IEC TR 61156-1-2:2009

IEC/TR 61156-1-2 ®
Edition 1.0 2009-05
TECHNICAL
REPORT
Multicore and symmetrical pair/quad cables for digital communications –
Part 1-2: Electrical transmission characteristics and test methods of symmetrical
pair/quad cables
IEC/TR 61156-1-2:2009(E)
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IEC/TR 61156-1-2 ®
Edition 1.0 2009-05
TECHNICAL
REPORT
Multicore and symmetrical pair/quad cables for digital communications –
Part 1-2: Electrical transmission characteristics and test methods of
symmetrical pair/quad cables
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
X
ICS 33.120.20 ISBN 978-2-88910-418-5
– 2 – TR 61156-1-2 © IEC:2009(E)
CONTENTS
FOREWORD.4
1 Scope.6
2 Normative references .6
3 Terms, definitions, symbols, units and abbreviated terms .6
3.1 Terms and definitions .6
3.2 Symbols, units and abbreviated terms .6
4 Basic transmission line equations.9
4.1 Introduction .9
4.2 Characteristic impedance and propagation coefficient equations .10
4.2.1 General .10
4.2.2 Propagation coefficient .10
4.2.3 Characteristic impedance .11
4.2.4 Phase and group velocity .12
4.3 High frequency representation of secondary parameters .13
4.4 Frequency dependence of the primary and secondary parameters .14
4.4.1 Resistance .14
4.4.2 Inductance.14
4.4.3 Characteristic impedance .15
4.4.4 Attenuation coefficient .15
4.4.5 Phase delay and group delay.16
5 Measurement of characteristic impedance .17
5.1 General .17
5.2 Open/short circuit single-ended impedance measurement made with a balun
(reference method).18
5.2.1 Principle .18
5.2.2 Test equipment.18
5.2.3 Procedure.19
5.2.4 Expression of results .19
5.3 Function fitting the impedance magnitude and angle .20
5.3.1 General .20
5.3.2 Impedance magnitude .20
5.3.3 Function fitting the angle of the characteristic impedance .22
5.4 Characteristic impedance determined from measured phase coefficient and
capacitance.22
5.4.1 General .22
5.4.2 Equations for all frequencies case and for high frequencies.22
5.4.3 Procedure for the measurement of the phase coefficient .23
5.4.4 Phase delay .25
5.4.5 Phase velocity .25
5.4.6 Procedure for the measurement of the capacitance .25
5.5 Determination of characteristic impedance using the terminated
measurement method.25
5.6 Extended open/short circuit method using a balun but excluding the balun
performance .26
5.6.1 Test equipment and cable-end preparation .26
5.6.2 Basic equations .26
5.6.3 Measurement principle .26

TR 61156-1-2 © IEC:2009(E) – 3 –
5.7 Extended open/short circuit method without using a balun.28
5.7.1 Basic equations and circuit diagrams.28
5.7.2 Measurement principle .30
5.8 Open/short impedance measurements at low frequencies with a balun.31
5.9 Characteristic impedance and propagation coefficient obtained from modal
decomposition technique .32
5.9.1 General .32
5.9.2 Procedure.33
5.9.3 Measurement principle .33
5.9.4 Scattering matrix to impedance matrix .35
5.9.5 Expression of results .37
6 Measurement of return loss and structural return loss .37
6.1 General .37
6.2 Principle.37
7 Propagation coefficient effects due to periodic structural variation related to the
effects appearing in the structural return loss .38
7.1 General .38
7.2 Equation for the forward echoes caused by periodic structural
inhomogeneities .38
8 Unbalance attenuation.40
8.1 General .40
8.2 Unbalance attenuation near end and far end .40
8.3 Theoretical background .42
Bibliography.46

Figure 1 – Secondary parameters extending from 1 kHz to 1 GHz.16
Figure 2 – Diagram of cable pair measurement circuit.19
Figure 3 – Determining the multiplier of 2π radians to add to the phase measurement .24
Figure 4 – Measurement configurations .27
Figure 5 – Measurement principle with four terminal network theory .27
Figure 6 – Admittance measurement configurations .30
Figure 7 – Admittance measurement principle.30
Figure 8 – Transmission line system .34
Figure 9 – Differential-mode transmission in a symmetric pair.40
Figure 10 – Common-mode transmission in a symmetric pair.40
Figure 11 – Circuit of an infinitesimal element of a symmetric pair .43
Figure 12 – Calculated coupling transfer function for a capacitive coupling of 0,4 pF/m
and random ±0,4 pF/m (l = 100 m; ε = ε = 2,3).45
r1 r2
Figure 13 – Measured coupling transfer function of 100 m Twinax 105 Ω .45

Table 1 – Unbalance attenuation at near end.41
Table 2 – Unbalance attenuation at far end.41
Table 3 – Measurement set-up.42

– 4 – TR 61156-1-2 © IEC:2009(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MULTICORE AND SYMMETRICAL PAIR/QUAD CABLES FOR DIGITAL
COMMUNICATIONS –
PART 1-2: ELECTRICAL TRANSMISSION CHARACTERISTICS AND TEST
METHODS OF SYMMETRICAL PAIR/QUAD CABLES

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC 61156-1-2, which is a technical report, has been prepared by subcommittee 46C: Wires
and symmetric cables, of IEC technical committee 46: Cables, wires, waveguides, R.F.
connectors, R.F. and microwave passive components and accessories.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
46C/853/DTR 46C/889/RVC
Full information on the voting for the approval of this technical report can be found in the
report on voting indicated in the above table.

TR 61156-1-2 © IEC:2009(E) – 5 –
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts of the IEC 61156 series, under the general title: Multicore and symmetrical
pair/quad cables for digital communications, can be found on the IEC website.
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.
A bilingual version of this publication may be issued at a later date.

– 6 – TR 61156-1-2 © IEC:2009(E)
MULTICORE AND SYMMETRICAL PAIR/QUAD CABLES FOR DIGITAL
COMMUNICATIONS –
PART 1-2: ELECTRICAL TRANSMISSION CHARACTERISTICS AND TEST
METHODS OF SYMMETRICAL PAIR/QUAD CABLES

