IEC 61338-1-4:2005

IEC 61338-1-4 ®
Edition 1.0 2005-11
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Waveguide type dielectric resonators –
Part 1-4: General information and test conditions – Measurement method of
complex relative permittivity for dielectric resonator materials at millimetre-wave
frequency
Résonateurs diélectriques à modes guidés –
Partie 1-4: Informations générales et conditions d'essais – Méthode de mesure
de la permittivité relative complexe des matériaux des résonateurs diélectriques
fonctionnant à des fréquences millimétriques

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IEC 61338-1-4 ®
Edition 1.0 2005-11
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Waveguide type dielectric resonators –

Part 1-4: General information and test conditions – Measurement method of

complex relative permittivity for dielectric resonator materials at millimetre-

wave frequency
Résonateurs diélectriques à modes guidés –

Partie 1-4: Informations générales et conditions d'essais – Méthode de mesure

de la permittivité relative complexe des matériaux des résonateurs diélectriques

fonctionnant à des fréquences millimétriques

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX V
ICS 31.140 ISBN 978-2-8322-1000-0

– 2 – 61338-1-4  IEC:2005
CONTENTS
FOREWORD . 4

1 Scope and object . 6
2 Normative references . 6
3 Measurement parameter . 7
4 Dielectric rod resonator method excited by NRD-guide . 8
4.1 Measurement equipment and apparatus . 8
4.2 Theory and calculation equations . 11
4.3 Measurement procedure . 16
4.4 Example of measurement result . 19
5 Cut-off waveguide method excited by coaxial cables with small loops . 21
5.1 Measurement equipment and apparatus . 21
5.2 Theory and calculation equations . 23
5.3 Measurement procedure . 28

Annex A (informative) Errors on ε caused by air gap between dielectric specimen
r
and upper conducting plate . 30
Annex B (informative) Derivation of equation (15) for σ . 31
r
Bibliography . 33

Figure 1 – Schematic diagram of measurement equipment . 8
Figure 2 – Measurement apparatus of dielectric rod resonator method excited by
NRD-guide . 9
Figure 3 – Waveguide transducer from NRD-guide to waveguide . 11
Figure 4 – Configuration of a cylindrical dielectric rod resonator short-circuited at both
ends by two parallel conducting plates . 12
2 2
Figure 5 –Calculations of u and W as a function of v for TE , TE and TE
011 021 031
resonance modes . 13
Figure 6 –Configuration of reference dielectric resonator for measurement of σ of
r
conducting plates . 15
Figure 7 – Diameter d of TE , TE and TE mode resonators with resonance
011 021 031
frequency of 60 GHz . 18
Figure 8 – Diameter d of TE , TE and TE mode resonators with resonance
011 021 031
frequency of 77 GHz . 19
Figure 9 – Example of TE mode resonant peak . 20
Figure 10 – Measurement result of temperature dependence of f and ε' of sapphire . 21
Figure 11 – Measurement apparatus for cut-off waveguide method . 22
Figure 12 – Frequency response for the empty cavity with dimensions of d = 7 mm and
h = 31 mm . 24
Figure 13 – Correction term ∆ε /ε . 26
a
Figure 14 – Correction terms ∆A/ A and ∆B / B . 27

61338-1-4  IEC:2005 – 3 –
Figure 15 – Measurement apparatus for temperature coefficient of relative permittivity . 28
Figure 16 – Mode chart of TE and TE modes for an empty cavity . 29
011 013
Figure A.1 – Error on caused by air gap between dielectric specimen and upper
ε'
conducting plates . 30

Table 1 – Diameter of conducting plate . 10
Table 2 – Dimension of dielectric strip of NRD-guide . 10
Table 3 – Dimensions of waveguide transducer . 10
Table 4 – Dimensions of reference sapphire resonators and their partial electric energy

filling factor P and geometric factor G . 15
e
Table 5 – Diameter d of test specimens for 60 and 77 GHz measurement. Height h is
fixed to 2,25 mm and 1,80 mm for 60 GHz and 77 GHz measurement, respectively . 17
Table 6 – Measurement results of σ of conducting plates . 20
r
Table 7 – Measurement results of ε' and tan δ of sapphire and PTFE specimen . 20
Table 8 – Recommended dimensions for conducting cylinder. 23

