IEC TR 63307:2020

IEC TR 63307 ®
Edition 1.0 2020-11
TECHNICAL
REPORT
colour
inside
Measurement methods of the complex relative permeability and permittivity of
noise suppression sheet
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IEC TR 63307 ®
Edition 1.0 2020-11
TECHNICAL
REPORT
colour
inside
Measurement methods of the complex relative permeability and permittivity of

noise suppression sheet
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.100.10 ISBN 978-2-8322-9085-9

– 2 – IEC TR 63307:2020 © IEC 2020
CONTENTS
FOREWORD . 6
INTRODUCTION . 8
1 Scope . 9
2 Normative references . 9
3 Terms, definitions and symbols. 9
3.1 Terms and definitions . 9
3.2 Symbols . 9
4 General . 10
5 Measurement methods . 11
5.1 Inductance method . 11
5.1.1 Measurement parameters . 11
5.1.2 Measurement frequency and accuracy . 11
5.1.3 Measurement principle. 12
5.1.4 Test sample . 14
5.1.5 Test fixture . 14
5.1.6 Measurement environment . 14
5.1.7 Measurement uncertainty. 14
5.1.8 Measurement system . 16
5.1.9 Measurement procedure . 16
5.1.10 Example of measurement results . 16
5.1.11 Remarks . 17
5.2 Nicolson Ross Weir method . 18
5.2.1 Principle . 18
5.2.2 Measurement frequency and accuracy . 20
5.2.3 Measurement parameters . 20
5.2.4 Test sample . 20
5.2.5 Measurement environment . 21
5.2.6 Measurement uncertainly . 21
5.2.7 Measurement system . 22
5.2.8 Test fixture . 22
5.2.9 Measurement procedure . 22
5.2.10 Example of measurement results . 23
5.2.11 Remarks . 23
5.3 Short-circuited microstrip line method . 24
5.3.1 Principle . 24
5.3.2 Measurement frequency and accuracy . 25
5.3.3 Measurement parameters . 25
5.3.4 Test sample . 25
5.3.5 Measurement environment . 26
5.3.6 Measurement system . 26
5.3.7 Test fixture (MSL jig) . 26
5.3.8 Measurement procedure . 27
5.3.9 Results (example) . 27
5.3.10 Remarks . 28
5.4 Short-circuited coaxial line method . 28
5.4.1 Principle . 28

5.4.2 Measurement frequency and accuracy . 29
5.4.3 Measurement parameters . 30
5.4.4 Test sample . 30
5.4.5 Measurement environments . 30
5.4.6 Measurement system . 30
5.4.7 Test fixture (coax jig) . 31
5.4.8 Measurement procedure . 31
5.4.9 Results (example) . 32
5.4.10 Remarks . 33
5.5 Shielded loop coil method . 33
5.5.1 Measurement principle. 33
5.5.2 Measurement frequency and accuracy . 38
5.5.3 Measurement parameters . 39
5.5.4 NSS sample dimension and recommendation . 39
5.5.5 Measurement environment . 40
5.5.6 Measurement system . 40
5.5.7 Measurement procedure . 40
5.5.8 Measurement results . 41
5.5.9 Summary . 44
5.6 Harmonic resonance cavity perturbation method . 45
5.6.1 Theory . 45
5.6.2 Permeability evaluation . 46
5.6.3 Permittivity evaluation. 53
Annex A (informative) Derivation of the complex relative permeability of the
inductance method . 59
Annex B (informative) Short-circuited microstrip line method. 61
B.1 Fundamental calculation . 61
B.2 Determination of C and G . 62
S S
B.3 Determination of demagnetization factor N and coupling coefficient η . 64
B.4 Analysis with the software to determine the μ . 64
r
Annex C (informative) Short-circuited coaxial line method . 66
C.1 Fundamental calculation to determine μ . 66
r
C.2 Open-circuited coaxial line . 67
C.2.1 Measurement of effective permittivity ε (ε’ – jε” ) . 67
r r r
C.2.2 Example of the complex permittivity . 70
C.3 Remarks on lumped element approximation . 71
Bibliography . 73

Figure 1 – In-plane and perpendicular measurement direction of NSS sample . 11
Figure 2 – Toroidal-shaped sample cut from the NSS . 12
Figure 3 – Test fixture with a toroidal-shaped NSS sample . 13
Figure 4 – Equivalent circuit model of the test fixture . 13
Figure 5 – Schematic diagram of measurement system . 16
Figure 6 – Measurement results of NSS samples . 17
Figure 7 – Schematic diagram of a test fixture with a sample and signal flow graph . 18
Figure 8 – Cross section of coaxial line with NSS . 20
Figure 9 – Dimensions of test sample . 21

