IEC 62562:2010
(Main)Cavity resonator method to measure the complex permittivity of lowloss dielectric plates
Cavity resonator method to measure the complex permittivity of lowloss dielectric plates
IEC 62562:2010 describes a measurement method of dielectric properties in the planar direction of dielectric plate at microwave frequency, called a cavity resonator method. It has been created in order to develop new materials and to design microwave active and passive devices for which standardization of measurement methods of material properties is more and more important. This first edition cancels and replaces the PAS published in 2008. This bilingual version, published in 201005, corresponds to the English version.
This publication contains colours which are considered to be useful for the correct understanding of its contents.
Méthode de la cavité résonante pour mesurer la permittivité complexe des plaques diélectriques à faibles pertes
IEC 62562:2010 décrit une méthode de mesure des propriétés diélectriques en hyperfréquence dans la direction du plan d'une plaque diélectrique. Cette méthode est appelée méthode de la cavité résonante. Elle a été créée pour élaborer de nouveaux matériaux et pour concevoir des dispositifs microondes actifs et passifs pour lesquels la normalisation des méthodes de mesure des propriétés des matériaux est de plus en plus importante. La présente version bilingue, publiée en 201005, correspond à la version anglaise.
Cette publication indique qu'elle contient des couleurs qui sont considérées comme utiles à une bonne compréhension de son contenu.
General Information
Standards Content (Sample)
IEC 62562
®
Edition 1.0 201002
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Cavity resonator method to measure the complex permittivity of lowloss
dielectric plates
Méthode de la cavité résonante pour mesurer la permittivité complexe des
plaques diélectriques à faibles pertes
IEC 62562:2010
 Page: 1 
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 Page: 2 
IEC 62562
®
Edition 1.0 201002
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Cavity resonator method to measure the complex permittivity of lowloss
dielectric plates
Méthode de la cavité résonante pour mesurer la permittivité complexe des
plaques diélectriques à faibles pertes
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
R
CODE PRIX
ICS 17.220 ISBN 9782889109319
® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
 Page: 3 
– 2 – 62562 © IEC:2010
CONTENTS
FOREWORD.3
1 Scope.5
2 Measurement parameters .5
3 Theory and calculation equations .6
3.1 Relative permittivity and loss tangent .6
′
3.2 Temperature dependence of ε and tanδ .9
3.3 Cavity parameters .9
4 Measurement equipment and apparatus .10
4.1 Measurement equipment .10
4.2 Measurement apparatus for complex permittivity .11
5 Measurement procedure.12
5.1 Preparation of measurement apparatus .12
5.2 Measurement of reference level .12
5.3 Measurement of cavity parameters: D , H , σ , α , TCρ .12
r c
5.4 Measurement of complex permittivity of test specimen: ε ' , tanδ .14
5.5 Temperature dependence of ε ' and tanδ .14
Annex A (informative) Example of measured result and accuracy .15
Bibliography.18
Figure 1 – Resonator structures of two types .6
Figure 2 – Correction term Δε’/ε’ .8
a
Figure 3 – Correction terms ΔA/A and ΔB/B .8
Figure 4 – Schematic diagram of measurement equipments.10
Figure 5 – Cavity resonator used for measurement .11
Figure 6 – Photograph of cavity resonator for measurement around 10 GHz .11
Figure 7 – Mode chart of cavity resonator .12
Figure 8 – Resonance peaks of cavity resonator.13
Figure 9 – Resonance frequency f , insertion attenuation IA and halfpower band
0 0
width f .13
BW
Figure 10 – Resonance frequency f of TE mode of cavity resonator with dielectric
0 011
plate (D = 35 mm, H = 25 mm) .14
Figure A.1 – Measured temperature dependence of f and Q .16
1 uc
Figure A.2 – Resonance peaks of cavity resonator clamping sapphire plate.16
Figure A.3 – Measured results of temperature dependence of f , Q , ε′ and tan δ for
0 u
sapphire plate.17
Table A.1 – Measured results of cavity parameters.15
Table A.2 – Measured results of of ε ' and tanδ for sapphire plate .17
 Page: 4 
62562 © IEC:2010 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISION
____________
CAVITY RESONATOR METHOD TO MEASURE THE COMPLEX
PERMITTIVITY OF LOWLOSS DIELECTRIC PLATES
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 cooperation on all questions concerning standardization in the electrical and electronic fields. To
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International Standard IEC 62562 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 first edition cancels and replaces the PAS published in 2008.