– 4 – 61338-1-4  IEC:2005
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
WAVEGUIDE TYPE DIELECTRIC RESONATORS –

Part 1-4: General information and test conditions –
Measurement method of complex relative permittivity for
dielectric resonator materials at millimetre-wave 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
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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Publications.
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.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61338-1-4 has been prepared by IEC Technical committee 49:
Piezoelectric and dielectric devices for frequency control and selection.
This bilingual version (2014-02) corresponds to the monolingual English version, published in
2005-11.
The text of this standard is based on the following documents:
FDIS Report on voting
49/748/FDIS 49/751/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
The French version of this standard has not been voted upon.

61338-1-4  IEC:2005 – 5 –
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
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 millimetre-wave frequency
Part 2: Guidelines for oscillator and filter applications
Part 4: Sectional specification
Part 4-1: Blank detail specification
The committee has decided that the contents of this publication will remain unchanged until
the maintenance result 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.
– 6 – 61338-1-4  IEC:2005
WAVEGUIDE TYPE DIELECTRIC RESONATORS –

Part 1-4: General information and test conditions –
Measurement method of complex relative permittivity for
dielectric resonator materials at millimetre-wave frequency

1 Scope and object
This part of IEC 61338 describes the measurement method of dielectric properties for
dielectric resonator materials at millimetre-wave frequency.
This standard consists of two measurement methods: a) the dielectric rod resonator method
excited by NRD-guide (Non-Radiative Dielectric waveguide) and b) the cut-off waveguide
method excited by coaxial cables with small loops.
a) The dielectric rod resonator method excited by NRD-guide is similar to the dielectric rod
resonator method given in IEC 61338-1-3. This method has the following characteristics:
– a complete and exact mathematical solution of complex permittivity is given by
computer software;
–4
– the measurement error is less than 0,3 % for ε′ and less than 0,05 ×10 for tan δ;
– the applicable measuring ranges of complex permittivity for this method are as follows:
frequency: 30 GHz < f < 100 GHz;
relative permittivity: 2 < ε′ < 30;
–6 –2
loss factor: 10 < tan δ < 10 .
b) The cut-off waveguide method excited by coaxial cables with small loops uses a dielectric
mode. This method has the
plate sample placed in a circular cylinder of the TE
following characteristics:
– fringe effect is corrected using the correction charts on the basis of rigorous analysis;
–4
– the measurement error is less than 0,5 % for ε' and less than 0,05 ×10 for tan δ;
– the TCF is measured with high accuracy;
– the applicable measuring ranges of dielectric properties for this method are as follows:
frequency: 30 GHz < f < 100 GHz;
relative permittivity: 2 < ε′ < 30;
–6 –2
loss factor: 10 < tan δ < 10 .
2 Normative references
The following referenced documents are indispensable for the application 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, 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

61338-1-4  IEC:2005 – 7 –
3 Measurement parameter
The measuring parameters are defined as follows:

ε = ε '− jε" = D /(ε E) (1)
r 0
tan δ = ε" / ε' (2)
−
ε ε
T ref 6
–6
TCε = ×10   (1×10 /K) (3)
T −
ε T
ref ref
f − f
T ref 6
–6
TCF = ×10   (1×10 /K) (4)
T −
f
T
ref
ref
where
D is the electric flux density;
E is the electric field strength;
ε is the permittivity in a vacuum;