1 Scope
This technical report is a revision of the symmetrical pair/quad electrical transmission
characteristics present in IEC 61156-1:2002 (Edition 2) and not carried into IEC 61156-1:2007
(Edition 3).
This technical report includes the following topics from IEC 61156-1:2002:
– the characteristic impedance test methods and function fitting procedures of 3.3.6;
– Annex A covering basic transmission line equations and test methods;
– Annex B covering the open/short-circuit method;
– Annex C covering unbalance attenuation.
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 60050-726, International Electrotechnical Vocabulary – Part 726: Transmission lines and
waveguides
IEC 61156-1:2007, Multicore and symmetrical pair/quad cables for digital communications –
Part 1: Generic specification
IEC/TR 62152, Background of terms and definitions of cascaded two-ports
3 Terms, definitions, symbols, units and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-726 and
IEC/TR 62152 apply.
3.2 Symbols, units and abbreviated terms
For the purposes of this document, the following symbols, units and abbreviated terms apply.
Transmission line equation electrical symbols and related terms and symbols:
R pair resistance (Ω/m)
L pair inductance (H/m)
G pair conductance (S/m)
C pair capacitance (F/m)
α attenuation coefficient (Np/m)
β phase coefficient (rad/m)
TR 61156-1-2 © IEC:2009(E) – 7 –
γ propagation coefficient (Np/m, rad/m)
νP phase velocity of cable (m/s)
νG group velocity of cable (m/s)
τP phase delay time (s/m)
τG group delay time (s/m)
Z
complex characteristic impedance, or mean characteristic impedance if the pair
C
is homogeneous or free of structure (also used to represent a function fitted
result) (Ω)
∠Z angle of the characteristic impedance in radians
C
Z high frequency asymptotic value of the characteristic impedance (Ω)
∞
l length (m)
j imaginary denominator
Re real part operator for a complex variable
Im imaginary part operator for a complex variable
ω radian frequency (rad/s)
f frequency (Hz)
R’ first derivative of R with respect to ω
C’ first derivative of C with respect to ω
L’ first derivative of L with respect to ω
R d.c. resistance of a round solid wire with radius r (Ω/m)
R constant with frequency component of resistance which is about 1/4 of the d.c.
C
resistance (Ω/m)
R square-root of frequency component of resistance (Ω/m)
S
L external (free space) inductance (H/m)
E
L internal inductance whose reactance equals the surface resistance at high
I
frequencies (H/m)
σ specific conductivity of the wire material (S/m)
ρ resistivity of the wire material (Ω/m )
μ permeability of the wire material (H/m)
r radius of the wire (m)
δ skin depth (not to be confused with the dissipation factor tan δ) (m)
δ =
πf μσ
tan δ dissipation factor
tan δ = G/(ωC)
q forward echo coefficient at the far end of the cable at a resonant frequency
p reflection coefficient measured from the near end of the cable at a
Z − Z
CM C
−PSRL / 20
resonant frequency, p = 10 =
Z + Z
CM C
– 8 – TR 61156-1-2 © IEC:2009(E)
A forward echo attenuation at a resonant frequency (dB)
Q
A = – 20 log ⎥q⎥
Q
PSRL structural return loss at a resonant frequency (dB)
PSRL = – 20 log ⎥p⎥
K = 2αl – 1 when 2αl >> 1 (Np)
A = 2 × PSRL – 20 log(2αl – 1) (dB) where 2αl is in Np
Q
Z complex measured open circuit impedance (Ω)
OC
Z complex measured short circuit impedance (Ω)
SC
Z characteristic impedance as measured (with structure) (Ω)
CM
=
Z Z Z
CM SC OC
Z complex measured impedance (open or short) (Ω)
MEAS
Z input impedance of the cable when it is terminated by Z (Ω)
IN L
Z output impedance of the cable when the input of the cable is terminated by
OUT
Z (Ω)
G
Z Z
nominal characteristic impedance of a cable and is the specified value at a
CN C
given frequency with tolerance and the structural return loss SRL limits in dB in
a frequency range (Ω)
Z nominal (reference) impedance of the link and/or terminals (the system)
N
between which the cable is operating (Ω)
Z
(nominal) reference impedance that is used in measurement. Normally (for
R
Z Z
actual return loss results), = . When using a return loss measurement to
R N
approximate SRL, it is practical to choose Z to give the best balance in the
R
given frequency range (Ω)
Z terminated impedance measurement made with the opposite end of the cable
T
pair terminated in the reference impedance Z (Ω)
R
ς reflection coefficient measured in the terminated measurement method
−
Z Z
R C
ς =
+
Z Z
R C
Z
termination at the cable input when defining the output impedance of the cable
G
Z (Ω)
OUT
Z
termination at the cable output when defining the input impedance of the cable
L
Z (Ω)
IN
L , L , L , L least squares fit coefficients for angle of the characteristic impedance
0 1 2 3
K , K , K , K least squares fit coefficients of the characteristic impedance
0 1 2 3
⎟Z ⎟ fitted magnitude of the characteristic impedance (Ω)
C
⎟Z ⎟ measured magnitude of the characteristic impedance (Ω)
CM
∠ (V ) input angle relative to a reference angle in radians
1N
∠ (V ) output angle relative to the same reference angle in radians
1F
k multiple of 2π radians
S
reflection coefficient measured with an S parameter test set
TR 61156-1-2 © IEC:2009(E) – 9 –
RL return loss (dB)
SRL structural return loss (dB)

Attenuation unbalance electrical symbols:
TA transverse asymmetry
LA longitudinal asymmetry
R , R resistance of one conductor per unit length (Ω)
1 2
L , L inductance of one conductor per unit length (H)
1 2
C , C capacitance of one conductor to earth (F)
1 2
G , G conductance of one conductor to earth (S)
1 2
α unbalance attenuation (dB)
u
T unbalance coupling transfer function
u
Z characteristic impedance of the common-mode circuit (Ω)
com
Z characteristic impedance of the differential-mode circuit (Ω)
diff
Z unbalance impedance (Ω)
unbal
l length of transmission line (m)
x length coordinate (m)
γ propagation factor of the common-mode circuit (Np/m, rad/m)
com
γ propagation factor of the differential-mode circuit (Np/m, rad/m)
diff
α operational differential-mode attenuation of the cable (dB)
diff
α operational common-mode attenuation of the cable (dB)
com
ΔR resistance unbalance of the sample length (Ω)
ΔL inductance unbalance of the sample length (H)
ΔC capacitance unbalance to earth (F)
ΔG conductance unbalance to earth (S)
S summing function
U voltage in the differential-mode circuit (V)
diff
U voltage in the common-mode circuit (V)
com
n, f index to designate the near end and far end, respectively
4 Basic transmission line equations
4.1 Introduction
A review of the relationships between the propagation coefficient and characteristic
impedance and the primary parameters R, L, G and C is useful here. Characteristic impedance
is commonly thought of as being a magnitude quantity. While this concept may suffice for high
frequency applications, this quantity is actually a complex one consisting of real and
imaginary components or magnitude and angle. The associated propagation coefficient is
readily viewed as being complex, consisting of the real attenuation and imaginary phase
coefficient components. The four secondary components are readily related to the primary
components. Frequency dependence of these parameters is also developed.
The cable pair parameters are represented as frequency domain dependent quantities. The
measurement methods are based on frequency domain techniques. Measurement methods
based on time domain techniques and combinations of time and frequency while useful in

– 10 – TR 61156-1-2 © IEC:2009(E)
many cases are not covered here. The present-day availability of excellent frequency domain
equipment such as the network analysers and impedance meters supports the frequency
domain approach.
4.2 Characteristic impedance and propagation coefficient equations
4.2.1 General
The frequency domain of the complex characteristic impedance Z relates to the primary
C
parameters as:
R + jωL
= (1)
Z
C
G + jωC
The propagation coefficient, γ, relates to the primary parameters as:
γ = α + jβ = (R + jωL)(G + jωC) (2)
4.2.2 Propagation coefficient
4.2.2.1 Attenuation and phase coefficients
Equation (2) is separated into its real and imaginary parts, the attenuation coefficient α and
the phase coefficient β:
1 1
2 2 2 2 2 2 2
α = − ( LC − RG) + ( + )( + ) (3)
ω R ω L G ω C
2 2
1 1
2 2 2 2 2 2 2
β = ( LC − RG) + ( + )( + ) (4)
ω R ω L G ω C
2 2
Further, by factoring out ω LC we obtain:
2 2
⎛ ⎞⎛ ⎞
1⎛ R G ⎞ 1
R G
⎜ ⎟⎜ ⎟
⎜ ⎟
β = ω LC 1 − + 1 + 1 + (5)
⎜ ⎟
2 2 2 2
⎜ ⎟⎜ ⎟
2 ωL ωC 2
ω L ω C
⎝ ⎠
⎝ ⎠⎝ ⎠
It can be shown that:
⎛ ⎞
R C
⎜ ⎟
αβ = ω LC  (6)
⎜ ⎟
2 L
⎝ ⎠
4.2.2.2 Equations useful at high frequencies
From Equations (5) and (6) we can solve for α and thus obtain for α and β the following
expressions, valid within the entire frequency range:

TR 61156-1-2 © IEC:2009(E) – 11 –
R C G L
+
2 L 2 C
α = (7)
2 2
⎛ ⎞⎛ ⎞
1⎛ R G ⎞ 1
R G
⎜ ⎟⎜ ⎟
⎜ ⎟
− + 1 + 1 +
⎜ ⎟
2 2 2 2
⎜ ⎟⎜ ⎟
2 ωL ωC 2
⎝ ⎠ ω L ω C
⎝ ⎠⎝ ⎠
2 2
⎛ ⎞⎛ ⎞
1⎛ R G ⎞ 1
R G
⎜ ⎟⎜ ⎟
⎜ ⎟
β = ω LC 1 − + 1 + 1 + (8)
⎜ ⎟
2 2 2 2
⎜ ⎟⎜ ⎟
2 ωL ωC 2
⎝ ⎠ ω L ω C
⎝ ⎠⎝ ⎠
Equations (7) and (8) are well suited for evaluation of high frequencies.
4.2.2.3 Equations useful at low frequencies
For low frequency evaluations, the expressions given by Equations (9) and (10) are suitable.
2 2 2
⎛ ⎞⎛ ⎞
ωRC G ωL
⎛ ⎞ ω L G
⎜ ⎟⎜ ⎟
⎜ ⎟
α =  − + 1 + 1 + (9)
⎜ ⎟
⎜ 2 ⎟⎜ 2 2⎟
2 ωC R
R ω C
⎝ ⎠
⎝ ⎠⎝ ⎠
2 2 2
⎛ ⎞⎛ ⎞
ωRC ωL G
⎛ ⎞ ω G
L
⎜ ⎟⎜ ⎟
⎜ ⎟
β = − + 1 + 1 + (10)
⎜ ⎟
⎜ 2 ⎟⎜ 2 2⎟
2 R ωC
R ω C
⎝ ⎠
⎝ ⎠⎝ ⎠
4.2.3 Characteristic impedance
4.2.3.1 Real and imaginary parts
Z
The characteristic impedance can also be separated into its real and imaginary parts as
C
developed in Equations (11) and (12).
R + jωL α + jβ
= Re  + j Im   =   =  (11)
ZC Z C ZC
G + jωC G + jωC
⎡ ⎤
1 ⎛ G ⎞ ⎛ G ⎞
⎜ β +  α⎟ − j ⎜α −  β⎟
⎢ ⎥
ωC ωC ωC
⎝ ⎠ ⎝ ⎠
⎣ ⎦
= (12)
Z
C
G
1 +
2 2
ω C
4.2.3.2 Equations useful at high frequencies
After substituting Equations (7) and (8) into Equation (12), the real and imaginary parts of the
characteristic impedance are obtained as given in Equations (13) and (14) respectively.
These are well suited for simplification (see 4.3) at high frequencies:
⎡ ⎤
2 2
⎛ ⎞⎛ ⎞
L 1 R G 1
⎛ ⎞
R G
⎢ ⎜ ⎟⎜ ⎟⎥
⎜1 − ⎟ + 1 + 1 +
⎜ 2 ⎟ 2 2
2 ⎜ ⎟
C ⎢ 2 L C 2 ⎥
ω ω
⎝ ⎠ ω L ω C
⎝ ⎠⎝ ⎠
⎣ ⎦
Re  = (13)
Z
C
2 2 2
⎛ ⎞ ⎛ ⎞⎛ ⎞
1 R G 1
⎛ ⎞
G R G
⎜ ⎟ ⎜ ⎟⎜ ⎟
1 + ⎜1 − ⎟ + 1 + 1 +
⎜ 2 2⎟ ⎜ 2 2⎟⎜ 2 2⎟
2 ωL ωC 2
ω ⎝ ⎠ ω ω
C L C
⎝ ⎠ ⎝ ⎠⎝ ⎠
– 12 – TR 61156-1-2 © IEC:2009(E)
⎡ ⎤
2 2
⎛ ⎞⎛ ⎞
R G L G L 1⎛ R G ⎞ 1
R G
⎢ ⎜ ⎟⎥
⎜ ⎟
+  −  ⎜1 − ⎟ + 1 + 1 +
⎜ 2 2⎟⎜ 2 2⎟
2ωC C ωC C ⎢ 2 ωL ωC 2 ⎥
2ω LC ⎝ ⎠
ω L ω C
⎝ ⎠⎝ ⎠
⎣ ⎦
− Im  = (14)
Z
C
2 2 2
⎛ ⎞ ⎛ ⎞⎛ ⎞
1⎛ R G ⎞ 1
G R G
⎜ ⎟ ⎜ ⎟⎜ ⎟
1 + ⎜1 − ⎟ + 1 + 1 +
⎜ 2 2⎟ ⎜ 2 2⎟⎜ 2 2⎟
2 ωL ωC 2
⎝ ⎠
ω C ω L ω C
⎝ ⎠ ⎝ ⎠⎝ ⎠
4.2.3.3 Equations useful at low frequencies
On the other hand, by substituting Equations (9) and (10) into Equation (12), the real and
imaginary parts given in Equations (15) and (16) respectively are obtained. These are useful
for simplification in the low frequency range:
⎡ ⎤
2 2 2 2 2 2
⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞
R ωL G G G ωL
ω L G ω L G
⎢ ⎥
⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
−  + 1 + 1 +  +  −  + 1 + 1 +
⎢ ⎜ 2 ⎟⎜ 2 2⎟ ⎜ 2 ⎟⎜ 2 2⎟⎥
2ωC R ωC ωC ωC R
R ω C R ω C
⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠
⎢ ⎥
⎣ ⎦
(15)
Re  =
Z
C
⎛ ⎞
G
⎜ ⎟
1 +
⎜ 2 2⎟
ω C
⎝ ⎠
⎡ ⎤
2 2 2 2 2 2
⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞
R G ωL G ωL G
ω L G ω L G
⎢ ⎥
⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
− + 1 + 1 + −  − + 1 + 1 +
⎢ ⎜ 2 ⎟⎜ 2 2⎟ ⎜ 2 ⎟⎜ 2 2⎟⎥
2ωC ωC R ωC R ωC
R ω C R ω C
⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠
⎢ ⎥
⎣ ⎦
(16)
− Im  =
Z
C
⎛ ⎞
G
⎜ ⎟
1 +
⎜ 2 2⎟
ω C
⎝ ⎠
4.2.4 Phase and group velocity
The phase propagation time (per unit length) is:
β
= (17)
τ P
ω
β from Equations (8) and (10), we obtain:
By introducing
2 2
⎛ ⎞⎛ ⎞
1 R G 1
⎛ ⎞
R G
⎜ ⎟⎜ ⎟
= LC ⎜1 − ⎟ + 1 + 1 + (18)
τ
P
⎜ 2 2⎟⎜ 2 2⎟
2 ωL ωC 2
⎝ ⎠ ω L ω C
⎝ ⎠⎝ ⎠
2 2 2
⎛ ⎞⎛ ⎞
RC ωL G
⎛ ⎞
ω L G
⎜ ⎟⎜ ⎟
and = ⎜ − ⎟ + 1 + 1 + (19)
τ
P
⎜ 2 ⎟⎜ 2 2⎟
2 ω R ωC
⎝ ⎠ R ω C
⎝ ⎠⎝ ⎠
The group propagation time (per unit length) is:
dβ
= (20)
τ
G
dω
⎡⎛ ⎞ ⎤⎡ ⎛ ⎞ ⎤
2 2
⎛ ⎞ ⎛ ⎞
⎜ R ⎟ ⎜ G ⎟
G R R G
⎢ ⎛ ⎞ ⎥⎢ ⎛ ⎞⎥
⎜ ⎟ ⎜ ⎟
1 +  1 +
β 1 L’ C ’ d ⎜ ⎟ d ⎜ ⎟
⎛ ⎞ ⎜ ⎟ ⎜ ⎟
(21)
2 ⎢ ⎜ 2 2⎟ ⎥⎢ ⎜ 2 2⎟ ⎥
=  +  ⎜ + ⎟ β + ωL ωC
τ LC G ω C ωL R ω L ωC
G ω ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠
⎜ ⎟ ⎜ ⎟
⎢ ⎥⎢ ⎥
ω 2 L C − +   + − +
⎝ ⎠
⎜ ⎟
⎜ ⎟
4β ⎢ ωC 2 dω ⎥⎢ ωL 2 dω ⎥
2 2
⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞
R G R G
⎜ ⎟ ⎜ ⎟
⎢ ⎜ ⎟⎜ ⎟ ⎥⎢ ⎜ ⎟⎜ ⎟ ⎥
1 + 1 + 1 + 1 +
⎜ 2 2⎟⎜ 2 2⎟ ⎜ 2 2⎟⎜ 2 2⎟
⎜ ⎟ ⎜ ⎟
⎢ ⎥⎢ ⎥
ω L ω C ω L ω C
⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠
⎝ ⎠ ⎝ ⎠
⎣ ⎦⎣ ⎦
TR 61156-1-2 © IEC:2009(E) – 13 –
The phase and group velocities are, respectively,
= (22)
ν
P
τ
P
= (23)
ν
G
τ
G
The above expressions are accurate and valid within the whole frequency range. If C and
G/(ωC) can be regarded as frequency independent coefficients, then we obtain:
⎡ ⎤
⎛ ⎞
R
G
⎢ ⎥
⎜ ⎟
1 +
⎜ 2 2⎟
⎢ ⎥
ωL
β β L’ C G L’ R
ω C ⎛ ⎞
⎝ ⎠
= +  +  ⎢− + ⎥ ⎜− R + R ’ ω −  ω⎟ (24)
τ
G
ω 2 L 4β ωC 2 2 L
⎢ ⎥⎝ ⎠
⎛ ⎞⎛ ⎞
R G
⎜ ⎟
⎜ ⎟
1 + 1 +
⎢ ⎥
⎜ 2 2⎟⎜ 2 2⎟
⎢ ω L ω C ⎥
⎝ ⎠⎝ ⎠
⎣ ⎦
The above expressions, which are valid within the entire frequency range, can be simplified
into approximate expressions, which are valid at high or low frequencies only.
4.3 High frequency representation of secondary parameters
The high frequency representations of the formulas are useful over a broad range of
frequencies extending from voice frequency on up because of the range of values for the
dissipation factor. G/(ωC) = tan δ < 0,03 (< 3 %) even for PVC insulated cables up to 1,5 MHz
and for the polyethylene (PE), insulation is very small at about 0,000 1 (0,01 %). This results
in approximations, which in practice are valid for the whole frequency range as follows:
L 1 1
R
Re ≈  + 1 + (25)
Z
C
2 2
C 2 2
ω L
G L
R G
2ωC C
− Im ≈ − Re + (26)
Z Z
C C
2ωC Re ωC Re
Z Z
C C
⎛ ⎞
L
⎜ ⎟
G
⎜ ⎟
C
R
⎝ ⎠
α ≈ + (27)
2 Re 2 Re
Z Z
C C
β ≈ ωC Re (28)
Z
C
≈ LC (29)
τ
P
⎛ ⎞
⎜ ⎟
R
⎜ ⎟
β β L’ C G L’ R
⎛ ⎞
ωL
≈ +  + ⎜− + ⎟ ⎜− R + R ’ ω − ω⎟ (30)
τ
G
ω 2 L 4β ωC L
⎝ ⎠
⎜ ⎟
R
1 +
⎜ ⎟
2 2
ω L
⎝ ⎠
– 14 – TR 61156-1-2 © IEC:2009(E)
when also R/(ωL) < 0,1, which is true for high frequencies (f > 1 MHz for 0,5 mm wire), the
formulas holding better than about 1 % accuracy can be further simplified as shown below.
L
Re ≈  (31)
Z
C
C
R G L R G
⎛ ⎞
⎜ ⎟
− Im ≈ − Re ≈ − (32)
Z Z
C C
⎜ ⎟
2ωC Re ωC C 2ωL 2ωC
Z
C
⎝ ⎠
R G R C G L
α ≈ +  Re ≈ + (33)
Z
C
2 Re 2 2 L 2 C
ZC
β ≈ ω C Re ≈ ω LC (34)
Z
C
≈ LC (35)
τ P
β L’ C G R L’ R
⎛ ⎞⎛ ⎞
≈ +  + ⎜− + ⎟ ⎜− R + R ’ ω − ω⎟ (36)
τ τ
G P
2 L 4β ωC ωL L
⎝ ⎠⎝ ⎠
4.4 Frequency dependence of the primary and secondary parameters
4.4.1 Resistance
The high frequency resistance (surface resistance) of a solid round wire for frequencies where
the wire radius r is greater than twice the skin depth δ can be regarded as consisting of two
0,5
parts where one is constant and the other f dependent.
⎛ 1 r ⎞
R = + = + ρ ω ≈  + (37)
⎜ ⎟
R R R R
C S C 0
4 2δ
⎝ ⎠
r
R R
S 0
ρ = = 2μσ (38)
ω
The above is true for a solid wire alone. In a pair, the proximity effects and the presence of
other pairs and possible screen contribute both to the resistance and inductance. These
effects can increase the R by about 15 % at 1 MHz and follow also approximately the square-
root of frequency law. Also, the constant component of resistance while often neglected, is
about 15 % of the frequency dependent component at 1 MHz for a 0,5 mm diameter copper
pair.
4.4.2 Inductance
The total inductance consists also of two main components such that
ρ
R
S
L ≈ + = + = + (39)
LE LI LE LE
ω
ω
The external free space inductance is reduced by the proximity effect of the pair and the free
space limiting effects of the nearby shield and/or other pairs. These inductive components are
negative and fairly frequency independent at high frequencies.

