ISO/IEC TS 11801-9903:2021
(Main)Information technology — Generic cabling systems for customer premises — Part 9903: Matrix modelling of channels and links
Information technology — Generic cabling systems for customer premises — Part 9903: Matrix modelling of channels and links
ISO/IEC 11801-9903:2021 (E) establishes a matrix-model for formulating limits for mixed mode parameters within and between two pairs of balanced cabling. This is for the purpose of supporting new, improved balanced cabling channel and link specifications.
Technologies de l'information — Câblage générique des locaux d'utilisateurs — Partie 9903: Modelage de la matrice des canaux et liens
General Information
Relations
Standards Content (Sample)
ISO/IEC TS 11801-9903
Edition 1.0 2021-03
TECHNICAL
SPECIFICATION
colour
inside
Information technology – Generic cabling systems for customer premises –
Part 9903: Matrix modelling of channels and links
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from
either IEC or IEC's member National Committee in the country of the requester. If you have any questions about
ISO/IEC copyright or have an enquiry about obtaining additional rights to this publication, please contact the address
below or your local IEC member National Committee for further information.
IEC Central Office Tel.: +41 22 919 02 11
3, rue de Varembé info@iec.ch
CH-1211 Geneva 20 www.iec.ch
Switzerland
About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.
About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigendum or an amendment might have been published.
IEC publications search - webstore.iec.ch/advsearchform IEC online collection - oc.iec.ch
The advanced search enables to find IEC publications by a Discover our powerful search engine and read freely all the
variety of criteria (reference number, text, technical publications previews. With a subscription you will always
committee, …). It also gives information on projects, replaced have access to up to date content tailored to your needs.
and withdrawn publications.
Electropedia - www.electropedia.org
IEC Just Published - webstore.iec.ch/justpublished
The world's leading online dictionary on electrotechnology,
Stay up to date on all new IEC publications. Just Published
containing more than 22 000 terminological entries in English
details all new publications released. Available online and
and French, with equivalent terms in 18 additional languages.
once a month by email.
Also known as the International Electrotechnical Vocabulary
(IEV) online.
IEC Customer Service Centre - webstore.iec.ch/csc
If you wish to give us your feedback on this publication or
need further assistance, please contact the Customer Service
Centre: sales@iec.ch.
ISO/IEC TS 11801-9903
Edition 1.0 2021-03
TECHNICAL
SPECIFICATION
colour
inside
Information technology – Generic cabling systems for customer premises –
Part 9903: Matrix modelling of channels and links
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 35.200 ISBN 978-2-8322-9498-7
– 2 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 9
2 Normative references . 9
3 Terms, definitions and abbreviated terms . 9
3.1 Terms and definitions . 9
3.2 Symbols and abbreviated terms . 10
4 Matrix model . 11
5 Matrix definition . 11
5.1 General . 11
5.2 Quadriports . 11
5.3 Matrix port definition for a two-pair system representative for modelling
purposes . 11
5.4 Operational scattering matrix . 12
5.5 General naming convention. 12
5.6 S-matrix . 13
5.7 Passivity . 13
5.8 Operational reflection loss matrix . 14
5.9 Transmission matrix (T-matrix) . 14
5.10 S-matrix of cabling . 14
6 Calculation with matrices using limit lines . 15
7 Extracting limit lines . 15
8 General case using mixed-mode matrices. 16
8.1 General . 16
8.2 M-parameters . 16
9 Submatrix DD . 17
9.1 General . 17
9.2 Equations to extract the cabling limit lines . 17
9.2.1 General . 17
9.2.2 Operational attenuation . 17
9.2.3 Near-end crosstalk . 17
9.2.4 Attenuation to far-end crosstalk ratio . 17
9.2.5 Reflection (RL) . 18
10 Component values to be used as input to the model . 18
10.1 General . 18
10.2 Cable . 19
10.2.1 General . 19
10.2.2 Wave attenuation . 19
10.2.3 Near-end crosstalk . 19
10.2.4 Far-end crosstalk . 19
10.2.5 Reflection . 20
10.3 Connections . 21
10.3.1 General . 21
10.3.2 As a point source of disturbance . 21
10.3.3 As a transmission line . 21
11 Submatrices CC, CD and DC . 22
ISO/IEC 2021
11.1 General . 22
11.2 Submatrix CD . 22
11.3 Submatrix DC . 22
11.4 Submatrix CC . 22
Annex A (informative) Matrix conversion formulas . 23
A.1 Overview. 23
A.2 Formulas. 23
A.2.1 Mixed-mode to T-matrix . 23
A.2.2 T-matrix to M-matrix . 23
A.2.3 Conversion matrices . 23
Annex B (normative) Channel and permanent link models for balanced cabling . 25
B.1 General . 25
B.2 Insertion loss . 25