ε is the complex relative permittivity;
r

ε' and ε" are the real and imaginary components of the complex relative permittivity ε ;
r
TCε is the temperature coefficient of relative permittivity, and TCF being the
temperature coefficient of resonance frequency;
ε and ε are the real parts of the complex relative permittivity at temperature T and
T
ref
reference temperature T ( T = 20 °C to 25 °C), respectively;
ref ref
f and f are the resonance frequency at temperature T and T , respectively.
T ref ref
The TCF is related to TCε by the following equation:
TCF = − TCε − α (5)
where α is the coefficient of thermal expansion of the dielectric specimen.
It should be noted that this equation is satisfied when the 100 % of electro-magnetic energy in
the measuring resonance mode is concentrated inside the dielectric specimen. In the actual
−6
case, TCF deviates by several 10 /K from the calculated value, because some portion of
electro-magnetic energy is stored outside the dielectric specimen.

– 8 – 61338-1-4  IEC:2005
4 Dielectric rod resonator method excited by NRD-guide
4.1 Measurement equipment and apparatus
The measurement equipment and apparatus are as follows:
a) Measurement equipment
Figure 1 shows a schematic diagram of the equipment 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. A scalar network analyzer can be used for the
measurement, but a vector network analyzer has an advantage in precision of the
measurement data.
Scalar
network
Sweeper
analyzer
Isolator Detector
Measurement
Directional
× N Doubler Isolator Isolator Detector
apparatus
coupler
Reference line
IEC  2002/05
Figure 1a − Scalar network analyzer

Vector
network
analyzer
S–paramater S–paramater
Measurement
millimeter wave millimeter wave
apparatus
module module
Reference line
IEC  2003/05
Figure 1b − Vector network analyzer
Figure 1 – Schematic diagram of measurement equipment

61338-1-4  IEC:2005 – 9 –
b) Measurement apparatus
Figure 2a shows a configuration of measuring apparatus of dielectric rod resonator method
excited by NRD-guide. Figure 2b shows a cross-sectional view of the apparatus for measuring
' and tan  of a dielectric specimen with height h and d. The dielectric specimen is placed at
the centre of the apparatus between two parallel conducting plates, and coupled to input and
output NRD-guides. There remains a small air gap h between the dielectric specimen and
the upper conducting plate. For h < 50 m, the air gap can be neglected for the calculation
of ' (see Annex A).
Upper conducting plate
Waveguide
transducer
Conductor
for NRD–guide
Spacer
IEC  2004/05
Figure 2a – Configuration of apparatus
Dimensions in millimetres
24 mm 80 mm 24 mm
14 mm
w
s
Spacer d '
Upper conducting plate
Dielectric strip
Waveguide
for NRD–guide
transducer
h = h + h
c
Conductor
Lower conducting plate
for NRD–guide
Specimen
IEC  2005/05
Figure 2b – Apparatus for ' and tan  measurement
Upper conducting plate
h
IEC  2006/05
Figure 2c – Apparatus for TCF and TC measurement
Figure 2 – Measurement apparatus of dielectric rod resonator method
excited by NRD-guide
– 10 – 61338-1-4  IEC:2005
Figure 2c shows an apparatus for measuring the temperature coefficient of resonance
frequency TCF or that of relative permittivity TCε . For this measurement, the upper
conducting plate should be contacted to the dielectric specimen. h T hoef hdieeilgehcttr ic
S
strip for NRD-guide is designed to be smaller than height h of the dielectric specimen. The
upper conducting plate is set gently to touch the top face of the specimen, so that an
excessive pressure does not damage the surface of conducting plate.
As shown in Table 1, a diameter of the conducting plates in Figure 2b is determined by the
diameter of dielectric specimen. In this measurement method, the ε' and tan δ are calculated
under the condition that the conducting plates have an infinitely large diameter. As actual
conducting plates have a finite diameter, a part of electro-magnetic energy leaks outward the
conducting plates. Although this leaky energy shifts the resonance frequency and decreases
the unloaded Q, its contribution is negligibly small under the condition of d ’/d > 5.
Table 2 shows the example of dimensions for dielectric strips of NRD-guide in Figure 2b.
Dielectric strips of the NRD-guide are made of PTFE or cross-linked styrene copolymer.
Figure 3 shows a waveguide transducer that connects the measuring apparatus to the
measurement equipment with WR-15 or WR-10 waveguides. Table 3 shows the dimensions of
the waveguide transducers. As shown in Figure 2b, the end of the dielectric strip of the NRD-
guide is sharpened in the transducer.
Table 1 – Diameter of conducting plate
Diameter d ’
d ’ = 5d～10d
d : diameter of dielectric specimen
Material of conducting plate Copper or silver is recommended