– 4 – IEC TR 63307:2020 © IEC 2020
Figure 10 – Schematic diagram of equipment system for measurement . 22
Figure 11 – Specification for test fixture of a 7 mm coaxial transmission line . 22
Figure 12 – Measurement results of noise suppression sheet . 23
Figure 13 – Equivalent circuits for the MSL . 25
Figure 14 – Rectangular shape of NSS sample . 26
Figure 15 – Measurement system . 26
Figure 16 – Short-circuited microstrip line test fixture (MSL jig) . 27
Figure 17 – Complex relative permeability of a NSS sample C with 0,236 mm
thickness, as measured at N = 0 (and η = 0,135 2) and corrected by demagnetization

factor N = 0,037 (and η = 0,135 2) . 28
Figure 18 – Equivalent circuits for the coax jig . 29
Figure 19 – Toroidal shape of NSS sample . 30
Figure 20 – Measurement system . 31
Figure 21 – Short-circuited coaxial line test fixture (coax jig) . 31
Figure 22 – Complex relative permeability of a NSS sample A with 0,29 mm thickness,
as measured and corrected by the permittivity . 32
Figure 23 – Complex relative permeability of a NSS sample B with 0,25 mm thickness,
as measured and corrected by the effective permittivity . 33
Figure 24 – Structure of shielded loop coil . 34
Figure 25 – Shielded loop coil and NSS sample arrangement . 34
Figure 26 – Whole structure of the measuring unit of the equipment . 35
Figure 27 – DC magnetization curve . 38
Figure 28 – Estimation of absolute value correction coefficient M’ . 38
s
Figure 29 – Recommended shape of NSS sample . 39
Figure 30 – Block diagram of measurement system . 40
Figure 31 – Measured complex relative permeability as a function of the size of a NSS
sheet (Sample A-01) . 42
Figure 32 – Measured complex relative permeability as a function of the size of a NSS
sheet (Sample B-01) . 43
Figure 33 – Measured complex relative permeability of a NSS sheet as a function of
DC bias field intensity (Sample A-02) . 43
Figure 34 – Measured complex relative permeability after absolute value calibration
(Sample A-01) . 44
Figure 35 – Measured complex relative permeability after absolute value calibration
(Sample B-01) . 44
Figure 36 – Electromagnetic flux to evaluate permeability in the harmonic resonance
cavity resonator . 47
Figure 37 – Example of the resonance characteristics change . 47
Figure 38 – Cavity resonator for 3,6 GHz to 7,2 GHz . 48
Figure 39 – Cavity resonator for 0,25 GHz to 2 GHz . 48
Figure 40 – Examples of resonance frequencies . 49
Figure 41 – Example of the resonance curves of a harmonic resonance cavity . 49
Figure 42 – Examples of samples . 50
Figure 43 – Measuring system . 50
Figure 44 – Sample installation in the cavity for the permeability measurement . 51
Figure 45 – Measured results of the permeability for Sample A and B and a copper rod . 53

Figure 46 – Electromagnetic flux to evaluate permittivity in the harmonic resonance
cavity resonator . 53
Figure 47 – Sample installation in the cavity for the permittivity measurement . 55
Figure 48 – Adjustment procedure and adjusted results . 56
Figure 49 – Measured results of the permittivity for the two samples, A and B . 58
Figure B.1 – Complex relative permeabilities of Sample C with 0,236 mm thickness for
toroidal shape and rectangular shape corrected by N = 0,037 and η = 0,135 2 . 64
Figure B.2 – Complex relative permeabilities of Sample C with 0,236 mm thickness for
rectangular shape corrected by N = 0, 0,018 5 and 0,037 with η = 0,135 2 . 65
Figure B.3 – Complex relative permeabilities of Sample C with 0,236 mm thickness for
rectangular shape corrected by η = 0,225 3, 0,169 and 0,135 2 with N = 0,037 . 65
Figure C.1 – Open-circuited coaxial line jig . 68
Figure C.2 – Equivalent circuits for the open-circuited coaxial line . 68
Figure C.3 – Complex relative permittivity of NSS Sample A with 0,29 mm thickness,
as measured and corrected by the permeability . 71
Figure C.4 – Complex relative permittivity of NSS Sample B with 0,25 mm thickness,
as measured and corrected by the permeability . 71
Figure C.5 – Dependence of phase shift βt on frequency . 72