TR 61156-1-2 © IEC:2009(E) – 15 –
4.4.3 Characteristic impedance
The characteristic impedance high frequency asymptotic value Z is given by Equation (40).
∞
LE
= (40)
Z
∞
C
The high frequency impedance formulas are given by Equations (41) and (42):
⎛ ⎞
L ρ
R
S
⎜ ⎟
Re ≈ ≈ 1 + = + (41)
Z
Z C Z ∞ ∞
⎜ ⎟
C 2 ω
L 2 C ω
E L
⎝ ⎠ E
L R G
⎛ ⎞
− Im ≈ ⎜ − ⎟
Z
C
C 2ωL 2ωC
⎝ ⎠
⎛ ⎞
+ ρ ω ρ tan δ
R L
C E
⎜ ⎟
≈ − 1 +
⎜ ⎟
⎛ ⎞ C 2
2 ω
ρ L
⎝ E ⎠
⎜ ⎟
2ω C 1 +
L
E
⎜ ⎟
(42)
2 ω
L
⎝ E ⎠
⎛ ⎞
ρ
RC Z LI
∞
⎜ ⎟
≈ + − 1+ tan δ
⎜ ⎟
2ω C 2 C ω L
L L ⎝ E⎠
E E
ρ
Z
∞
≈ − tanδ
2 C ω
L
E
4.4.4 Attenuation coefficient
Using the above approximations with Equations (31) through (36) results in the remaining
equations of this subclause:
⎛ ⎞
ρ
⎜ ⎟
−
R
C
⎜ ⎟
L
E ω C tan δ
ρ ω ρ ω tan δ L
⎝ ⎠ E
α ≈ + + + (43)
2 2Z 4 2
Z Z
∞ ∞ ∞
which is of the form:
α ≈ A + B ω + Cω (44)
where A, B and C are constants.
The first term of Equation (44) indicates that at the low end of the high frequency range the

0,5
attenuation increases a little more slowly than the square-root-law. The first ω term in
Equation (43) which is dominant in the high frequency attenuation formula also appears in the
phase coefficient, Equation (45).
⎛ ⎞
R ρ ω
β ≈ ω LC ≈ ω C ⎜1 + ⎟ ≈ ω L C + (45)
L
E E
⎜ ⎟
2 ω 2
L Z
⎝ E⎠ ∞
– 16 – TR 61156-1-2 © IEC:2009(E)
4.4.5 Phase delay and group delay
The phase and group delay are given in Equations (46) and (47) respectively:
⎛ R ⎞ ρ
⎜ ⎟
≈ LC = C 1 + ≈ C + (46)
τ L L
P E E
⎜ ⎟
2ω
L 2 Z ω
⎝ E⎠
∞
L’ C G R L’ R
β ⎛ ⎞⎛ ⎞
≈ +  + ⎜− + ⎟ ⎜− R + R ’ ω − ω⎟
τ τ
G P
2 L 4β ωC ωL L
⎝ ⎠⎝ ⎠
⎛ R ⎞ R ⎛ R G ⎞
≈ ⎜1 − ⎟ − ⎜ − ⎟
4ωL 8ωL ωL ωC
⎝ ⎠ ⎝ ⎠
⎛ R ⎞
≈ ⎜1 − ⎟
τ (47)
P
4ωL
⎝ ⎠
⎛ ⎞
R
⎜ ⎟
≈ C 1 +
L
E
⎜ ⎟
4ω
L
E
⎝ ⎠
ρ
≈ C +
LE
4 ω
Z
∞
10 000
β
1 000
|Z |
C
Re Z
C
α
α-R
–1
–2
–3 –2 –1 1 2 3
10 10 10 10 10 10
Frequency  (MHz)
IEC  839/09
Figure 1 – Secondary parameters extending from 1 kHz to 1 GHz
Figure 1 shows the secondary parameters of a UTP pair with 0,5 mm conductors versus
frequency. At voice frequencies, the attenuation and phase coefficients are substantially
equal. At these frequencies, the absolute value of the characteristic impedance and the real
part of the characteristic impedance differ by the square-root of 2. At frequencies above
100 kHz, attenuation is much less than the phase coefficient on the Nepers and radians scale,
and the characteristic impedance is mostly real. The total attenuation (Alpha) differs from the
conductor attenuation (Alpha-R) by the dielectric component of attenuation for this example,
where the dissipation factor is assumed to be 0,01.

