Multicore and symmetrical pair/quad cables for digital communications - Part 1-3: Electrical transmission parameters for modelling cable assemblies using symmetrical pair/quad cables

IEC/TR 61156-1-3:2011(E) is a supplement to IEC 61156-1 Edition 3 (2007): Multicore and symmetrical pair/quad cables for digital communications - Part 1: Generic specification. It covers the following topics:
- the near-end crosstalk test methods and length correction procedures of 6.3.5;
- the far-end crosstalk test methods and length correction procedures of 6.3.6;
- the concatenation of measured cable segments, even if they are of different design.

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Status
Published
Publication Date
06-Apr-2011
Current Stage
PPUB - Publication issued
Start Date
07-Apr-2011
Completion Date
07-Apr-2011
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IEC/TR 61156-1-3
Edition 1.0 2011-04
TECHNICAL
REPORT
colour
inside
Multicore and symmetrical pair/quad cables for digital communications –
Part 1-3: Electrical transmission parameters for modelling cable assemblies
using symmetrical pair/quad cables
IEC/TR 61156-1-3:2011(E)
---------------------- Page: 1 ----------------------
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---------------------- Page: 2 ----------------------
IEC/TR 61156-1-3
Edition 1.0 2011-04
TECHNICAL
REPORT
colour
inside
Multicore and symmetrical pair/quad cables for digital communications –
Part 1-3: Electrical transmission parameters for modelling cable assemblies
using symmetrical pair/quad cables
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
ICS 33.120.20 ISBN 978-2-88912-429-9
® Registered trademark of the International Electrotechnical Commission
---------------------- Page: 3 ----------------------
– 2 – TR 61156-1-3  IEC:2011(E)
CONTENTS

FOREWORD ........................................................................................................................... 3

1 Scope ............................................................................................................................... 5

2 Normative references ....................................................................................................... 5

3 Terms, definitions, symbols, units and abbreviated terms ................................................. 6

3.1 Terms and definitions .............................................................................................. 6

3.2 Symbols, units and abbreviated terms ..................................................................... 6

4 Traditional length correction formulae ............................................................................... 7

4.1 Introduction ............................................................................................................. 7

4.2 Length correction formulae in IEC 61156-1 .............................................................. 7

4.3 The development of the traditional cross-talk length correction formulae

NEXT and EL FEXT [3] ............................................................................................ 8

5 Using traditional cross-talk length correction formulae .................................................... 16

5.1 Background (see [4]) ............................................................................................. 16

5.2 Example (see [5], [6]) Length and frequency dependency of direct near-end

crosstalk attenuation ............................................................................................. 17

6 On length concatenation of measured cables, using scattering and scattering

transfer parameters, see informative reference [7]. ......................................................... 21

7 Matrix (model) status, comparison of different calculations [8] ........................................ 24

8 Recommendations for applying length correction formulae to modelling cross-talk

in cable assemblies ........................................................................................................ 25

Bibliography .......................................................................................................................... 26

Figure 1 – Coupling between two circuits due to unbalances of the primary parameters .......... 9

Figure 2 – Integration of the coupled near- and far-end currents over the length of the

cable .................................................................................................................................... 13

Figure 3 – Delta A at different frequencies as a function of length ....................................... 19

Figure 4 – Delta A for different lengths as a function of frequency ....................................... 20

Figure 5 – Delta A for different lengths as a function of frequency (= Delta A + Delta

A ) f = 500 MHz ................................................................................................................... 21

2 0
Figure 6 – Typical port assignment resulting out of the numbering of the VNA

measuring ports .................................................................................................................... 21

Figure 7 – Incident and reflected waves, schematically represented for a 2n × 2n

multiport network .................................................................................................................. 23

Table 1 – Delta A as a function of length or frequency, the other being a parameter ........... 19

Table 2 – Delta A as a function of frequency (= Delta A + Delta A ) ..................................... 20

1 2
---------------------- Page: 4 ----------------------
TR 61156-1-3  IEC:2011(E) – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MULTICORE AND SYMMETRICAL PAIR/QUAD
CABLES FOR DIGITAL COMMUNICATIONS –
Part 1-3: Electrical transmission parameters for modelling cable
assemblies using 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

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expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC

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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.