Table 1 – Measurement method and frequency . 10
Table 2 – Measurement sample table. 42

– 6 – IEC TR 63307:2020 © IEC 2020
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT METHODS OF THE COMPLEX RELATIVE
PERMEABILITY AND PERMITTIVITY OF NOISE SUPPRESSION SHEET

FOREWORD
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all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
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example "state of the art".
IEC TR 63307, which is a technical report, has been prepared by IEC technical committee 51:
Magnetic components, ferrite and magnetic powder materials.
The text of this Technical Specification is based on the following documents:
Draft TR Report on voting
51/1349/DTR 51/1356/RVDTR
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this Technical Report is English.

This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
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The committee has decided that the contents of this document will remain unchanged until the
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the specific document. At this date, the document will be
• reconfirmed,
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• amended.
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of its contents. Users should therefore print this document using a colour printer.

– 8 – IEC TR 63307:2020 © IEC 2020
INTRODUCTION
Noise suppression sheet (NSS) is used near the source of high frequency electromagnetic noise,
path of noise propagation and source of emission. It is used like a patch and is different from
an electromagnetic wave absorber in free space. IEC 62333-2 specifies five measurement
methods in order to estimate the effect of NSS. To evaluate the effect by computer simulation,
it is indispensable to know the frequency characteristics of both permeability and permittivity.
And to make a rough estimate of the noise suppression effect of NSS, it is useful to understand
effective permeability and effective permittivity, which are the permeability and permittivity of
an actually used shape.
As most NSSs are flexible, and both complex relative permeability and complex relative
permittivity have anisotropy, careful study and understanding of the principles are indispensable
for the measurement of the frequency characteristics of permeability and permittivity.
There are various methods to measure permeability and permittivity under the frequency range
where NSS is used. This document is intended to be used for the proper selection of the
measurement method and the preparation of the test sample to achieve the above purpose
when measuring permeability and permittivity, the two parameters which largely influence the
noise suppression effect of the NSS.

MEASUREMENT METHODS OF THE COMPLEX RELATIVE
PERMEABILITY AND PERMITTIVITY OF NOISE SUPPRESSION SHEET

1 Scope
This document provides guidelines on the methods for measuring the frequency characteristics
of permeability and permittivity in the frequency range of 1 MHz to 6 GHz for a noise
suppression sheet for each electromagnetic noise countermeasure.
2 Normative references
There are no normative references in this document.
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
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
3.1.1
noise suppression
suppression which consists of signal decoupling, radiation suppression and attenuation of the
transmission power of noise by an electronic product
Note 1 to entry: Each function above is achieved by absorption and/or shielding.
3.1.2
noise suppression sheet
NSS
sheet which enables noise suppression and is composed of magnetic, dielectric or conductive
material with electromagnetic losses
EXAMPLE Sheet made of soft magnetic metal powder and resin or rubber.
3.1.3
suppression ratio
ratio of the noise level with and without suppression sheets
Note 1 to entry: The suppression ratio is classified into intra-decoupling ratio, inter-decoupling ratio, transmission
attenuation power ratio and radiation suppression ratio. It is expressed in dB.
3.2 Symbols
µ complex relative permeability
r
μ′ real part of complex relative permeability
r
μ′′ imaginary part of complex relative permeability
r
ε complex relative permittivity
r
– 10 – IEC TR 63307:2020 © IEC 2020
ε′ real part of complex relative permittivity
r
ε″ imaginary part of complex relative permittivity
r
Z impedance (Ω)
ω = 2πf angular frequency (rad/s)
I current (A)
B = µ µ H magnetic flux density (T)
0 r
H magnetic field strength (A/m)
−7
µ
permeability of vacuum (4π × 10 H/m)
f frequency
4 General
Composite materials made by embedding magnetic metal flakes in a plastic sheet are widely
used in PCs or mobile phone handsets. This sheet is well known as a noise suppression sheet
(NSS) and is used to reduce unwanted signals in transmission lines or unwanted couplings
between circuit elements in the devices described above.
Electromagnetic compatibility (EMC) designers recently have been using simulations for the
design of the circuit boards for PCs and mobile phone handsets. In these simulations, it is
important to know the complex relative permeability μ and the complex relative permittivity ε
r r
of NSS. This document shows the six measurement methods of μ and ε of NSS. The
r r
measurement frequency range is from 1 MHz to 6 GHz, as shown in Table 1. Figure 1 illustrates
the in-plane and perpendicular measurement direction of Table 1.
Table 1 – Measurement method and frequency
µ and ε
r r
Frequency
In-plane Perpendicular
Method Name
1 MHz to
ε
µ ε µ
100 MHz 1 GHz 10 GHz 100 GHz
r
r r r
10 MHz
1 MHz to 1 GHz
5.1 Inductance ○
5.2 Nicolson
500 MHz to
○ ○
Ross Weir
5.3 Short-
10 MHz to 10 GHz
circuited micro ○
strip line
5.4 Short-
1 MHz to 18 GHz
circuited coaxial ○ ○
line
5.5 Shielded
1 MHz to 10 GHz
○
loop coil
250 MHz to 18 GHz
○ ○
5.6 Harmonic
resonance cavity
perturbation
1,8 MHz
○ ○
Range of frequency (1 MHz to 6 GHz)