Table 2 – Dimension of dielectric strip of NRD-guide
Material Measurement Height h Width w
s s
frequency range
mm mm
GHz
PTFE 55 to 65 2,25 2,50
75 to 80 1,80 1,90
ε'
（ = 2,0）
Cross-linked styrene 55 to 65 2,25 2,00
75 to 80 1,80 1,60
ε'
Copolymer ( = 2,5)
Table 3 – Dimensions of waveguide transducer
Waveguide Frequency range h w h
wg wg s
GHz mm mm mm
WR-15 55 to 65 3,80 1,90 2,25
WR-10 75 to 80 2,54 1,27 1,80
61338-1-4  IEC:2005 – 11 –
Flange
Waveguide
W
wg 12,0 mm
12,0 mm 12,0 mm
W
wg
12,0 mm
h
h
wg s
IEC  2007/05
Figure 3 – Waveguide transducer from NRD-guide to waveguide
4.2 Theory and calculation equations
4.2.1 Measurement of relative permittivity and loss factor
Figure 4 shows a configuration of the TE mode resonator. The cylindrical dielectric
0m1
specimen is short-circuited at both ends by the two parallel conducting plates. The values
ε'
and tan δ of the dielectric resonator are calculated from the resonance frequency f and
unloaded quality factor Q measured for the TE resonance mode. It is recommended to
u 0m1
use the TE , TE and TE resonance modes for the materials with ε' = 2 to 4, 4 to 20
011 021 031
and 20 to 30, respectively.
The resonance wavelength λ in free space and the guiding wavelength λ in the dielectric
g
transmission line are given by the following equations:
c
λ = ,   λ = 2h (6)
0 g
f
where c is the velocity of light in a vacuum (c = 2,997 9 × 10 m/s).
As described in 4.1b), the air gap ∆h can be neglected for the calculation of ε' and tan δ in
the case of ∆h < 50 µm . So, the height h is used in equation (6).

– 12 – 61338-1-4  IEC:2005
d '
d
Z
h
Conducting
ε
r
plates
Y
Dielectric rod
X
IEC  2008/05
Figure 4 – Configuration of a cylindrical dielectric rod resonator short-circuited
at both ends by two parallel conducting plates
The value v is calculated from λ and λ :
0 g
 
 
  λ
πd
2 0
 
 
 
v =  − 1 (7)
 
 
 
λ
λ
0 g
 
 
 
 
2 2
Using the value v , the value u is calculated:
J (u) K (v)
0 0
u = −v (8)
J (u) K (v)
1 1
where J (u) is the Bessel function of the first kind and K (v) is the modified Bessel function
n n
of the second kind. For any value of v, the m-th solution u exists between u and u ,
0m 1m
where J (u ) = 0 and J (u ) = 0. The first, second and third solution of m = 1, 2 and 3 are
0 0m 1 1m
shown in Figure 5.
61338-1-4  IEC:2005 – 13 –
82 1,2
TE
1,0
u
0,8
78 0,6
0,4
W
0,2
74 0,0
37 1,2
TE
1,0
u
0,8
0,6
0,4
W
0,2
30 0,0
11 1,2
TE
10 1,0
u
9 0,8
8 0,6
7 0,4
W
6 0,2
5 0,0
0 2 4 6 8 10 12 14 16
v
IEC  2009/05
2 2
Figure 5 –Calculations of u and W as a function of v
for TE , TE and TE resonance modes
011 021 031
2 2
The relative permittivity ε' is calculated by the following equation using the values v and u :
λ
 