Alpha, Beta  (Np, Rad/100 m)
Z (Ω)
C
TR 61156-1-2 © IEC:2009(E) – 17 –
5 Measurement of characteristic impedance
5.1 General
Z
The characteristic impedance of a homogeneous cable pair is defined as the quotient of a
C
voltage wave and current wave which are propagating in the same direction, either
forwards (f) or backwards (r). For homogeneous cables (with no structural variations), the
characteristic impedance can be measured directly as the quotient of voltage U and current I
at the cable ends.
U U
f r
Z = = (48)
C
I I
f r
A number of methods for obtaining characteristic impedance are described. Some of these
methods offer convenience (perhaps at the cost of accuracy in portions of the frequency
range). Others offer capability beyond what is currently needed for routine product inspection
but are useful in laboratory evaluation where measurement throughput is not as critical.
in 5.2 is
The open/short circuit single-ended impedance measurement made with a balun
viewed as the reference method for obtaining the data. Alternative methods are listed below:
a) characteristic impedance determined from phase coefficient and capacitance
measurements (see 5.4);
b) terminated cable impedance measurements (see 5.5);
c) extended open/short impedance measurements excluding balun performance (see 5.6);
d) extended open/short impedance measurements made without a balun (see 5.7);
e) open/short impedance measurements at low frequencies with a balun (see 5.8;
f) impedance measurements obtained by modal decomposition technique (see 5.9).
It is intended that impedance measurements will be performed using sufficiently closely
spaced frequencies so that impedance variation is adequately represented. Either a linear
sweep or a logarithmic sweep may be used depending on whether the high end or low end,
respectively, of the desired frequency range is to be more fully represented. Typically, several
hundred points (such as the available 401 points) are required depending on frequency range
and cable length.
The balun used for connecting the symmetric cable pair to the coaxial port on the test
instrument shall have a pass-band frequency range adequate for the desired measurement
range. It shall be capable of transforming from the instrument port impedance to the nominal
pair impedance. The three step impedance measurement calibration is performed at the
secondary (pair side) of the balun.
Function fitting (discussed in 5.3) of the impedance data is useful for separating structural
effects from the characteristic impedance when such effects are substantial. Where function
fitting is used, the concept is that measurements from nearby frequencies aid in the
interpretation of the values obtained at a particular frequency. Function fitting of the
impedance magnitude or real part results in high values (typically 0,5 Ω or less) because of
the positive and negative deviations not being symmetrical on the impedance scale. Function
fitting can be carried out on the S-parameter values, which are linear responses, if more
rigorous results (both impedance and SRL) are desired.

– 18 – TR 61156-1-2 © IEC:2009(E)
5.2 Open/short circuit single-ended impedance measurement made with a balun
(reference method)
5.2.1 Principle
Open and short circuit measurements made with a balun from one end of a symmetric cable
pair is the reference method for obtaining characteristic impedance values. The characteristic
impedance is the geometric mean of the product of the open and short circuit measured
values and is defined as:
Z = Z Z (49)
C OC SC
When the cable is not homogenous, an impedance inclusive of structural effects is obtained:
Z = Z Z (50)
CM OC SC
Z
where CM is the complex characteristic impedance together with structure (input impedance),
expressed in ohms (Ω).
Z
Equation (49) represents the characteristic impedance, , when structural effects are
C
negligible. The fitting of the open/short impedance data with a characteristic impedance such
Z Z
as function of frequency can be employed to obtain from the input impedance, ,
C CM
Equation (50) when structural effects are substantial. Equations (49) and (50) (and this
measurement technique) are valid for frequencies extending from low values, where the cable
length is only a fraction of a wavelength, to high frequencies where cable length represents
many wavelengths.
5.2.2 Test equipment
A network analyser (together with an S-parameter unit) or an impedance meter can be used to
obtain the data. Figure 2 shows the main components of an impedance measurement circuit
where the generator and receiver are parts of the network analyser. An S-parameter unit,
where the key component is the reflection bridge, is used with a network analyser to separate
the reflected signal from the incident signal. A balun with the appropriate frequency range,
impedance (such as 50 Ω to 100 Ω for 50 Ω equipment and 100 Ω pair) and balanced at least
as well as the pair under test facilitates making measurements on symmetric pairs under
balanced conditions. Three terminating conditions, open, short and the nominal load
resistance, are used as appropriate for the type of measurement being made (open, short or
terminated).
TR 61156-1-2 © IEC:2009(E) – 19 –
Z
G
Open Short Load
Reflection
Generator
Cable under test
Balun
bridge
Z
R
Receiver
IEC  840/09
Figure 2 – Diagram of cable pair measurement circuit
5.2.3 Procedure
A three step calibration procedure using the same open, short and load terminations as used
for the actual measurements is carried out at the secondary of the balun with the cable pair
disconnected. Upon completing the 3-step calibration procedure at the secondary of the
balun, the network analyser is capable of measuring directly the complex reflection coefficient
(S-parameter) or impedance of a cable pair. An internal 3-step calibration procedure including
calculations is provided by most network analysers when an S-parameter unit is used. The
method presented in 5.6 covers a similar 3-step calibration procedure by using the F-matrix
principle where all the quantities are stated as impedances. This method is useful when the
network analyser is not suitably equipped, in which case the computations can be
accomplished external to the analyser.
The measured impedance (open or short) is computed from the reflection coefficient
S
measurements by means of Equation (51) either by the networ
...

IEC TR 61156-1-2 ®
Edition 1.1 2014-09
CONSOLIDATED VERSION
TECHNICAL
REPORT
colour
inside
Multicore and symmetrical pair/quad cables for digital communications –
Part 1-2: Electrical transmission characteristics and test methods of
Symmetrical pair/quad cables
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IEC TR 61156-1-2 ®
Edition 1.1 2014-09
CONSOLIDATED VERSION
TECHNICAL
REPORT
colour
inside
Multicore and symmetrical pair/quad cables for digital communications –

Part 1-2: Electrical transmission characteristics and test methods of

Symmetrical pair/quad cables
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.120.20 ISBN 978-2-8322-1857-0

IEC TR 61156-1-2 ®
Edition 1.1 2014-09
CONSOLIDATED VERSION
REDLINE VERSION
colour
inside
Multicore and symmetrical pair/quad cables for digital communications –
Part 1-2: Electrical transmission characteristics and test methods of
Symmetrical pair/quad cables
– 2 – IEC TR 61156-1-2:2009
+AMD1:2014 CSV  IEC 2014
CONTENTS
FOREWORD . 5

1 Scope . 7

2 Normative references . 7

3 Terms, definitions, symbols, units and abbreviated terms . 7

3.1 Terms and definitions . 7

3.2 Symbols, units and abbreviated terms . 8

4 Basic transmission line equations . 11

4.1 Introduction . 11
4.2 Characteristic impedance and propagation coefficient equations . 11
4.2.1 General . 11
4.2.2 Propagation coefficient . 11
4.2.3 Characteristic impedance . 12
4.2.4 Phase and group velocity . 13
4.3 High frequency representation of secondary parameters . 14
4.4 Frequency dependence of the primary and secondary parameters . 15
4.4.1 Resistance . 15
4.4.2 Inductance . 16
4.4.3 Characteristic impedance . 16
4.4.4 Attenuation coefficient . 16
4.4.5 Phase delay and group delay . 17
5 Measurement of characteristic impedance . 18
5.1 General . 18
5.2 Open/short circuit single-ended impedance measurement made with a balun
(reference method) . 19
5.2.1 Principle . 19
5.2.2 Test equipment . 20
5.2.3 Procedure . 20
5.2.4 Expression of results . 21
5.3 Function fitting the impedance magnitude and angle . 21
5.3.1 General . 21
5.3.2 Impedance magnitude . 21
5.3.3 Function fitting the angle of the characteristic impedance . 23

5.4 Characteristic impedance determined from measured phase coefficient and
capacitance . 23
5.4.1 General . 23
5.4.2 Equations for all frequencies case and for high frequencies . 24
5.4.3 Procedure for the measurement of the phase coefficient . 24
5.4.4 Phase delay . 26
5.4.5 Phase velocity . 26
5.4.6 Procedure for the measurement of the capacitance . 26
5.5 Determination of characteristic impedance using the terminated
measurement method . 26
5.6 Extended open/short circuit method using a balun but excluding the balun
performance . 27
5.6.1 Test equipment and cable-end preparation . 27
5.6.2 Basic equations . 27

+AMD1:2014 CSV  IEC 2014
5.6.3  Measurement principle . 27

5.7  Extended open/short circuit method without using a balun . 29

5.7.1  Basic equations and circuit diagrams . 29

5.7.2  Measurement principle . 31

5.8  Open/short impedance measurements at low frequencies with a balun. 32

5.9  Characteristic impedance and propagation coefficient obtained from modal

decomposition technique . 33

5.9.1  General . 33

5.9.2  Procedure . 34

5.9.3  Measurement principle . 34

5.9.4  Scattering matrix to impedance matrix . 36
5.9.5  Expression of results . 38
6  Measurement of return loss and structural return loss . 38
6.1  General . 38
6.2  Principle . 38
7  Propagation coefficient effects due to periodic structural variation related to the
effects appearing in the structural return loss . 39
7.1  General . 39
7.2  Equation for the forward echoes caused by periodic structural
inhomogeneities . 39
8  Unbalance attenuation . 40
8.1  General . 40
8.2  Unbalance attenuation near end and far end . 41
8.3  Theoretical background . 43
9  Balunless test method . 46
9.1  Overall test arrangement . 46
9.1.1  Test instrumentation . 46
9.1.2  Measurement precautions . 47
9.1.3  Mixed mode S-parameter nomenclature . 47
9.1.4  Coaxial cables and interconnect for network analysers . 48
9.1.5  Reference loads for calibration . 49
9.1.6  Calibration . 49
9.1.7  Termination loads for termination of conductor pairs . 50
9.1.8  Termination of screens . 51
9.2  Cabling and cable measurements . 52