Figure 1 – In-plane and perpendicular measurement direction of NSS sample
5 Measurement methods
5.1 Inductance method
5.1.1 Measurement parameters
The measurement parameters of a magnetic material are defined as follows:
′ ′′  (1)
μ μμ− j
rr r
where
′ ′′
μ and μ are the real part and the imaginary part of the complex relative permeability,
r r
respectively.
5.1.2 Measurement frequency and accuracy
The objective of this method is to evaluate the in-plane permeability of toroidal-shaped thin
NSS samples shown in Figure 2 and is applicable for the measurements under the following
conditions:
frequency : 1 MHz ≤ f ≤ 1 GHz
relative permeability : ′
1 ≤ μ ≤ 1 000
r
′′
0 ≤ μ ≤ 1 000
r
accuracy : ′
value error ±20 % for μ
r
′′
value error ±20 % for μ
r
The measurement frequency range is affected by the dimensions and the permeability values
of the NSS sample. The higher the permittivity, the lower the upper limit of the frequency range
will be.
=
– 12 – IEC TR 63307:2020 © IEC 2020

Figure 2 – Toroidal-shaped sample cut from the NSS
5.1.3 Measurement principle
The test fixture shown in Figure 3 forms the ideal one-turn inductor. The self-inductance is given
by
Z 1
= B ds (2)
∫
S
jωI
where
Z is the impedance (Ω);
ω = 2πf is the angular frequency (rad/s);
I is the current (A);
B = µ µ H is the magnetic flux density (T);
0 r
H is the Magnetic field strength (A/m);
−7
µ is the permeability of vacuum (4π × 10 H/m);
S is the surface shown in Figure 3.
Therefore, the complex relative permeability is
ZZ− Z
22ππm sm NSS
μ 1 +1 (3)
r
μ jjωF μFω
or
2π xx− 2π x
m sm NSS
(4)
′
µ 11+
r
µ ωFFµω
2π rr− 2π r
m sm NSS
(5)
′′
µ
r
µ ωFFµω
where
Z = r + jx is the measured impedance with a sample;
m m m
Z = r + jx is the measured impedance without a sample (in short state);
sm sm sm
Z = r + jx is the impedance of a NSS sample;
NSS NSS NSS
==
+= =
+= =
b

is the shape factor of a sample, inner diameter a, outer diameter b, and
F=t ln

a
thickness t.
Z is used to minimize errors due to residual impedance by compensation. The equivalent
sm
circuit model of the test fixture is shown in Figure 4. g + jb is the admittance of the test fixture
p p
and its effect can be neglected in a simplified case. Therefore, the impedance Z of a NSS
NSS
sample is Z − Z .
m sm
The derivation procedure is shown in detail in Annex A.

a) Structure b) Parameters
Figure 3 – Test fixture with a toroidal-shaped NSS sample