0 2 2
ε'= (u + v )+1 (9)
 
πd
 
By using the measured unloaded Q, Q , the loss factor tan δ is calculated:
u
A A B′
tan δ = − BR = − (10)
S
Q Q
σ
u u r
2 2 2
u u u
W W W
– 14 – 61338-1-4  IEC:2005
where
πf µ πf µ
0 0
R (Ω) = = (11)
S
σ σ σ
0 r
W
A = 1+ (12)
ε'
 
λ πf µ
1+ W
0 0
 
B = ,   B' = B (13)
  2
λ σ
g 30π ε' 0
 
2 2
J (u) K ( v)K ( v) − K ( v)
0 2 1
W = ⋅ (14)
2 2
K (v) J (u) − J (u)J (u)
1 1 0 2
Here, R is the surface resistance of the conducting plates and σ is the conductivity of the
S
conducting plates. The relative conductivity σ is defined as σ = σ σ , where σ is the
r 0 r 0
conductivity of the international standard annealed copper ( σ = 5,8 ×10 S/m at 20 °C). µ
−7
is the permeability of conducting plates which has the value of µ = µ = 4π ×10 H/m for
non-magnetic conductors such as Cu or Ag.
The tan δ is calculated by using R and B , or, σ and B' . As σ is independent of
S r r
frequency and being a good indicator for the degradation level of conductivity caused by the
surface roughness or oxidation on conducting plates, σ is conveniently used.
r
The function W /ε' equals the ratio of electric-field energy stored outside to inside of the
dielectric specimen. The W equals zero when 100 % electric-field energy is concentrated
inside the specimen. The calculated results of W against v for the TE , TE and TE
011 021 031
resonance modes are shown in Figure 5.
4.2.2 Relative conductivity of conducting plates
The value of σ or R of the conducting plates is determined in advance of the calculation
r S
for the tan δ of dielectric specimens. The measurement accuracy of has vital importance
σ
r
on the accuracy of tan δ, because A/Q and B'/ σ in equation (10) have the same order of
u r
–4
magnitude for tan δ of 10 .
Figure 6 shows a configuration of the apparatus to measure the σ of conducting plates. Two
r
single crystal sapphires with the TE and TE resonance modes are used for measuring
021 02δ
the σ . The sapphires used as reference resonators have low tan δ at millimetre-wave
r
frequency and have the same ε' and tan δ. The axis of each rod is parallel to C-axis. The
dimensions of the TE and TE resonance modes are designed so that they have the
021 02δ
same resonance frequency. Table 4 shows the dimensions of sapphires for the resonance
frequency of 60 GHz and 77 GHz.

61338-1-4  IEC:2005 – 15 –
d
d
NRD guide
h
Sapphire rod
Sapphire rod
Conducting
plates
IEC  2010/05 IEC  2011/05
Electric field line
Magnetic field line
Figure 6a – TE mode resonator Figure 6b – TE mode resonator
02δ
Figure 6 –Configuration of reference dielectric resonator
for measurement of σ of conducting plates
r
Table 4 – Dimensions of reference sapphire resonators and their partial electric energy
filling factor P and geometric factor G
e
TE
02δ
TE
d h P G d h P G
e1 1 eδ δ
f
mm mm mm mm
Ω Ω
GHz
60 3,14 2,25 0,915 1 182 4,49 0,80 0,906 409
77 2,42 1,80 0,901 1 208 3,60 0,60 0,894 382