This bilingual version, published in 201002, corresponds to the English version.
The text of this standard is based on the following documents:
CDV Report on voting
46F/118/CDV 46F/143/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.
 Page: 5 
– 4 – 62562 © IEC:2010
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 web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
 Page: 6 
62562 © IEC:2010 – 5 –
CAVITY RESONATOR METHOD TO MEASURE THE COMPLEX
PERMITTIVITY OF LOWLOSS DIELECTRIC PLATES
1 Scope
The object of this International Standard is to describe a measurement method of dielectric
properties in the planar direction of dielectric plate at microwave frequency. This method is
called a cavity resonator method. It has been created in order to develop new materials and to
design microwave active and passive devices for which standardization of measurement
methods of material properties is more and more important.
This method has the following characteristics:
• the relative permittivity ε ' and loss tangent tanδ values of a dielectric plate sample can be
measured accurately and nondestructively;
• temperature dependence of complex permittivity can be measured;
–6
• the measurement accuracy is within 0,3 % for ε ' and within 5×10 for tanδ ;
• fringing effect is corrected using correction charts calculated on the basis of rigorous
analysis.
This method is applicable for the measurements on the following condition:
– frequency : 2 GHz < f < 40 GHz;
– relative permittivity: 2 < ε ' < 100;
–6 –2
– loss tangent : 10 < tanδ < 10 .
2 Measurement parameters
The measurement parameters are defined as follows:
ε = ε'− jε"= D /(ε E) (1)
r 0
'tanδ = ε" / ε (2)

ε ε
1
T ref 6
–6
TC = ×10 (1×10 /K) (3)
ε
T − T
ε
ref
ref
where
D is the electric flux density;
E is the electric field strength;
ε is the permittivity in a vacuum;
0
ε
ε ' and ε '' are the real and imaginary components of the complex relative permittivity ;
r
TCε is the temperature coefficient of relative permittivity;
ε and ε are the real parts of the complex relative permittivity at temperature T and
T ref
reference temperature T (= 20 °C to 25 °C), respectively.
ref
 Page: 7 
– 6 – 62562 © IEC:2010
3 Theory and calculation equations
3.1 Relative permittivity and loss tangent
A resonator structure used in the nondestructive measurement of the complex permittivity is
shown in Figure 1a.
A cavity having diameter D and length H = 2M is cut into two halves in the middle of its
length.
A dielectric plate sample having ε ' , tanδ and thickness t is placed between these two halves.
The TE mode, having only the electric field component tangential to the plane of the
011
sample, is used for the measurement, since air gaps at the platecavity interfaces do not
affect the electromagnetic field. Taking account of the fringing field in the plate region outside
diameter of the cavity on the basis of the rigorous mode matching analysis, we determine ε '
and tanδ from the measured values of the resonant frequency f and the unloaded Qfactor
0
Q . This numerical calculation, however, is rather tedious.
u
Therefore,
a) approximated values ε' and tanδ from the f and Q values by using simple formula for
a a 0 u
a resonator structure shown in Figure 1b, where a fringing effect for Figure 1a is neglected,
will be determined;
b) then, accurate values ε ' and tanδ from ε' and tanδ using charts calculated from the
a a
rigorous analysis will be obtained.
Dielectric plate
DDielecielecttrricic PPlalatete
y
yy
with ε’
wiwitthh εε’’
r rr
HHH
E
EE
EEE
x
xx
ⅠⅡⅠⅡ
MMMMMM MMMMMM
tttt
t t
(a(a)) (b(b))
IEC 127/10 IEC 128/10
Figure 1a – Resonator used Figure 1b – Resonator to
in measurement
calculate ε’ and tan δ
a a
Figure 1 – Resonator structures of two types
The value of ε' is given by
a
2
2
⎧ ⎫
⎛ ⎞
c ⎪ ⎛ t ⎞ ⎪
2 2
⎜ ⎟
ε' = X − Y +1 (4)
⎜ ⎟
⎨ ⎬
a
⎜ ⎟
πt f 2M
⎝ ⎠
⎝ 0⎠ ⎪ ⎪
⎩ ⎭
8
where c is the velocity of light in a vacuum ( c = 2,997 9 ×10 m/s ) and the first root X is
calculated from a given value Y , using the following simultaneous equations:
t
X tan X = Y cot Y (5)
2M
D DD==2=2 2RRR
 Page: 8 
62562 © IEC:2010 – 7 –
2 2
Y = M k − k = jY' (6)
0 r
with k = 2πf c , k = j' R, and j' = 3,83173 for the TE mode. When k − k < 0 , Y is
0 0 r 01 01 011 0 r
replaced by jY ' .