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/TR 61156-1-3, 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.
---------------------- Page: 5 ----------------------
– 4 – TR 61156-1-3  IEC:2011(E)
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
46C/924/DTR 46C/932/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.

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

A list of all the parts in the IEC 61156 series, published 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 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.
---------------------- Page: 6 ----------------------
TR 61156-1-3  IEC:2011(E) – 5 –
MULTICORE AND SYMMETRICAL PAIR/QUAD
CABLES FOR DIGITAL COMMUNICATIONS –
Part 1-3: Electrical transmission parameters for modelling cable
assemblies using symmetrical pair/quad cables
1 Scope

This technical report is a supplement to IEC 61156-1 Edition 3 (2007): Multicore and

symmetrical pair/quad cables for digital communications – Part 1: Generic specification.

This technical report covers the following topics following this standard:
– the near-end crosstalk test methods and length correction procedures of 6.3.5;
– the far-end crosstalk test methods and length correction procedures of 6.3.6;

– the concatenation of measured cable segments, even if they are of different design.

The final objective of this technical report is to describe the mathematics involved to model

the concatenation of cable sections of different length, not based upon measurements but

based upon the specification limits of the cables involved. This is required as a base

foundation of the complete channel modelling, involving also the connectivity covered by IEC

SC48B towards channels, as required and requested by ISO/IEC JTC1/SC25 WG3 for
incorporation into ISO/IEC 11801:2002 [1] .

This TR is informative and contains observations and recommendations applicable to using

the length correction formulas for either measurements or modelling of balanced cables.

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 61156-1-2, Multicore and symmetrical pair/quad cables for digital communications –

Part 1-2: Electrical transmission characteristics and test methods of symmetrical pair/quad

cables

IEC 61156-5, Multicore and symmetrical pair/quad cables for digital communications – Part 5:

Symmetrical pair/quad cables with transmission characteristics up to 1 000 MHz – Horizontal

floor wiring – Sectional specification
___________
The figures in square brackets refer to the Bibliography.
---------------------- Page: 7 ----------------------
– 6 – TR 61156-1-3  IEC:2011(E)

IEC 61156-6, Multicore and symmetrical pair/quad cables for digital communications – Part 6:

Symmetrical pair/quad cables with transmission characteristics up to 1 000 MHz – Work area

wiring – Sectional specification

IEC/TR 62152, Transmission properties of cascaded two-ports or quadripols – Background of

terms and definitions
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,

IEC/TR 61156-1-2, 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, or dB as indicated)
β phase coefficient (rad/m)
γ propagation coefficient (Np/m, rad/m)
x length coordinate (m)
complex characteristic impedance, or mean characteristic impedance if the pair
is homogeneous or free of structure (also used to represent a function fitted
result) (Ω)
l length, variable (m)
M length, reference, disturbing (m)
Λ length, reference, disturbed (m)
j imaginary denominator
ω radian frequency (rad/s)
f frequency (Hz)
I current, coupled
I current in the differential-mode circuit (I)
diff
I current in the common-mode circuit (I)
com
U voltage in the differential-mode circuit (V)
diff
U voltage in the common-mode circuit (V)
com
index to designate the pair 1 and pair 2, respectively
1, 2
index to designate the near end and far end, respectively
N, F
TU transverse unbalance
LU longitudinal unbalance
K coupling coefficient
near end cross-talk coupling coefficient
far end cross-talk coupling coefficient
---------------------- Page: 8 ----------------------
TR 61156-1-3  IEC:2011(E) – 7 –
k , k , k attenuation coefficients for the twisted pair
1 2 3
FEXT far-end crosstalk loss (dB)
NEXT near-end crosstalk loss (dB)
EL FEXT equal-level far-end crosstalk loss (dB)
ACR-F attenuation-to-crosstalk-ratio far-end loss (dB)
∆ length correction coefficient
S parameter matrix
S parameter
T parameter matrix
T parameter
index to designate the incident port and reflected port, of multiport parameter
4 Traditional length correction formulae
4.1 Introduction

The traditional length correction formulae were intended for measurements on long

manufactured lengths to be corrected to the specified nominal length; i.e. for cables

complying to IEC 61156-5 and IEC 61156-6, as outlined in IEC 61156-1. Therein the length

corrections apply to measurements made on longer lengths than 100 m, to be corrected to the

100 m specification. Moreover, these formulae were normally used in the cable industry for

quality assurance purposes.