NOTE 1 Specifications for sapphire rod are as follows:
ε' =9,4, flatness: <0,005 mm, roughness of both ends: R < 0,01 , roughness of side of rod: R < 1 ,
µm µm
a a
perpendicular : <0,1°, axis: parallel to c-axis < 0,3°.
NOTE 2 Values P and G are effective for the standard sapphire rod having the tolerance of ε' to be 9,4 ± 0,1
eδ
δ
and the dimensional tolerance of d and h to be ±0,1 mm, respectively.
As shown in Figure 6, the TE mode resonator has a larger d/h ratio. The electromagnetic
02δ
field of this mode is more concentrated near the surface of the lower conductor compared with
the TE mode resonator. The different contribution of conductor loss on unloaded Q for
0m1 u
. High accuracy on is obtained by enlarging
each resonator enables the calculation of σ σ
r r
the difference of the Q values between the TE and TE mode resonators.
u 021 02δ
The resonance frequency and unloaded Q for the TE and TE mode resonators are
021 02δ
noted by using the subscripts 1 and : and for the TE resonator, and for
δ f Q f Q
01 u1 021 0δ u δ
the TE resonator. The reference TE and TE resonators have the same resonance
02δ 021 02δ
frequency = , and different unloaded Q, ( > ). The value at the resonance
f f Q Q σ
01 0δ u1 uδ r
frequency = is given by the following equation:
f f
01 0δ
 