The value of tanδ is given by
a
A
tanδ = − R B (7)
a s
Q
u
where R is the surface resistance of the conductor of cavity, given by
s
πf μ
0
R = (1/S), σ = σ σ (S/m) (8)
s 0 r
σ
Here, μ and σ are the permeability and conductivity of the conductor. Furthermore, σ is the
r
7
relative conductivity and is the conductivity of standard copper. Constants A
σ = 5,8 ×10 S/m
0
and B are given by
e
W
2
A = 1+ (9)
e
W
1
P + P + P
cy1 cy2 end
B = (10)
e
ωR W
s
1
e e
In the above, W and W are electric field energies stored in the dielectric plate of region 1
1 2
and air of region 2 shown in Figure 1a. Furthermore, P , P and P are the conductor
cy1 cy2
end
loss at the cylindrical wall in the region 1, 2 and at the end wall. These parameters are given
by
π ⎛ sin2X⎞
e 2 2 ' 2 2 '
W = ε ε' μ ω j J ( j )t⎜1+ ⎟ (11)
0 a 01
1 0 01 0
8 2X
⎝ ⎠
2
π ⎛ sin2Y⎞ cos X
e 2 2 ' 2 2
W = ε μ ω j J ()j' M⎜1− ⎟ (12)
0 01
2 0 01 0
2
4 2Y
⎝ ⎠
sin Y
π ⎛ sin2X⎞
2 4
P = R J ()j' tRk ⎜1+ ⎟ (13)
cy1 s
01 r
0
4 2X
⎝ ⎠
2
π ⎛ sin2Y⎞ cos X
2 4
P = R J ()j' MRk ⎜1− ⎟ (14)
cy2 s
01 r
0
2
2 2Y
⎝ ⎠
sin Y
2
2
π ⎛ Y ⎞ cos X
2 2
P = R j' J ()j' ⎜ ⎟ (15)
end s 01
01 0
2
2 M
⎝ ⎠
sin Y
Then, accurate values of ε ' and tanδ are given by
⎛ ⎞
Δε'
⎜ ⎟
ε'= ε' 1− (16)
a
⎜ ⎟
ε'
a
⎝ ⎠
 Page: 9 
– 8 – 62562 © IEC:2010
A ΔA ΔB
⎛ ⎞ ⎛ ⎞
tanδ = ⎜1+ ⎟ − R B⎜1+ ⎟ (17)
s
Q A B
⎝ ⎠ ⎝ ⎠
u
where correction terms due to the fringing field Δε' ε' , ΔA A and ΔB B are calculated
a
numerically on the basis of rigorous mode matching analysis using the RitzGalerkin method,
as shown in Figures 2 and 3. It is found from the analysis for a circular dielectric plate with
diameter d that f converges to a constant value for d D > 1,2. The correction terms shown
0
in Figures 2 and 3 were calculated for d D > 1,5 . Therefore, the correction terms are
applicable to dielectric plates with any shape if d D > 1,2 .
Measurement uncertainties of ε ' and tanδ , Δε ' and Δ tanδ are estimated as the mean
square errors and given respectively by
2 2 2 2 2
(Δε' ) = (Δε' ) + (Δε' ) + (Δε' ) + (Δε' ) (18)
f t D H
2 2 2
(Δ tanδ ) = (Δ tanδ ) + (Δ tanδ ) (19)
Q σ
where Δε ' , Δε ' , Δε ' and Δε ' are the uncertainties of ε ' due to standard deviations of f ,
f
t D H 0
t , D , and H , respectively. Also, Δ tanδ is mainly attributed to measurement errors of Q
u
and σ , and Δ tanδ and Δ tanδ are uncertainties of tanδ due to standard deviations of
r Q σ
them, respectively.
ε’ = 1
–1
10
t/D
–2
10
ε’ = 100
–3
10
TE mode
TE mode
011011
D/H = 1,4
TE mode
TE mode
011011
–4
D/H = 1,4
10
1 10 100
ε’
a
t/D
IEC 129/10 IEC 130/10
Figure 3 – Correction terms
Figure 2 – Correction term Δε’/ε’
a
ΔA/A and ΔB/B
Δε/ε’
a
ΔB/B ΔA/A
 Page: 10 
62562 © IEC:2010 – 9 –
3.2 Temperature dependence of ε′ and tanδ
′
Temperature dependence of ε and tanδ also can be measured using this method.