Figure 4 – Equivalent circuit model of the test fixture

– 14 – IEC TR 63307:2020 © IEC 2020
5.1.4 Test sample
The sample shall be fabricated in the shape of a toroidal ring. A good round sample can be
obtained by a punching tool. The preferable sample size is as follows:
For the fixture of 24 mm diameter in 5.1.5:
inner diameter :  a ≥ 3,1 mm
outer diameter :  b ≤ 8 mm
thickness :  t ≤ 3 mm
For the fixture of 30 mm diameter:
inner diameter :  a ≥ 5 mm
outer diameter :  b ≤ 20 mm
thickness :  t ≤ 8,5 mm
Each parameter should be measured with a precision of less than 1/100 mm using a micrometer.
5.1.5 Test fixture
The structure of the test fixture is shown in Figure 3. The test fixture is a conductive shield
surrounding the central conductor and terminates in a short circuit. The connector of the test
fixture is connected through the coaxial connector to the measurement equipment. The
alignment error of the NSS sample from the centre affects the measurement results, so the use
of a sample holder is recommended to place a sample coaxially. Examples of features of a test
fixture are as follows:
diameter : b = 24 mm
height : t = 30 mm
resistance : r = 100 mΩ
sm
inductance : x /ω = 1,0 nH
sm
or
= 30 mm
diameter : b
height : t = 35 mm
resistance : r = 300 mΩ
sm
inductance : x /ω = 5,5 nH
sm
The diameter of a centre conductor is a = 3 mm for both fixtures.
5.1.6 Measurement environment
The fixture and the samples shall be kept in a clean and dry state. The room temperature and
the relative humidity shall preferably be 23 °C ± 5 °C and less than 60 %.
5.1.7 Measurement uncertainty
'
and ′′ , and , are estimated as the combined
Measurement uncertainties of u µ u µ′ u µ′′
( ) ( )
r
r r r
standard uncertainty and given respectively by

2 2
∂∂µµ′′
2 2 2
rr
u µ′= ux++ux
( ) ( ) ( )

r  m sm
∂∂xx
m sm

2 22
′ ′′
∂µ 2 ∂∂µµ22
r rr
(6)
u a ++ub ut
( ) ( ) ()
  
∂∂ab ∂t
  
2 2
2 22
 ′′ ′′ ′′ ′′ ′′
22∂∂µµ 2 ∂µ 2 ∂∂µµ22
rr r rr
(7)
u µ′′= ur+ ur+ u a ++ub ut
( ) ( ) ( ) ( ) ( ) ()
r   m  sm   
∂∂rr ∂∂ab ∂t
  
 m sm
where u(x ), u(x ), u(r ), u(r ), u(a), u(b) and u(t) are standard uncertainties of x , x , r ,
m sm m sm m sm m
r , a, b and t, respectively. The sensitivity coefficients in Formulae (6) and (7) are as follows:
sm
∂µ′ 2π1
r
(8)
=
∂x µωF
m0
′
∂µ 2π1
r
(9)
−

∂x µωF
sm 0
′
∂µ 2π xx− t
r m sm
(10)
=
∂aaµω F
′ xx− 
∂µ 2π t
r m sm
(11)
−

∂b µω bF

′ − 
∂µ 2π1xx
m sm
r
(12)
−

∂htµω F

′′
∂µ
2π1
r
(13)
=
∂r µωF
m0
∂µ′′
2π1
r
(14)
−

∂r µωF
sm 0
∂µ′′
rr−
2π t
r
m sm
(15)
=
∂aaµω F
∂µ′′

2π rr− t
r
m sm
(16)
−

∂bbµω F
0 
∂µ′′
2π1rr− 
r
m sm
(17)
−

∂htµω F
0 
=
=
=
=
=
=
– 16 – IEC TR 63307:2020 © IEC 2020
5.1.8 Measurement system
Figure 5 shows a schematic diagram of the measurement system. For the measurement of the
magnetic properties, the information on the ratio of the current and voltage values and the
phase difference between current and voltage are needed. An impedance analyzer, LCR meter
or vector network analyzer (VNA) can be used for the measurement.

Figure 5 – Schematic diagram of measurement system
5.1.9 Measurement procedure
1) Calibrate the measurement equipment
When the measurement equipment is turned ON, the calibration shall be performed with the
proper calibration kit to measure within its specified measurement accuracy. The
measurement system shall be warmed up sufficiently before starting the calibration.
2) Connect the test fixture
Connect the connector of the test fixture to the coaxial connector of the previously calibrated
measurement equipment.
3) Place the sample holder and measure the impedance Z
sm
Place only the sample holder in the test fixture. Enter the measurement parameters,
frequency range and oscillator output voltage level and other values, into the measurement
equipment and measure the impedance Z of the test fixture.
sm
4) Place the NSS sample and measure the impedance Z
m
Place the toroidal-shaped NSS sample with the sample holder in the test fixture coaxially
and measure the impedance Z of the test fixture with a sample.
m
5) Calculate the relative permeability µ′ and µ′′ and uncertainties ′ and ′′
u(µ) u(µ)
r r r r
Calculate the values of ′ and ′′ by using Formula (4) and Formula (5), respectively. The
µ µ
r r
measurement uncertainties are also calculated by using Formula (6) to Formula (17).
5.1.10 Example of measurement results
The measurement results of µ′ and µ′′ for a NSS (sample A and B) are shown in Figure 6. The
r r
parameters of the sample are a = 3,00 mm, b = 7,00 mm and t = 0,20 mm (sample A) or 0,25 mm
(sample B), and the oscillator output voltage level, about 0,1 V, is selected in order not to affect
the results.
a) Sample A (t = 0,20mm)
b) Sample B (t = 0,25mm)
Figure 6 – Measurement results of NSS samples
5.1.11 Remarks
Subclause 5.1 provides some helpful information on measuring the magnetic properties of
toroidal-shaped NSS samples using the inductance method.
1) The test sample should be made correctly in a toroidal shape and placed in the test fixture
coaxially.
2) The measurement accuracy depends on the measured impedance values and gets worse in
low frequencies because the measurement error increases with a decrease in the frequency.