The formulae are intended for measurements of crosstalk within cables with length

uncorrelated crosstalk coupling characteristics. Thus they do not readily adapt to the limit

lines for crosstalk loss, which are the upper-bounds for the characteristic length correlated

crosstalk coupling, i.e. a homogeneous coupling along a cable that is at the limit line at every

frequency, at the specified length.
4.2 Length correction formulae in IEC 61156-1
The formulae are
 
FEXT = FEXT − 10⋅log  −α +α (1)
 M 10 M 
 
and
  
 
1− 10
 
NEXT = NEXT − 10⋅log (2)
 M 10
 4α 
 20 
1− 10
 
where
ℓ is the actual cable conversion length;
M is the reference cable specification length;
α is the attenuation for the indexed length in dB.

Normally, we measure FEXT and derive from it, using the corresponding attenuation, either

the EL FEXT or more pertinent to data grade cables the ACR-F.
---------------------- Page: 9 ----------------------
– 8 – TR 61156-1-3  IEC:2011(E)
For these last two values, we have then the following length corrections:
  
EL FEXT = EL FEXT − 10⋅ log   (3)
 M 10
 
and
 
ACR− F = ACR− F − 10⋅log   (4)
 Λ 10
 

Here a distinction between the length M and Λ is made to indicate the difference between

disturbing and disturbed pair attenuation, respectively.

The measurement magnitude values or the complex values of the actual cable may be used to

compute the crosstalk parameter when applying the traditional length correction formula,

though these formulae refer only to magnitude values.

4.3 The development of the traditional cross-talk length correction formulae NEXT

and EL FEXT [3]

First only in-put to out-put and the out-put to out-put cross-talk coupling are considered.

These correspond to the near-end cross-talk and the equal level far-end cross-talk. These are

called in the cable industry generally NEXT (IO–NEXT though this denomination is in the

present case irrelevant) and EL FEXT (or OO–FEXT). These two terms are treated first,

before going over to the in-put to out-put FEXT (IO–FEXT).

NOTE It should be noted that the following derivation was first published by the members of the technical staff of

the Bell telephone laboratories [6].

If we consider the coupling between two infinitesimal short circuits, we have to take first the

unbalances of the primary parameters of both circuits 1 and 2 into account. This inherently

implies the assumption that the primary parameters as prime responsible factor for the

crosstalk coupling are statistically distributed over the length of the cable.
---------------------- Page: 10 ----------------------
TR 61156-1-3  IEC:2011(E) – 9 –
Z R /2 L /2
1 1
I (x)
L /2 R /2
1 1
L /2 R /2
2 2
I (x)
dI (x) I (x)
N C dI (x)
R /2 L /2
2 2
IEC 631/11
Key
I (x) current induced at the length x due to capacitive coupling

I (x) current going into the infinitesimal length of the line dx at the length x

I (x) current induced at the length x due to inductive coupling

dI (x) current increment flowing through the near end termination of the infinitesimal length

element

dI (x) current increment flowing through the far end termination of the infinitesimal length

element

Z impedance of the termination of the length element. It is assumed here to be identical

for all source and load impedances, and corresponds additionally to the characteristic

impedance of the pairs
Figure 1 – Coupling between two circuits due to unbalances
of the primary parameters

We get then according to Figure 1 for the corresponding crosstalk values of interest between

two infinitesimally short circuits.

As a result of the above, it is implied that the integration direction of the infinitesimal current

or voltage increments is reversed in direction.

Besides the mathematically easier treatment, this has also an historical background. Thus the

telephone linesmen could not determine the IO-FEXT, but they could easily measure the OO-

FEXT on the poles.