πµf Q Q G P − G P
0 u1 uδ 1 e1 δ eδ
σ = σ / σ = ⋅ (15)
r 0  
σ G G Q P − Q P
0  1 δ u1 e1 uδ eδ 
– 16 – 61338-1-4  IEC:2005
where P and P are the partial electric energy filling factors of the reference TE and
eδ 021
e1
TE resonators, respectively. G and G being the geometric factors for each reference
02δ 1 δ
resonators. Calculated values of P and G for the reference sapphire resonators with ε' = 9,4
e
are given in Table 4. These values are applicable when the actual dimensions agree with the
designed dimensions within the deviation of 0,01 mm. The derivation of equation (15) and the
formulas for P and G are given in Annex B.
NOTE 3 Loss factor of reference resonators is calculated by the following equation if needed.
1 G Q − G Q
1 uδ δ u1
tan δ =tan δ = ⋅ (16)
1 δ
Q Q G P G P
−
u1 uδ 1 e1 δ e δ
4.2.3 Temperature coefficient of resonance frequency and relative permittivity
The temperature coefficient of resonance frequency TCF is given by measuring the
resonance frequency at temperature T and reference temperature T using equation (4). In
ref
the same way, temperature coefficient of relative permittivity TCε is given by calculating
relative permittivity at temperature T and reference temperature T using equation (3).
ref
A dielectric material generally has nonlinear dependence of relative permittivity on
temperature. A procedure to deal with this non-linear temperature dependence of resonance
frequency or relative permittivity is described in IEC 61338-1-3.
4.2.4 Temperature dependence of loss factor
The temperature dependence of tan δ is given by measuring the tan δ at various temperatures.
For the calculation of tan δ at each temperature, the temperature dependence of σ is needed.
r
The temperature dependence of conductivity for the annealed copper in conformity with the
international standard is given as follows.
5,8 ×10
σ (T ) = (S/m) (17)
−3
1+ 3,93 ×10 (T − 20)
When the σ at reference temperature T is measured, one can use following equation for
r ref
as the first order approximation of σ at temperature T .
r
σ
r
σ (T) = (%) (18)
r
−3
1+ 3,93 ×10 (T − T )
ref
4.3 Measurement procedure
The preparation of dielectric specimens and measurement procedure are as follows:
a) Preparation of reference sapphire resonator
Prepare the reference sapphire resonators with the dimensions shown in Table 4. In order to
minimize the measurement error on σ of the conducting plates, their c-axes shall be parallel
r
to z-direction, and both ends of the rod shall be polished parallel to each other and
perpendicular to c-axis.
61338-1-4  IEC:2005 – 17 –
b) Preparation of test specimens
The TE mode dielectric resonators have very small dimensions for the measurement at
millimetre-wave frequency. It is preferable to use the TE or TE resonance modes
021 031
especially for measuring the high- ε ' materials. Table 5 shows recommended diameters for
the materials with ε ' from 2 to 40. The height h is fixed to 2,25 mm and 1,80 mm for the
measurement at 60 GHz and 77 GHz, respectively. Figures 7 and 8 show the diameter d of
the TE , TE and TE mode resonators with resonance frequencies 60 GHz and 77 GHz,
011 021 031
respectively.
Table 5 – Diameter d of test specimens for 60 and 77 GHz measurement. Height h is
fixed to 2,25 mm and 1,80 mm for 60 GHz and 77 GHz measurement, respectively
d (mm) d (mm)
ε '
f = 60 GHz f = 77 GHz
0 0
TE TE TE TE TE TE
011 021 031 011 021 031
2,0 5,05 - 3,68
2,5 3,80 - 2,83
3,0 3,16 - 2,38
3,5 2,75 - 2,08
4,0 2,47 5,49 1,88 4,20
5,0 - 4,67  3,59
6,0 - 4,14  3,19
8,0 - 3,45  2,67
10,0 - 3,02  2,34
12,0 2,72  2,11
14,0 2,50  1,93
16,0 2,32  1,80
18,0 2,17  1,69
20,0 2,05 3,21 1,59 2,49
25,0  2,85  2,21
30,0  2,58  2,01
35,0  2,38  1,85
40,0  2,22  1,73
c) Preparation of measurement apparatus
Set up the measurement equipment and apparatus as shown in Figures 1 and 2. All measure-
ment equipments, apparatus and dielectric specimens shall be kept in a clean, dry state as
high humidity degrades unloaded Q. The relative humidity is preferable to be less than 60 %.
d) Measurement of reference level
Measure the through level of transmission power, reference level. Connect the input and
output NRD-guides with a dielectric strip, the length of which is 14 mm, and the height h and
s
width W shown in Table 2. Measure the through transmission power level over the
s
measurement frequency range.
– 18 – 61338-1-4  IEC:2005
e) Measurement of conductivity of the conducting plates
Connect the measurement apparatus as shown in Figure 6. Insert the TE sapphire
resonator at the center of the conducting plates and adjust the distance between resonator
and NRD-guide strip.
Figure 9 shows an example of the TE mode resonance peak. The identification of this peak
is relatively easy, since the TM or hybrid resonance modes are suppressed in the resonator
excited by the NRD-guide. This peak is identified as it shifts downward in frequency when the
upper plate separates slowly from top face of the resonator.
Adjust the insertion attenuation IA (dB) of the resonance peak to be from 15 dB and 30 dB
from the reference level by changing the distance between sapphire resonators and NRD-
guide strip. Measure the and the half-power band-width of the TE mode resonator.
f ∆f
01 021
Calculate the unloaded Q, , using the following equation.
Q
u1
f / ∆f
(19)
Q =
u
−IA / 20
1−10
In a similar way, insert the TE mode sapphire resonator in the apparatus and measure the
02δ
and .
f Q
0δ uδ
In order to improve the measurement accuracy of σ , repeat this measurement several times
r
for the TE and TE mode resonators. Using the mean values of , , and ,
f Q f Q
021 02δ 01 u1 0δ uδ
calculate σ using equation (15). As the of the conducting plates degrades day by day due
σ
r r
to wear or oxidation of the metal surface, this measurement shall be repeated every time prior
to the measurement of test specimens. It is preferable to polish the surface of the conducting
degrades more than 10 %.
plates when the σ
r
f) Measurement of complex permittivity of test specimen
In a similar way, measure the f and Q of the TE resonance mode of the test specimens.
0 u 0m1
Calculate their ε ' and tan δ from equation (10).