B.2.1 Insertion loss of the channel configuration . 25
B.2.2 Insertion loss of the permanent link configurations . 26
B.2.3 Assumptions for insertion loss . 26
B.3 NEXT . 27
B.3.1 NEXT of the channel configuration . 27
B.3.2 NEXT of the permanent link configurations . 27
B.3.3 Assumptions for NEXT . 28
B.4 ACR-F . 31
B.4.1 ACR-F of the channel configuration . 31
B.4.2 ACR-F for the permanent link configurations . 31
B.4.3 Assumptions for ACR-F . 32
B.5 No Return loss . 32
B.5.1 Return loss of the channel and permanent link configurations . 32
B.5.2 Assumptions for the return loss circuit analysis method . 33
B.6 PS ANEXT link modelling . 36
B.6.1 General . 36
B.6.2 PS ANEXT between connectors . 36
B.6.3 PS ANEXT between cable segments . 36
B.6.4 Principles of link modelling . 36
B.7 PS AACR-F link modelling . 37
B.7.1 General . 37
B.7.2 PS AFEXT between connectors . 37
B.7.3 PS AACR-F between cable segments . 37
B.7.4 Principles of link modelling . 37
B.7.5 Impact of PS AACR-F in channels and links with substantially different
lengths . 38
B.8 Component assumptions for modelling purposes. 41
Annex C (informative) Terms and definitions . 43
C.1 Comparison of namings . 43
C.2 General . 44
C.3 Background of terms and definitions . 44
C.3.1 Operational attenuation . 44
C.3.2 Operational transfer function (T ) . 46
B
C.3.3 Image or wave transfer function (T) . 46
C.3.4 Insertion transfer function of a two-port (T ) . 46
BI
– 4 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
C.3.5 Insertion transfer function (T ) measured with a vector network
BI
analyser . 46
C.3.6 Operational reflection loss transfer function (T = S ) of a junction . 46
ref ref
Bibliography . 48
Figure 1 – Link configurations of ISO/IEC 11801-1 . 7
Figure 2 – Matrix definition of a 4-port two twisted pair system . 12
Figure 3 – Operational scattering parameters example from port 2 . 12
Figure 4 – Transmission matrix concatenation showing an example of a 2-connector
permanent link . 14
Figure 5 – Graphical example of a NEXT calculation showing statistical results (red)
and final calculation (blue) . 16
Figure 6 – One pair M-matrix showing the submatrices . 16
Figure 7 – 100 m cable return loss without reflection at both ends . 20
Figure 8 – 100 m cable return loss with a reflection of 0,03 at both ends (6 Ω
mismatch, ~23 dB return loss at 1 MHz) . 21
Figure A.1 – X matrices . 24
Figure B.1 – Example of computation of NEXT with higher precision . 28
Figure B.2 – Example of increased impact of PS AFEXT . 38
Figure C.1 – Defining the operational attenuation and the operational transfer functions
of a two-port . 45
Figure C.2 – Defining the reflection transfer functions and the return loss of a junction . 47
Table 1 – All four ports operational scattering parameter definition . 12
Table 2 – Equal S-parameters for real components . 13
Table B.1 – Insertion loss deviation . 26
Table B.2 – Modelling assumptions for cable transmission parameters . 41
Table B.3 – Model input assumptions used in the statistical calculation (Class E ) . 41
A
Table B.4 – Model input assumptions used in the statistical calculation (Class F ) . 42
A
Table C.1 – Comparison of naming in ISO/IEC 11801-1 and ISO/IEC TS 11801-9903 . 43
ISO/IEC 2021
INFORMATION TECHNOLOGY –
GENERIC CABLING SYSTEMS FOR CUSTOMER PREMISES –
Part 9903: Matrix modelling of channels and links
FOREWORD
1) ISO (the International Organization for Standardization) and IEC (the International Electrotechnical Commission)
form the specialized system for worldwide standardization. National bodies that are members of ISO or IEC
participate in the development of International Standards through technical committees established by the
respective organization to deal with particular fields of technical activity. ISO and IEC technical committees
collaborate in fields of mutual interest. Other international organizations, governmental and non-governmental,
in liaison with ISO and IEC, also take part in the work.
2) The formal decisions or agreements of IEC and ISO 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 and ISO National bodies.
3) IEC and ISO documents have the form of recommendations for international use and are accepted by IEC and
ISO National bodies in that sense. While all reasonable efforts are made to ensure that the technical content of
IEC and ISO documents is accurate, IEC and ISO cannot be held responsible for the way in which they are used
or for any misinterpretation by any end user.
4) In order to promote international uniformity, IEC and ISO National bodies undertake to apply IEC and ISO
documents transparently to the maximum extent possible in their national and regional publications. Any
divergence between any IEC and ISO document and the corresponding national or regional publication shall be
clearly indicated in the latter.