For the transverse and the longitudinal unbalances of the primary parameters, we get

following the indications in Figure 1:
TU= ( G + j⋅ω⋅ C )− ( G + j⋅ω⋅ C ) (5)
21 21 12 12
LU= ( R + j⋅ω⋅ L )− ( R + j⋅ω⋅ L ) (6)
2 2 1 1
where
TU is the transverse unbalance between the pairs of the corresponding primary
parameters G and C;
LU is the longitudinal unbalance between the pairs of the corresponding primary
parameters R and L;
G /2
C /2
G /2
C /2
C /2
G /2
C /2
G /2
Z Z
o o
---------------------- Page: 11 ----------------------
– 10 – TR 61156-1-3  IEC:2011(E)
1,2 are indices indicating pair 1 and 2;
G is the conductance unbalance between the pairs;
C is the capacitance unbalance between the pairs;
R is the mutual resistance unbalance of the pairs;
L is the mutual inductance unbalance of the pairs;
j is the complex operator;
ω is the circular frequency.

We neglect the conductance unbalance between the pairs which we can – at least for modern

data grade cables – assume to be zero. This is the result of the use of insulating materials

with a very low tanδ, like PE or FEP. In fact, the resulting conductance unbalance is generally

so small that it would be extremely hard to determine it at all.
We then get
G = G ≈ 0 (7)
12 21
TU= j⋅ω⋅ C − j⋅ω⋅ C = j⋅ω⋅(C − C ) (8)
21 12 21 12
LU= ( R − R )+ j⋅ω⋅( L − L ) (9)
2 1 2 1

We can furthermore assume that both infinitesimal elements of Figure 1 are on each side

terminated in Z , which is also the characteristic impedance of the pairs considered. In other

words, we consider only the case of perfectly matched pairs. The impedance of the

capacitance unbalances is as a result much higher than the characteristic impedance, such

that we may neglect the latter one to calculate the current going through each termination. In

this case – due to the fact of matched impedances – we have then for the infinitesimal

element the transverse and the longitudinal unbalances of the primary parameters of the pairs

considered:
We then get
C − C Z ⋅ I (x)
12 21 o o
(10)
2⋅ I (x)=− j⋅ω⋅ ⋅
2 2
and
R − R L − L
2 1 1 2
I (x)=− − j⋅ω⋅ (11)
2⋅ Z 2⋅ Z
o o
or with
(12)
C= C − C
12 21
(13)
R= R − R
2 1
(14)
L= L − L
1 2
we get
C⋅ Z ⋅ I (x)
o o
I (x)=− j⋅ω⋅ (15)
---------------------- Page: 12 ----------------------
TR 61156-1-3  IEC:2011(E) – 11 –
and
 
R L
 
I (x)=− + j⋅ω⋅ ⋅ I (x) (16)
L o
 
2⋅ Z 2⋅ Z
 o o

In a further step, we can neglect also the longitudinal resistance unbalance between the pairs,

i.e. we assume R ≈ 0. This is definitely acceptable for modern data grade cables.

However, in the past, this approximation was only justifiable on a large scale statistical basis.

The main reason for this was the fact that frequently, the tangential line between the twisted

conductors was – due to tension unbalances in the twisters – not a straight line. In other

words, one conductor is more or less wrapped around the other wire. This resulted of course

in the result that one wire was longer than the other, and there resulted a relatively high

resistance unbalance which definitely affected severely the cross-talk.

For the currents at the near end and the far end of the infinitesimal element, we then get

 
C⋅ Z L
  (17)
dI (x)=− j⋅ω⋅ + ⋅ I (x)
N N
 
8 2⋅ Z
 o 
and
 C⋅ Z 
 
dI (x)=− j⋅ω⋅ − ⋅ I (x) (18)
F F
 
8 2⋅ Z
 
where

I (x) is the current flowing through the near end termination of the length element at the

termination point x, i.e. just before the infinitesimal length element as seen from the

right side;

I (x) is the current flowing through the far end termination point (ℓ-x), i.e. just before the

infinitesimal length element as seen from the left side;
x is the length coordinate of the considered cable element.
If we use the abbreviations
 
Z ⋅ C L
 
K = + (19)
 
8 2⋅ Z
 o 
 Z ⋅ C 
 
K = − (20)
 
8 2⋅ Z
 

we get for the near end and far end currents, respectively, taking additionally the propagation

constants of each pair into account:
−(γ +γ )⋅x
1 2
I (x)= I ⋅ K ⋅ e
(21)
N o N
−(γ +γ )⋅(−x)
1 2
I (x)= I ⋅ K ⋅ e
(22)
F o F
where
---------------------- Page: 13 ----------------------
– 12 – TR 61156-1-3  IEC:2011(E)
γ is the propagation constant of the first pair;
γ is the propagation constant of the second pair.

