 3 mm.
0 2
Therefore, the correction factors shown in Figure 2 and Figure 3 are applicable to a dielectric
sample rod with d <3 mm and ε’ below the value calculated by the following equation for the
measured value of the resonant frequency:
−25
−30
IA
f
−35
BW
−40
−45
f
Frequency  (Hz)
IEC
, insertion attenuation IA
Figure 5 – Resonance frequency f
0 0
and half-power band width f
BW
6 Measurement procedure
6.1 Preparation of measurement apparatus
Set up the measurement equipment and apparatus as shown in Figure 4. The cavity resonator
and dielectric samples shall be kept in a clean and dry state, as high humidity degrades
unloaded Q. The relative humidity shall preferably be less than 60 %.
6.2 Measurement of reference level
The reference level, level of full transmission power, is measured first. Connect the reference
line to the measurement equipment and measure the full transmission power level over the
entire measurement frequency range.
6.3 Measurement of cavity parameters: σ
r
Set the empty cavity and adjust the insertion attenuation IA to be around 30 dB by changing
the distance between two semi-rigid cables, as shown in Figure 5.
Insertion attenuation  (dB)
3 dB
Measure f , f , and IA of the TM resonant mode. Calculate Q by using Equation (12).
0 BW 0 010 u0
Then, calculate σ by using Equation (8). Since the value of σ degrades due to oxidation of
r r
the metal surface, it shall be measured periodically. σ shall preferably be more than 0,9.
r
6.4 Measurement of complex permittivity of test sample: ε', tan d
Insert the test sample into the holes. Figure 6 shows the frequency responses of the TM
mode in the cavity with and without a sample. Measure the resonant frequency f , half-power
band width f and the insertion attenuation IA . Calculate the values of ε ' and tan d by
BW 0 p p
using Equations (3) and (4), respectively. Then, calculate ε' and tand values by using
Equations (5) and (6).
Cavity without a sample
Cavity with a sample
−20
TM
−40
−60
−80
2,98 2,99 3,00 3,01 3,02
Frequency  (GHz)
IEC
Assumptions
D 76,5 mm d 3,0 mm
H 20,0 mm g 10,0 mm
Figure 6 – Frequency responses of the TM mode of cylindrical cavity
Insertion attenuation  (dB)
– 16 – IEC 62810:2015 © IEC 2015
Annex A
(informative)
Example of measurement results and accuracy
A.1 Measurement of ε' and tand values
The measurement results of ε' and tand for polyethylene rod sample are obtained as followed.
a) The parameters such as D, H and d of the cavity and d of the polyethylene sample used
2 1
in the measurements are shown in Table A.1.
Table A.1 – The parameters of the cavity and the rod sample
D H d d
2 1
mm mm mm mm
76,50 20,00 3,00 2,52
±0,02 ±0,01 ±0,01 ±0,01
b) The resonant frequency f and unloaded Q-factor Q of the TM mode in the cavity
0 u0 010
without a sample and f and Q in the cavity with a sample are measured and shown in
1 u1
Table A.2.
Table A.2 – The resonant frequencies and unloaded Q-factors

c) The approximate values ε and tand and the value of relative conductivity σ are
p p r
calculated numerically by Equations (3), (4), and (8), respectively, and the results are
shown in Table A.3.
Table A.3 – The approximate values and the relative conductivity value

d) The correction factors C and C are found from Figure 2 and Figure 3b, respectively,
1 2
using the calculated values of ε , tand and σ . The results are shown in Table A.4.
p p r
Table A.4 – Correction factors and the measurement results

e) The accurate values ε' and tand are obtained from Equations (5) and (6), and these results
are also shown in Table A.4.
A.2 Measurement uncertainty of ε' and tand
The measurement uncertainty (see ISO/IEC Guide 98-3) of ε' and tand is calculated for the
polyethylene sample mentioned above by Equation (10) and (11). Each sensitivity coefficients
in Equations (10) and (11) are as follows:
′  
∂ ε 1 1 D
 