9.2.1  Insertion loss and EL TCTL . 52
9.2.2  NEXT . 53
9.2.3  ACR-F . 55
9.2.4  Return loss and TCL . 57
9.2.5  PS alien near-end crosstalk (PS ANEXT-Exogenous crosstalk) . 59
9.2.6  PS attenuation to alien crosstalk ratio, far-end crosstalk (PS AACR-
F- Exogenous crosstalk . 62
Annex A (informative) Example derivation of mixed mode parameters using the modal
decomposition technique . 66
Bibliography . . 69

Figure 1 – Secondary parameters extending from 1 kHz to 1 GHz . 18
Figure 2 – Diagram of cable pair measurement circuit . 20

– 4 – IEC TR 61156-1-2:2009
+AMD1:2014 CSV  IEC 2014
Figure 3 – Determining the multiplier of 2radians to add to the phase measurement . 25

Figure 4 – Measurement configurations . 28

Figure 5 – Measurement principle with four terminal network theory . 28

Figure 6 – Admittance measurement configurations . 31

Figure 7 – Admittance measurement principle . 31

Figure 8 – Transmission line system . 35

Figure 9 – Differential-mode transmission in a symmetric pair . 41

Figure 10 – Common-mode transmission in a symmetric pair . 41

Figure 11 – Circuit of an infinitesimal element of a symmetric pair . 43
Figure 12 – Calculated coupling transfer function for a capacitive coupling of 0,4 pF/m
and random 0,4 pF/m ( = 100 m;  =  = 2,3) . 45
r1 r2
Figure 13 – Measured coupling transfer function of 100 m Twinax 105  . 46
Figure 14 – Diagram of a single-ended 4-port device . 47
Figure 15 – Diagram of a balanced 2-port device . 48
Figure 16 – Possible solution for calibration of reference loads . 49
Figure 17 – Resistor termination networks . 50
Figure 18 – Insertion loss and EL TCTL measurement . 53
Figure 19 – NEXT measurement . 55
Figure 20 – FEXT measurement . 57
Figure 21 – Return loss and TCL measurement . 59
Figure 22 – Alien NEXT measurement . 61
Figure 23 – Alien FEXT . 64
Figure A.1 – Voltage and current on balanced DUT . 66
Figure A.2 – Voltage and current on unbalanced DUT . 67

Table 1 – Unbalance attenuation at near end . 42
Table 2 – Unbalance attenuation at far end . 42
Table 3 – Measurement set-up . 42
Table 4 – Mixed mode S-parameter nomenclature . 48
Table 5 – Requirements for terminations at calibration plane . 51

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INTERNATIONAL ELECTROTECHNICAL COMMISSION

____________
MULTICORE AND SYMMETRICAL PAIR/QUAD CABLES FOR DIGITAL

COMMUNICATIONS –
Part 1-2: Electrical transmission characteristics and test methods of

symmetrical pair/quad cables
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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agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
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.
This consolidated version of the official IEC Standard and its amendment has been
prepared for user convenience.
IEC TR 61156-1-2 edition 1.1 contains the first edition (2009-05) [documents 46C/853/DTR
and 46C/889/RVC] and its amendment 1 (2014-09) [documents 46C/993/DTR and
46C/1000/RVC].
In this Redline version, a vertical line in the margin shows where the technical content is
modified by amendment 1. Additions and deletions are displayed in red, with deletions
being struck through. A separate Final version with all changes accepted is available in
this publication.
– 6 – IEC TR 61156-1-2:2009
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The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected

data of a different kind from that which is normally published as an International Standard, for

example "state of the art".
IEC 61156-1-2, which is a technical report, has been prepared by subcommittee 46C: Wires

and symmetric cables, of IEC technical committee 46: Cables, wires, waveguides, R.F.

connectors, R.F. and microwave passive components and accessories.

This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.

A list of all parts of the IEC 61156 series, under the general title: Multicore and symmetrical
pair/quad cables for digital communications, can be found on the IEC website.
The committee has decided that the contents of the base publication and its amendment 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.
A bilingual version of this publication may be issued at a later date.

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.
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MULTICORE AND SYMMETRICAL PAIR/QUAD CABLES FOR DIGITAL

COMMUNICATIONS –
Part 1-2: Electrical transmission characteristics and test methods of

symmetrical pair/quad cables
1 Scope
This technical report is a revision of the symmetrical pair/quad electrical transmission
characteristics present in IEC 61156-1:2002 (Edition 2) and not carried into IEC 61156-1:2007
(Edition 3).
This technical report includes the following topics from IEC 61156-1:2002:
– the characteristic impedance test methods and function fitting procedures of 3.3.6;
– Annex A covering basic transmission line equations and test methods;
– Annex B covering the open/short-circuit method;
– Annex C covering unbalance attenuation.
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 60050-726, International Electrotechnical Vocabulary – Part 726: Transmission lines and
waveguides
IEC 60169-15, Radio-frequency connectors – Part 15: R.F. coaxial connectors with inner
diameter of outer conductor 4,13 mm (0,163 in) with screw coupling – Characteristic
impedance 50 ohms (Type SMA)
IEC 61156-1:2007, Multicore and symmetrical pair/quad cables for digital communications –
Part 1: Generic specification
IEC 61169-16, Radio-frequency connectors – Part 16: Sectional specification – RF coaxial
connectors with inner diameter of outer conductor 7 mm (0,276 in) with screw coupling –

Characteristics impedance 50 ohms (75 ohms) (type N)
IEC/TR 62152, Background of terms and definitions of cascaded two-ports
3 Terms, definitions, symbols, units and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-726 and,
IEC TR 62152 and the following apply:
3.1.1
single-ended
measurement with respect to a fixed potential, usually ground

– 8 – IEC TR 61156-1-2:2009
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3.2 Symbols, units and abbreviated terms

For the purposes of this document, the following symbols, units and abbreviated terms apply.

Transmission line equation electrical symbols and related terms and symbols:

R pair resistance (Ω/m)
L pair inductance (H/m)
G pair conductance (S/m)
C pair capacitance (F/m)
α attenuation coefficient (Np/m)
β phase coefficient (rad/m)
γ propagation coefficient (Np/m, rad/m)
νP phase velocity of cable (m/s)
νG group velocity of cable (m/s)
τP phase delay time (s/m)
τG group delay time (s/m)
Z
complex characteristic impedance, or mean characteristic impedance if the pair
C
is homogeneous or free of structure (also used to represent a function fitted
result) (Ω)
∠Z angle of the characteristic impedance in radians
C
Z high frequency asymptotic value of the characteristic impedance (Ω)
∞
l length (m)
j imaginary denominator
Re real part operator for a complex variable
Im imaginary part operator for a complex variable
ω radian frequency (rad/s)
f frequency (Hz)
R’ first derivative of R with respect to ω
C’ first derivative of C with respect to ω
L’ first derivative of L with respect to ω
R d.c. resistance of a round solid wire with radius r (Ω/m)
R constant with frequency component of resistance which is about 1/4 of the d.c.
C
resistance (Ω/m)
R square-root of frequency component of resistance (Ω/m)
S
L external (free space) inductance (H/m)
E
L internal inductance whose reactance equals the surface resistance at high
I
frequencies (H/m)
σ specific conductivity of the wire material (S/m)
ρ resistivity of the wire material (Ω/m )
µ permeability of the wire material (H/m)
r radius of the wire (m)
δ skin depth (not to be confused with the dissipation factor tan δ) (m)