– 18 – IEC TR 63307:2020 © IEC 2020
3) The use of an impedance analyzer is recommended to measure the impedance because the
impedance analyzer has the advantages of higher accuracy and wider impedance
measurement range than a network analyzer.
′ ′′
4) The measurement results of µ and µ may be obtained after measuring the impedance
r r
Z and Z if the material analyzer is used. The measurement results of the impedance Z
sm m sm
and Z are not displayed because the software installed on the analyzer calculates and
m
compensates the measurement results.
5) A sample with a low permeability or a thin thickness leads to measurement error. It is difficult
to measure its permeability accurately due to the low impedance Z of a NSS sample.
NSS
Stacking some samples is a better way to get the results needed.
6) When the permittivity of a NSS sample is high (more than about 10), current flows through
the space between the NSS sample and the test fixture. This introduces an equivalent
capacitance connected in parallel to the impedance of the sample Z . The resonance of
NSS
this parallel LC circuit occurs at around 1 GHz or below and precise measurements will be
difficult.
5.2 Nicolson Ross Weir method
5.2.1 Principle
The objective of this method is to evaluate the broadband properties of the complex relative
permeability and permittivity of a noise suppression sheet by using a transmission line as
coaxial line and waveguide. Measurement frequency ranges and accuracy depend on the test
fixture and electromagnetic properties of a sample. This document describes a measurement
method using a 7 mm coaxial transmission line. Complex relative permittivity and permeability
are to be derived from the reflection and transmission coefficient of a sample inserted into a
transmission line. Reflection and transmission coefficients are calculated from S-parameters
S and S measured by a vector network analyzer. Figure 7 shows a schematic diagram of a
11 21
test fixture with a sample and signal flow graph.

Figure 7 – Schematic diagram of a test fixture with a sample and signal flow graph
A signal is inserted from Port1. L and t are the length of a test fixture and sample L and L are
1 2
the length from the respective reference plane to the sample faces.

From a signal flow graph, the S-parameters on a transmission line with sample are given by
Γ−1 T
( )
S = R
(18)
11 1
1−ΓT
T 1−Γ
( )
S = RR (19)
21 1 2
1−ΓT
R exp−γ L i=1,2 (20)
( ) ( )
ii0
where
Γ is the reflection coefficient at sample faces;
T is the transmission coefficient of a sample;
γ is the propagation constant of air;
R is the transmission coefficient from the reference plane to the sample face at the respective
i
ports.
Reflection coefficient Γ is defined by
ZZ−
L0
Γ=
(21)
ZZ+
L0
µ
r
ZZ= (22)
L0
ε
r
where
Z and Z are the characteristic impedance of a sample and air in the transmission line.
L 0
The transmission coefficient and propagation constant of a sample on a transmission line are
given by
(23)
Tdexp()−γ
γ=γ µε
(24)
0 rr
where
γ is the propagation constant of a sample.
From Formula (18) to Formula (24), the complex relative permeability and permittivity of a
sample are calculated by
=
=
– 20 – IEC TR 63307:2020 © IEC 2020
 
1+Γ 11
  
µ = ln
(25)
 
r   
1−Γ γ d T
  
 
 
1−Γ 11
  
ε = ln (26)
r   
1+Γ γ d T
  
 0 
It shall be noted that the calculated value is divergent at integral multiples of half wavelength
in a sample.
5.2.2 Measurement frequency and accuracy
The objective of this method is to measure the broadband electromagnetic properties of a
sample. Measurement frequency ranges and accuracy depend on the test fixture and
electromagnetic properties of a test sample. The lower frequency is limited by the smallest
measurable phase shift through a sample. The upper frequency limit is determined by the
excitation of higher order modes that invalidates the domina
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