Temperature coefficient of relative permittivity TCε is calculated by equation (3).
′ ′
When the temperature dependences of ε is linear, particularly, ε()T is given by
′ ′
ε()T = ε(T )[]1+ TCε(T − T ) (20)
0 0
where T and T are the temperatures in measurement and the reference temperature,
0
respectively. In this case, TCε can be determined by the least squares method for many
measurement points against T .
The thermal linear expansion coefficient of the dielectric plate α and that of the conductor
cavity α should be considered in the TCε measurement. Furthermore, the temperature
c
coefficient of resistivity TCρ should be considered in the temperature dependence
measurement of tanδ . Using these parameters, temperature dependent values of t()T , D()T ,
H()T , and ρ()T are given by
t()T = t(T )[]1+ α(T − T ) (21)
0 0
D()T = D(T )[]1+ α (T − T ) (22)
0 c 0
H()T = H(T )[]1+ α (T − T ) (23)
0 c 0
1
ρ()T = = ρ()T[]1+ TCρ(T − T ) (24)
0 0
σ()T
3.3 Cavity parameters
Cavity parameters such as D , H = 2M , α , σ and TCρ are determined from the
c r
measurements for the TE and TE resonance modes of an empty cavity without a sample,
011 012
in advance of complex permittivity measurements. At first, D and H are determined from two
measured resonant frequencies, f for the TE mode and f for the TE mode, by using
1 011 2 012
cj'
3
01
D = (25)
2 2
π
4 f − f
1 2
c 3
H = (26)
2 2
2
f − f
2 1
which can be derived easily from the resonance condition of the cavity.
Secondly, α is determined from the measurement of temperature dependence of f , by
c 1
using
 Page: 11 
– 10 – 62562 © IEC:2010
1 Δf
1
α = − (27)
c
f ΔT
1
Thirdly, σ is determined from the measured values D , H , f , Q , which is the unloaded
r 1 uc
Qfactor for the TE mode, by the following equation:
011
2
3
⎧ ⎫
⎪ ⎛ D ⎞ ⎪
2 2 2
4πf Q j' +2π
⎜ ⎟
1 uc ⎨ 01 ⎬
2H
⎝ ⎠
⎪ ⎪
⎩ ⎭
σ (28)
=
r
3
2
⎧ ⎫
⎪ ⎛ πD⎞ ⎪
2
2
σ μ c j' +
⎜ ⎟
⎨ ⎬
0 0 01
2H
⎝ ⎠
⎪ ⎪
⎩ ⎭
Finally, is determined from the measurement of temperature dependence of ρ = σ σ
TCρ
r 0
by using
Δρ
1
r
TCρ = (29)
ρ ΔT
r
4 Measurement equipment and apparatus
4.1 Measurement equipment
Figure 4 shows a schematic diagram of two equipment systems required for millimetre wave
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 analyzer can be used for the
measurement shown in Figure 4a. However, a vector network analyzer, as shown in Figure 4b,
has an advantage in precision of the measurement data.
Scalar
network
Sweeper
analyzer
Vector
network
analyzer
Detector
Measurement
Power
Detector
Measurement
splitter
apparatus
apparatus
Reference line Reference line
IEC 131/10 IEC 132/10
Figure 4a – Scalar network Figure 4b – Vector network
analyzer system analyzer system
Figure 4 – Schematic diagram of measurement equipments
 Page: 12 
62562 © IEC:2010 – 11 –
4.2 Measurement apparatus for complex permittivity
The structure of the cavity resonator used in the complex permittivity measurement is shown
in Figure 5. A cylindrical cavity containing two cupshaped parts is machined from a copper
block. The cavity resonator has D = 35 mm, H = 25 mm and a flange diameter D > 1,5 mm
f
for the measurement around 10 GHz. A specimen with diameter d > 1,2 × D is placed between
the two parts and clamped with clips to fix this structure. This cavity resonator is excited by
the two semirigid coaxial cables, each of which has a small loop at the top. The transmission
type resonator is constituted and undercoupled equally to the input and output loops with
setting S = S . The photograph is shown in Figure 6.
11 22
The resonance frequency f , halfpower band width f , and the insertion attenuation IA
0 BW 0
(dB) at f are measured using a network analyzer by means of the sweptfrequency method.