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δ =
πf µσ
tan δ dissipation factor
tan δ = G/(ωC)
q forward echo coefficient at the far end of the cable at a resonant frequency

p reflection coefficient measured from the near end of the cable at a

Z − Z
CM C
−PSRL / 20
resonant frequency, p = 10 =
Z + Z
CM C
A forward echo attenuation at a resonant frequency (dB)
Q
A = – 20 log q
Q
PSRL structural return loss at a resonant frequency (dB)
PSRL = – 20 log p
K = 2αl – 1 when 2αl >> 1 (Np)
A = 2 × PSRL – 20 log(2αl – 1) (dB) where 2αl is in Np
Q
complex measured open circuit impedance (Ω)
Z
OC
Z complex measured short circuit impedance (Ω)
SC
Z characteristic impedance as measured (with structure) (Ω)
CM
=
Z Z Z
CM SC OC
Z complex measured impedance (open or short) (Ω)
MEAS
input impedance of the cable when it is terminated by Z (Ω)
Z
IN L
Z output impedance of the cable when the input of the cable is terminated by
OUT
Z (Ω)
G
Z Z
nominal characteristic impedance of a cable and is the specified value at a
CN C
given frequency with tolerance and the structural return loss SRL limits in dB in
a frequency range (Ω)
Z nominal (reference) impedance of the link and/or terminals (the system)
N
between which the cable is operating (Ω)
Z
(nominal) reference impedance that is used in measurement. Normally (for
R
Z Z
actual return loss results), = . When using a return loss measurement to
R N
approximate SRL, it is practical to choose Z to give the best balance in the
R
given frequency range (Ω)
Z terminated impedance measurement made with the opposite end of the cable
T
pair terminated in the reference impedance Z (Ω)
R
ς reflection coefficient measured in the terminated measurement method
−
Z Z
R C
ς =
+
Z Z
R C
Z
termination at the cable input when defining the output impedance of the cable
G
Z (Ω)
OUT
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Z
termination at the cable output when defining the input impedance of the cable
L
Z (Ω)
IN
L , L , L , L least squares fit coefficients for angle of the characteristic impedance

0 1 2 3
K , K , K , K least squares fit coefficients of the characteristic impedance
0 1 2 3
Z  fitted magnitude of the characteristic impedance (Ω)
C
Z  measured magnitude of the characteristic impedance (Ω)

CM
∠ (V ) input angle relative to a reference angle in radians
1N
∠ (V ) output angle relative to the same reference angle in radians
1F
k multiple of 2π radians
S
reflection coefficient measured with an S parameter test set
RL return loss (dB)
SRL structural return loss (dB)

Attenuation unbalance electrical symbols:
TA transverse asymmetry
LA longitudinal asymmetry
R , R resistance of one conductor per unit length (Ω)
1 2
L , L inductance of one conductor per unit length (H)
1 2
C , C capacitance of one conductor to earth (F)
1 2
G , G conductance of one conductor to earth (S)
1 2
α unbalance attenuation (dB)
u
T unbalance coupling transfer function
u
Z characteristic impedance of the common-mode circuit (Ω)
com
Z characteristic impedance of the differential-mode circuit (Ω)
diff
Z unbalance impedance (Ω)
unbal
 length of transmission line (m)
x length coordinate (m)
γ propagation factor of the common-mode circuit (Np/m, rad/m)
com
γ propagation factor of the differential-mode circuit (Np/m, rad/m)
diff
α operational differential-mode attenuation of the cable (dB)
diff
α operational common-mode attenuation of the cable (dB)
com
∆R resistance unbalance of the sample length (Ω)
∆L inductance unbalance of the sample length (H)
∆C capacitance unbalance to earth (F)
∆G conductance unbalance to earth (S)
S summing function
U voltage in the differential-mode circuit (V)
diff
U voltage in the common-mode circuit (V)
com
n, f index to designate the near end and far end, respectively

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4 Basic transmission line equations

4.1 Introduction
A review of the relationships between the propagation coefficient and characteristic

impedance and the primary parameters R, L, G and C is useful here. Characteristic impedance

is commonly thought of as being a magnitude quantity. While this concept may suffice for high

frequency applications, this quantity is actually a complex one consisting of real and

imaginary components or magnitude and angle. The associated propagation coefficient is

readily viewed as being complex, consisting of the real attenuation and imaginary phase
coefficient components. The four secondary components are readily related to the primary

components. Frequency dependence of these parameters is also developed.

The cable pair parameters are represented as frequency domain dependent quantities. The
measurement methods are based on frequency domain techniques. Measurement methods
based on time domain techniques and combinations of time and frequency while useful in
many cases are not covered here. The present-day availability of excellent frequency domain
equipment such as the network analysers and impedance meters supports the frequency
domain approach.
4.2 Characteristic impedance and propagation coefficient equations
4.2.1 General
The frequency domain of the complex characteristic impedance Z relates to the primary
C
parameters as:
R + jωL
= (1)
Z
C
G + jωC
The propagation coefficient, γ, relates to the primary parameters as:
γ = α + jβ = (R + jωL)(G + jωC) (2)
4.2.2 Propagation coefficient
4.2.2.1 Attenuation and phase coefficients
Equation (2) is separated into its real and imaginary parts, the attenuation coefficient α and
the phase coefficient β:
1 1
2 2 2 2 2 2 2
(3)
α = − ( LC − RG) + ( + )( + )
ω R ω L G ω C
2 2
1 1
2 2 2 2 2 2 2
(4)
β = ( LC − RG) + ( + )( + )
ω R ω L G ω C
2 2
Further, by factoring out we obtain:
ω LC
2 2
  
1  R G  1
R G
 
 
 
β = ω LC 1 − + 1 + 1 + (5)
 
2 2 2 2
  
2 ωL ωC 2
  ω L ω C
  
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It can be shown that:
 
R C
 
αβ = ω LC  (6)
 
2 L
 
4.2.2.2 Equations useful at high frequencies

From Equations (5) and (6) we can solve for α and thus obtain for α and β the following

expressions, valid within the entire frequency range:

R C G L
+
2 L 2 C
α = (7)
2 2
  
1 1
 R G 
R G
  
 
1 − + 1 + 1 +
 
2 2 2 2
  
2 ωL ωC 2
  ω L ω C
  
2 2
  
1  R G  1
R G
 
 
 
β = ω LC 1 − + 1 + 1 + (8)
 
2 2 2 2
  
2 ωL ωC 2
  ω L ω C
  
Equations (7) and (8) are well suited for evaluation of high frequencies.
4.2.2.3 Equations useful at low frequencies
For low frequency evaluations, the expressions given by Equations (9) and (10) are suitable.
2 2 2
  
ωRC  G ωL 
ω L G
  
 
α =  − + 1 + 1 + (9)
 
 2  2 2 
2 ωC R
R ω C
 
  
2 2 2

 
ωRC  ωL G 
ω L G
  
 
β = − + 1 + 1 + (10)
 
 2  2 2 
2 R ωC
R ω C
 
  
4.2.3 Characteristic impedance

4.2.3.1 Real and imaginary parts
Z
The characteristic impedance can also be separated into its real and imaginary parts as
C
developed in Equations (11) and (12).
R + jωL α + jβ
= Re  + j Im   =   =  (11)
Z Z Z
C C C
G + jωC G + jωC
1  G G 
   
 β +  α  − j α −  β 
 
ωC ωC ωC
   
 
= (12)
Z
C
G
1 +
2 2
ω C
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4.2.3.2 Equations useful at high frequencies

After substituting Equations (7) and (8) into Equation (12), the real and imaginary parts of the

characteristic impedance are obtained as given in Equations (13) and (14) respectively.

These are well suited for simplification (see 4.3) at high frequencies:

 
2 2
  
L 1  R G  1
R G
 
  
1 − + 1 + 1 +
 
 2 2  2 2 
C  2 ωL ωC 2 
  ω L ω C
  
 
Re  = (13)
Z
C
2 2 2
    
1  R G  1
G R G
    
1 + 1 − + 1 + 1 +
 
 2 2   2 2  2 2 
2 ωL ωC 2
ω C   ω L ω C
    
 
2 2
  
R G L G L 1  R G  1
R G
 
  
+  −  1 −  + 1 + 1 +
 2 2  2 2 
2ωC C ωC C  2 ωL ωC 2 
2ω LC  
ω L ω C
  
 
− Im  = (14)
Z
C
2 2 2
    
1  R G  1
G R G
    
1 + 1 −  + 1 + 1 +
 2 2   2 2  2 2 
2 ωL ωC 2
 
ω C ω L ω C
    
4.2.3.3 Equations useful at low frequencies
On the other hand, by substituting Equations (9) and (10) into Equation (12), the real and
imaginary parts given in Equations (15) and (16) respectively are obtained. These are useful
for simplification in the low frequency range:
 
2 2 2 2 2 2
     
R ωL G G G ωL
ω L G ω L G
 
     
−  + 1 + 1 +  +  −  + 1 + 1 +
  2  2 2   2  2 2  
2ωC R ωC ωC ωC R
R ω C R ω C
     
 
 