d
ε’
h = 2,25 mm
TE
TE
3 011
TE
0 10 20 30 40
ε’
IEC  2012/05
Figure 7 – Diameter d of TE , TE and TE mode resonators
011 021 031
with resonance frequency of 60 GHz
d  mm
61338-1-4  IEC:2005 – 19 –
d
ε’
h = 1,80 mm
TE
TE
TE
0 10 20 30 40
ε’
IEC  2013/05
Figure 8 – Diameter d of TE , TE and TE mode resonators
011 021 031
with resonance frequency of 77 GHz
4.4 Example of measurement result
a) Measurement result of σ of conducting plates
r
Table 6 shows a measurement result of of conducting plates at 60 GHz. The reference
σ
r
sapphire resonators with dimensions of 3,13 mm ×2,25 mm and 4,49 mm ×0,87 mm were
used for the measurement. The height h = 2,279 mm of the apparatus was used for the
C
calculation of σ . The measurement errors are shown in each column using the term “ ± ”.
r
b) Measurement results of and tan δ
ε'
Table 7 shows the measurement results of and tan δ at 57 GHz. Sapphire and PTFE were
ε'
used as the test specimens. The values σ = 80,5 % and h = 2,323 were used for the
C
r
calculation.
c) Measurement results of TCF and TCε
Figure 10 shows a measurement result of temperature dependence for resonance frequency
and relative permittivity of sapphire crystal at 60 GHz.

d  mm
– 20 – 61338-1-4  IEC:2005
–10
–15
–20
–25
–30
–35
–40
–45
–50
55 56 57 58 59 60
Frequency  GHz
IEC  2014/05
Figure 9 – Example of TE mode resonant peak
Table 6 – Measurement results of σ of conducting plates
r
Reference d h P G f IA
Q tan δ
e 0 0
u
σ
r
resonators
–5
mm mm GHz dB
（Mode）
%
Sapphire 3,130 2,250 0,910 1 197 59,876 19,0 8 782
(TE ) ±0,005 ±0,001 ±0,008 ±1,0 ±119 87 6,2
±4 ±0,3
Sapphire 4,490 0,807 0,907 413 59,692 19,0 4510
±0,004 ±0,001 ±0,047 ±0,3 ±50
(TE )
02δ
Temperature： 20 °C, Humidity： 50 %
Table 7 – Measurement results of ε' and tan δ of sapphire and PTFE specimen
Specimen Mode d  h f IA Q δ
tan
0 0 u
ε'
–5
mm mm GHz dB
Sapphire -1 TE 3,276 2,269 57,540 21,6 8 868 9,417 5,80
±0,001 ±0,001 ±0,003 ±0,1 ±14 ±0,005 ±0,05
Sapphire -2 TE 3,277 2,261 57,528 21,7 8 972 9,416 5,65
±0,001 ±0,001 ±0,010 ±0,1 ±40 ±0,007 ±0,06
PTFE -1 TE 5,456 2,267 56,610 20,5 2 820 2,065 18,8
±0,005 ±0,002 ±0,010 ±0,1 ±12 ±0,002 ±0,2
PTFE -2 TE 5,443 2,266 56,640 20,1 2 816 2,066 18,9
±0,004 ±0,002 ±0,013 ±0,1 ±14 ±0,002 ±0,3
Temperature： 25 °C, Humidity： 50 %

I.A.  dB
61338-1-4  IEC:2005 – 21 –
9,48
–6
1st: TCε = 86,9 ⋅ 10 /°C
–6
2nd: TCε = 85,8 ⋅ 10 /°C
9,46
9,44
9,42
9,40
9,38
9,36
–50 0 50 100
Temperature  °C
IEC  2015/05
Figure 10a – Resonance frequency

60,25
1st
60,20
2nd
60,15
60,10
60,05
60,00
59,95
59,90
59,85
–50 0 50 100
Temperature  °C
IEC  2016/05
Figure 10b – Relative permittivity
Figure 10 – Measurement result of temperature dependence of f and ε' of sapphire
5 Cut-off waveguide method excited by coaxial cables with small loops
5.1 Measurement equipment and apparatus
The measurement equipment and apparatus are as follows:
a) Measurement equipment
The same measurement equipment used for the dielectric rod resonator method is used for
the cut-off waveguide method (Figure 1). 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.
f  GHz ε'
o
– 22 – 61338-1-4  IEC:2005
b) Measurement apparatus
Figure 11a shows an apparatus for measuri
...