= C
 
∂f α f d
0 1  1 
 
∂ ε ′ f  
1 D
 
= −   C
 
 
∂f α d
1 f  1 
 1 
 
∂ ε ′ f − f
1 D
0 1
 
= − 2 C
 
∂d α f
1 1 d
 1 
 
∂ ε ′ 1 f − f 2D
0 1
 
= C
 
∂D α f
d
 1 
′  
∂ ε 1 f − f D
0 1
 
=
 
∂C α f d
1 1 1
 
∂ tand    
1 1 D 1 1
= −   − C
 
 
∂ε 2α d Q Q
p ε  1   u1 u0 
p
 
 
∂ tand 1 1 D 1 1
 
= − 2 − C
 
 
∂d ε 2α Q Q
1 p d  u1 u0 
 1 
 
∂ tand  
1 1 2D 1 1
 
= − C
 
 
∂D ε 2α Q Q
d
p  u1 u0 
 1 
 
 
∂ tand 1 1 D 1
 
 
= C
 


∂Q ε 2α d
u0 p  1   Q 
 u0 
 
∂ tand 1 1  D  1
 
=   − C
  2
 
∂Q ε 2α d
 Q 
u1 p  1 
 u1 
   
∂ tand 1 1 D 1 1
 
== −
 
 
∂C ε 2α d Q Q
2 p  1   u1 u0 
The results are shown in Table A.5 and A.6.
Table A.5 – The measurement uncertainty of ε’

– 18 – IEC 62810:2015 © IEC 2015
Table A.6 – The measurement uncertainty of tand

Bibliography
[1] ISO/IEC Guide 98-3, Uncertainty of meaσurement – Part 3: Guide to the expreσσion of
uncertainty in meaσurement (GUM:1995)
[2] IEC 60556, Gyromagnetic materialσ intended for application at microwave frequencieσ
– Meaσuring methodσ for propertieσ
[3] ESTIN, A.J. and H.E.BUSSEY, H.E., Errorσ in dielectric meaσurementσ due to a
σample inσertion hol in a cavity, IRE Trans. Microwave Theory & Tech., vol.MTT-8,
no.6, pp.650-653, Nov. 1960
[4] KAWABATA, H., TANPO, H. and KOBAYASHI, Y., An improvement of the perturbation
method uσing a TM mode cylindrical cavity, IEICE Trans. Electron., vol.E86-C,
no.12, pp.2371-2379, Dec. 2003
[5] KANEKO, S., KAWABATA, H.and KOBAYASHI, Y., Improved perturbation method of
complex permittivity uσing correction chartσ for TM and TM modeσ of a circular
010 020
cylindrical cavity" Proc. 2010 Asia-Pacific Microwave Conf., TH3G-47, pp.1448-1451,
Dec. 2010
[6] WEISSTEIN, Eric W., Galerkin Method, from MathWorld – A Wolfram Web Resource.
http://mathworld.wolfram.com/GalerkinMethod.html (website checked 2014.12.22)

_____________
– 20 – IEC 62810:2015 © IEC 2015

SOMMAIRE
AVANT-PROPOS . 21
1 Domaine d'application . 23
2 Références normatives . 23
3 Paramètres de mesure . 23
4 Théorie et équations de calcul . 24
5 Système de mesure . 31
6 Procédure de mesure . 33
6.1 Préparation de l'appareil de mesure . 33
6.2 Mesure du niveau de référence . 33
6.3 Mesure des paramètres de la cavité: σ . 34
r
6.4 Mesure de la permittivité complexe de l'échantillon d'essai: ε', tan d . 34
Annexe A (informative) Exemple de résultats de mesure et précision de mesure . 35
A.1 Mesure des valeurs ε' et tand  . 35
A.2 Incertitude de mesure de ε' et de tand . 36
Bibliographie . 38

Figure 1 – Structure d'un résonateur à cavité cylindrique . 24
Figure 2 – Facteur de correction C pour ε’ . 26
Figure 3 – Facteur de correction C pour tand avec les différentes valeurs de d . 28
2 1
Figure 4 – Représentation schématique des systèmes de mesure . 32
Figure 5 – Fréquence de résonance f , affaiblissement d'insertion IA et bande
0 0
passante à mi-puissance f . 33
BW
Figure 6 – Réponses en fréquences du mode TM de la cavité cylindrique . 34
Tableau 1 – Valeurs numériques du facteur de correction C . 26
Tableau 2 – Valeurs numériques du facteur de correction C . 29
Tableau 3 – Valeurs numériques du facteur de correction C . 30
Tableau A.1 – Paramètres de la cavité et de l'échantillon de barreau . 35
Tableau A.2 – Fréquences de résonance et facteurs Q à vide . 35
Tableau A.3 – Valeurs approchées et valeur de la conductivité relative . 35
Tableau A.4 – Facteurs de correction et résultats de mesure . 36
Tableau A.5 – Incertitude de mesure de ε’ . 37
Tableau A.6 – Incertitude de mesure de tand . 37

COMMISSION ÉLECTROTECHNIQUE INTERNATIONALE
____________
MESURE DE LA PERMITTIVITÉ COMPLEXE DES BARREAUX
DIÉLECTRIQUES À FAIBLES PERTES PAR LA MÉTHODE
DE LA CAVITÉ CYLINDRIQUE
AVANT-PROPOS
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