(15)
Re  =
Z
C
 
G
 
1 +
 2 2 
ω C
 
 
2 2 2 2
2 2
     
R G ωL G ωL G
ω L G ω L G
 
     
− + 1 + 1 + −  − + 1 + 1 +
 2  2 2   2  2 2 
 
2ωC ωC R ωC R ωC
R ω C R ω C
     
 
 
(16)
− Im  =
Z
C
 
G
 
1 +
 2 2 
ω C
 
4.2.4 Phase and group velocity
The phase propagation time (per unit length) is:
β
= (17)
τ
P
ω
By introducing β from Equations (8) and (10), we obtain:
2 2
  
1 R G 1
 
R G
  
= LC 1 −  + 1 + 1 + (18)
τ
P
 2 2  2 2 
2 ωL ωC 2
 
ω L ω C
  
– 14 – IEC TR 61156-1-2:2009
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2 2 2
  
RC ωL G
 
ω L G
  
and =  −  + 1 + 1 + (19)
τ
P
 2  2 2 
2 ω R ωC
  R C
ω
  
The group propagation time (per unit length) is:

dβ
= (20)
τ
G
dω
      
2 2
   
 R   G 
G R R G
       
   
1 +  1 +
β 1 L’ C ’ d   d  
     
(21)
2   2 2     2 2  
=  +   +  β + ωL ωC
τ LC G ω C ωL R ω L ωC
G ω        
   
   
ω 2 L C − +   + − +
 
   
4β  ωC dω   ωL dω 
2 2 2 2
     
R G R G
   
         
1 + 1 + 1 + 1 +
 2 2  2 2   2 2  2 2 
   
   
ω L ω C ω L ω C
     
   
   
The phase and group velocities are, respectively,
= (22)
ν
P
τ
P
= (23)
ν
G
τ
G
The above expressions are accurate and valid within the whole frequency range. If C and
G/(ωC) can be regarded as frequency independent coefficients, then we obtain:
 
 
R
G
 
 
1 +
 2 2 
 
ωL
β β L’ C G ω C  L’ R 
 
= +  +  − +  − R + R ’ ω −  ω  (24)
τ
G
ω 2 L 4β ωC 2 L
2  
   
 
R G
  
1 + 1 +
 
 2 2  2 2 
ω L ω C
 
  
 
The above expressions, which are valid within the entire frequency range, can be simplified
into approximate expressions, which are valid at high or low frequencies only.
4.3 High frequency representation of secondary parameters
The high frequency representations of the formulas are useful over a broad range of

frequencies extending from voice frequency on up because of the range of values for the
dissipation factor. G/(ωC) = tan δ < 0,03 (< 3 %) even for PVC insulated cables up to 1,5 MHz
and for the polyethylene (PE), insulation is very small at about 0,000 1 (0,01 %). This results
in approximations, which in practice are valid for the whole frequency range as follows:
L 1 1
R
(25)
Re ≈  + 1 +
Z
C
2 2
C 2 2
ω L
G L
R G
2ωC C
− Im ≈ − Re + (26)
Z Z
C C
2ωC Re ωC Re
Z Z
C C
+AMD1:2014 CSV  IEC 2014
 
L
 
G
 
C
R
 
α ≈ + (27)
2 Re 2 Re
Z Z
C C
β ≈ ωC Re (28)
Z
C
≈ LC (29)
τ
P
 
 R 
 
β β L’ C G  L’ R 
ωL
≈ +  + − + − R + R ’ ω − ω (30)
τ    
G
ω 2 L 4β ωC 2 L
   
R
1 +
 
2 2
ω L
 
when also R/(ωL) < 0,1, which is true for high frequencies (f > 1 MHz for 0,5 mm wire), the
formulas holding better than about 1 % accuracy can be further simplified as shown below.
L
Re ≈  (31)
Z
C
C
R G L  R G 
 
− Im ≈ − Re ≈ − (32)
Z Z
C C
 
2ωC Re ωC C 2ωL 2ωC
Z
C
 
R G R C G L
α ≈ +  Re ≈ + (33)
Z
C
2 Re 2 2 L 2 C
Z
C
β ≈ ω C Re ≈ ω LC (34)
Z
C
≈ LC (35)
τ
P
β L’ C  G R   L’ R 
≈ +  + − + − R + R ’ ω − ω (36)
   
τ τ
G P
2 L 4β ωC ωL L
   
4.4 Frequency dependence of the primary and secondary parameters
4.4.1 Resistance
The high frequency resistance (surface resistance) of a solid round wire for frequencies where
the wire radius r is greater than twice the skin depth δ can be regarded as consisting of two
0,5
parts where one is constant and the other f dependent.
 1 r 
R = + = + ρ ω ≈  +  (37)
R R R R
C S C 0
4 2δ
 
– 16 – IEC TR 61156-1-2:2009
+AMD1:2014 CSV  IEC 2014
r
R R
S 0
ρ = = 2µσ (38)
ω
The above is true for a solid wire alone. In a pair, the proximity effects and the presence of

other pairs and possible screen contribute both to the resistance and inductance. These

effects can increase the R by about 15 % at 1 MHz and follow also approximately the square-

root of frequency law. Also, the constant component of resistance while often neglected, is

about 15 % of the frequency dependent component at 1 MHz for a 0,5 mm diameter copper

pair.
4.4.2 Inductance
The total inductance consists also of two main components such that
ρ
R
S
L ≈ + = + = + (39)
L L L L
E I E E
ω
ω
The external free space inductance is reduced by the proximity effect of the pair and the free
space limiting effects of the nearby shield and/or other pairs. These inductive components are
negative and fairly frequency independent at high frequencies.
4.4.3 Characteristic impedance
The characteristic impedance high frequency asymptotic value Z is given by Equation (40).
∞
L
E
= (40)
Z ∞
C
The high frequency impedance formulas are given by Equations (41) and (42):
L   ρ
R
S
 
Re ≈ ≈ 1 + = + (41)
Z Z Z
C ∞ ∞
 
C 2 ω
L 2 C ω
 E  L
E
L  R G 
− Im ≈  −
 
Z
C
C 2ωL 2ωC
 
 
+ ρ ω ρ tan δ
R L
C E
 
≈ − 1 +
 
  C 2
ρ 2 ω
L
 E 
 
2ω C 1 +
L
E
 
(42)
2 ω
L
 E 
 
ρ
R Z L
C ∞ I
 
≈ + − 1+ tan δ
 
2ω C 2 C ω L
E
L L  
E E
ρ
Z
∞
≈ − tanδ
2 C ω
L
E
4.4.4 Attenuation coefficient
Using the above approximations with Equations (31) through (36) results in the remaining
equations of this subclause:
 
ρ
 
−
R
C
 
L
E ω C tan δ
ρ ω ρ ω tan δ L
  E
α ≈ + + + (43)
2 2Z 4 2
Z Z
∞ ∞ ∞
+AMD1:2014 CSV  IEC 2014
which is of the form:
α ≈ A + B ω + Cω (44)
where A, B and C are constants.

The first term of Equation (44) indicates that at the low end of the high frequency range the

0,5
attenuation increases a little more slowly than the square-root-law. The first ω term in

Equation (43) which is dominant in the high frequency attenuation formula also appears in the

phase coefficient, Equation (45).

 
R ρ ω
β ≈ ω LC ≈ ω C 1 +  ≈ ω L C + (45)
L
E E
 
2 ω 2
L Z
 E  ∞
4.4.5 Phase delay and group delay
The phase and group delay are given in Equations (46) and (47) respectively:
 
R ρ
≈ LC = C 1 +  ≈ C + (46)
τ L L
P E E
 
2ω
L 2 Z ω
 E 
∞
β L’ C G R L’ R
   
≈ +  + − +  − R + R ’ ω − ω 
τ τ
G P
2 L 4β ωC ωL L
   
R R R G
   
≈ 1 −  −  − 
4ωL 8ωL ωL ωC
   
R
 
≈ 1 − 
τ (47)
P
4ωL
 
 R 
 
≈ C 1 +
L
E
 
4ω
L
 E 
ρ
≈ C +
L
E
4 ω
Z
∞
– 18 – IEC TR 61156-1-2:2009
+AMD1:2014 CSV  IEC 2014
10 000
β
1 000
|Z |
C
Re Z
C
α α-R
–1
–2
–3 –2 –1 1 2 3
10 10 10 10 10 10
Frequency  (MHz)
IEC  839/09
Figure 1 – Secondary parameters extending from 1 kHz to 1 GHz
Figure 1 shows the secondary parameters of a UTP pair with 0,5 mm conductors versus
frequency. At voice frequencies, the attenuation and phase coefficients are substantially
equal. At these frequencies, the abs
...