We can now determine the current ratio representing the current ratio of the near– and far–

end cross-talk coupling:
We have
( )
dI x
N −(γ +γ )⋅x
1 2
=− j⋅ω⋅ K ⋅ e (23)
dI (x)
−(γ +γ )⋅(−x)
1 2
=− j⋅ω⋅ K ⋅ e (24)

If the cross-talk is uncorrelated with the length, then we can integrate Equations (23), (24) to

calculate the crosstalk. We then obtain
2 x=
⊗ ⊗
 
I (0) −(γ +γ )⋅x
N 2 2 −(γ +γ )⋅x
1 2 1 2
 
d NEXT= =ω ⋅ K ⋅ e ⋅ e ⋅ dx (25)
∫   ∫
 o 
x=0
− 2⋅(α +α )⋅ −2⋅(α +α )⋅
1 2 1 2
1− e 1− e
2 2 2 2 2
d NEXT= ω ⋅ K ⋅ = 4⋅π ⋅ K ⋅ f (26)
N N
(α +α )⋅ (α +α )⋅
1 2 1 2
2 x=
⊗ ⊗
 
I () −(γ −γ )⋅(− x)
F 2 2 −(γ −γ )⋅(− x)
1 2 1 2
 
d EL FEXT= =ω ⋅ K ⋅ e ⋅ e ⋅ dx (27)
∫   ∫
 o 
x=0
2 2 2 2 2
d EL FEXT=ω ⋅ K ⋅= 4⋅π ⋅ K ⋅⋅ f (28)
F F
where
dNEXT is the increment of the NEXT ration due to the element dx;
dEL FEXT` is the increment of the FEXT ration due to the element dx;
α is the attenuation of pair 1;
α is the attenuation of pair 2;
f is the frequency;
ℓ is the length of the cross-talk coupled pairs;

⊗ indicates that the conjugate complex has to be taken to calculate the square of

a complex number.

Note that we were reversing the direction of the integration in the last case, see also Figure 2

and get as a result the equal level far-end cross-talk.
---------------------- Page: 14 ----------------------
TR 61156-1-3  IEC:2011(E) – 13 –
I I (x)
o o
dI (x) I dI (x)
N I F F
dx dx
(F) (N)
ℓ – x
0 ℓ
IEC 632/11
Figure 2 – Integration of the coupled near- and far-end currents
over the length of the cable

Equations (26) and (28) are simplified more if we assume equal attenuations for the disturbing

and the disturbed pair . We have then
α=α =α (29)
1 2
2 2 2
π ⋅ f ⋅ K
N −4⋅α⋅
NEXT (, f )= ⋅(1− e ) (30)
α⋅
2 2 2
EL FEXT (, f )= 4⋅π ⋅ K ⋅⋅ f (31)

If we want to express NEXT and EL FEXT as functions of the frequency and length, we get

with the following constants:
2 2
C = π ⋅ K (32)
N N
2 2
C = 4⋅π ⋅ K (33)
F F
C ⋅ f
N −4⋅α⋅
NEXT (, f )= ⋅(1− e ) (34)
α⋅
EL FEXT (, f )= C ⋅⋅ f (35)

Obviously in Equations (34), (35), only the attenuation is calculated in Neper per length,

whereas the entire formulae are in absolute values. To convert them into decibels (dB), we

use the following formula:
___________

It should be mentioned however, that the modelling using different propagation constants is also feasible.

Z Z
o o
---------------------- Page: 15 ----------------------
– 14 – TR 61156-1-3  IEC:2011(E)
NEXT (, f )=−10⋅log ( C )− 20⋅log ( f )+ 20⋅log ()
10 N 10 10
(36)
−4⋅α⋅
( )
+10⋅log (α )−10⋅log 1− e
10 10
EL FEXT (, f )=−10⋅log (C )− 20⋅log ( f )
10 F 10
(37)
− 10⋅log ( )

If we know now the function relating the attenuation to the frequency, we can simplify

Equations (34), (35):
We have
α⋅= k ⋅ f [Neper at Length l ] (38)

where k is a heuristic parameter to approximate in a simplified way the attenuation as

compared to Equation (40).
We have then for NEXT as a function of cab
...

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