0
The value of Q is given by
u
Q f
L 0
= , = (30)
Q Q
u L
− IA (dB) / 20
0 f
1−10 BW
2M + t
22M M ++tt
CoaCoaxxiaiall
H = 2M
t
tt HH=2=2MM
Coaxial cable
CaCablblee
Dielectric
DiDieelleecctritricc
Conductor
ConCondduucctortor PTFE rPTPTFEFE iRiRing nngg
plate
PlPlatatee
IEC 133/10 IEC 134/10
Figure 5a – Resonator clamping Figure 5b – Empty cavity resonator
dielectric specimen
Figure 5 – Cavity resonator used for measurement
Thermal sensor
Thermal sensor
Cavity resonator
Cavity resonator
CoCaxoiaaxl cial cableable
CCololdd s sttageage
IEC 135/10
Figure 6 – Photograph of cavity resonator for measurement around 10 GHz
D >1,5 × D
DDf >>1.1.5×5×DD
ff
d >1,2 × D
d d >>1.2×1.2×DD
D
DD
 Page: 13 
TTMM111100
TTMM001100
– 12 – 62562 © IEC:2010
5 Measurement procedure
5.1 Preparation of measurement apparatus
Set up the measurement equipment and apparatus as shown in Figure 4. The cavity resonator
and dielectric specimens shall be kept in a clean and dry state, as high humidity degrades
unloaded Q. The relative humidity shall preferable be less than 60 %.
5.2 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.
5.3 Measurement of cavity parameters: D , H , σ , α , TCρ
r c
Rough values of f of the TE resonance mode and f of the TE resonance modes can
1 011 2 012
be estimated from the mode chart shown in Figure 7. Resonance peaks of cavity resonator
with 3D =5 mm and H = 25 mm are shown in Figure 8.
202020
151515
101010
5 55
0 00
0 0,5 1,0 1,5 2,0 2,5
0000.511511.522522.55
222
((D/D/HH))
(D/H)
IEC 136/10
Figure 7 – Mode chart of cavity resonator
TTEE331111
TTEE001111,,TTMM111111
11
TTEE2211
TTMM001111
TTEE111111
EE
TT 331122
,,TTMM
TTEE001122 111122
TTEE221122
TTMM001122
TTEE111122
TTEE221133
TTMM001133
TTEE111133
22
11.44 ==11.9966
2 –16 2 2
(f D) 22× 10 16 16 (H m22 ) 22
z
((fDfD)) ×1×100 (H(Hzz mm ))
 Page: 14 
62562 © IEC:2010 – 13 –
0
00
–10
1010
–20
2020
–30
3030
–40
4040
–50
5050
–60
6060
7070–70
–80
8080
10 11 12 13 14 15 16 17
1010 1111 1122 1313 1414 1515 1616 1717
f (GHz)
ff ( (GHGHzz))
IEC 137/10
Figure 8 – Resonance peaks of cavity resonator
Attach PTFE rings to the end plates of the cavity to separate the degenerate TM (ℓ=1, 2)
11ℓ
modes from the TE modes, as shown in Figure 5. Set the empty cavity and adjust the
01ℓ
insertion attenuation IA to be around 30 dB by changing the distance between two semirigid
0
cables, as shown in Figure 9.
22–28 88
f
0
f f
00
–30
3300 IA
0
IAIA
00
3 dB
3d3dBB
33–32 22
–34
3344
f f
f BWBW
BW
–36
3366
–38
3388
12,0444 12,0446 12,0448 12,0450 12,0452
1212.00444444 112.2.04044646 12.12.04044848 1212.045045 112.2.04045252
f (GHz)
FrFreeqquenuencycy ( (GHzGHz))
IEC 138/10
Figure 9 – Resonance frequency f , insertion
0
attenuation IA and halfpower band width f
0 BW
Measure f and Q of the TE resonance mode and measure f of the TE resonance
1 uc 011 2 012
modes. Calculate Q by using equation (30). Calculate the dimensions D , H , and σ of
u1 r
cavity resonator from equations (25), (26) and (28). Since the value of σ degrades due to
r
oxidation of the metal surface, it shall be measured periodically. Next, measure temperature
dependence of f and Q using the cavity placed in a temperaturestabilized oven. Calculate
1 uc
α and from equations (27) and (29).
TCρ
c
Insertion attenuation (dB)
IInnserserttiioon n attenuaattenuatintin ((ddBB)) IA (dB)
IAIA ( (dBdB))
TE
TETE211211211
TMTMTM1111 00
110
TE , TM
TETE011 ,M,M111
010111 111111
TE
TETE
112112112
TMTMTM
210212100
TM
211
TMTM211211
TE
TETE
121
...
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