5) IEC and ISO do not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC and ISO marks of conformity. IEC and ISO are not
responsible for any services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this document.
7) No liability shall attach to IEC and ISO or their directors, employees, servants or agents including individual
experts and members of its technical committees and IEC and ISO National bodies 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 ISO/IEC document or any
other IEC and ISO documents.
8) Attention is drawn to the Normative references cited in this document. Use of the referenced publications is
indispensable for the correct application of this document.
9) Attention is drawn to the possibility that some of the elements of this ISO/IEC document may be the subject of
patent rights. IEC and ISO shall not be held responsible for identifying any or all such patent rights.
ISO/IEC TS 11801-9903 has been prepared by subcommittee 25: Interconnection of information
technology equipment, of ISO/IEC joint technical committee 1: Information technology. It is a
Technical Specification.
This first edition of ISO/IEC TS 11801-9903 cancels and replaces ISO/IEC TR 11801-9903
published in 2015. This edition constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) the addition of further clarifications of the relations of parameters described in this edition
and referenced analogous parameters in IEC TR 62152, e.g. operational attenuation versus
operational transfer loss;
b) the introduction and description of the higher order M-parameters 8 × 8 matrix of mixed-
mode parameters, which includes the 4 × 4 submatrix of 4-port differential-mode-to-
differential-mode (DD) parameters, among three other submatrices of mixed-mode
parameters;
c) Annex A, matrix conversion formulas, covers up to 16-port parameters matrices;
d) the expanded Annex B description of example calculations for channel and permanent link,
and updated component parameter tables.
– 6 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
The list of all currently available parts of the ISO/IEC 11801 series, under the general title
Information technology – Generic cabling for customer premises, can be found on the IEC and
ISO web sites.
The text of this Technical Specification is based on the following documents:
Draft Report on voting
JTC1-SC25/2959/DTS JTC1-SC25/2993/RVDTS
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 Specification is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1, available at www.iec.ch/members_experts/refdocs.
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.
ISO/IEC 2021
INTRODUCTION
The pass/fail limits for defined channel and permanent link cabling configurations have an
implicit impact on the component limits for the cabling components used. The channel
configurations and the link configurations are specified in ISO/IEC 11801-1:2017, Clause 6 and
Clause 7, respectively.
The permanent link configurations, which represent the fixed portion of the cabling, have two
possible topologies:
– a connection plus a segment of cable plus a connection (2-connector topology);
– a connection plus a segment of cable plus a connection plus another segment of cable plus
another connection (3-connector topology).
The link configurations of ISO/IEC 11801-1 are shown in Figure 1.
a) Configuration PL1
b) Configuration PL2
c) Configuration PL3
d) Configuration CP1
Figure 1 – Link configurations of ISO/IEC 11801-1
This document includes models and assumptions, which support pass/fail limits for the channel
and permanent link test configurations in ISO/IEC 11801-1. These are based on the
performance requirements of cable and connecting hardware as specified in IEC standards.
This document provides reasonable assurance that a channel created by adding compliant
patch cords to a previously certified permanent link will meet the applicable channel
performance limits.
– 8 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
Over the years the frequencies of the classes increased, but the theory for calculating the limits
stayed the same. Especially the higher order effects had to be considered and in the end only
by doing a Monte Carlo calculation, assuming that not all components would be at the limit at
the same time, allowed compliance to be proved.
The model uses two pairs for all calculations. The limits are equal for pairs or pair combinations
but in reality measured values could be different. If results are required that need more pairs to
be considered, then this calculation can be done based on the results from multiple two-pair
calculations with appropriate inputs (worst case). An example of such a calculation is the power
sum and average limit lines for four pairs.
Symmetry and additional contributions that result from unbalanced signals and differential-to-
common and common-to-differential mode coupling are included in this document by increasing
the matrix size.
For details on the naming of transmission parameters, see Clause 3 and Clause C.1.
ISO/IEC 2021
INFORMATION TECHNOLOGY –
GENERIC CABLING SYSTEMS FOR CUSTOMER PREMISES –
Part 9903: Matrix modelling of channels and links
1 Scope
This part of ISO/IEC 11801, which is a Technical Specification, establishes a matrix-model for
formulating limits for mixed-mode parameters within and between two pairs of balanced cabling.
This is for the purpose of supporting new, improved balanced cabling channel and link
specifications.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments)
applies.
ISO/IEC 11801-1, Information technology – Generic cabling for customer premises – Part 1:
General requirements
3 Terms, definitions and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC 11801-1 and the
following 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
attenuation
diminishing of signal strength
Note 1 to entry: Details need to be added to indicate the exact usage.
3.1.2
connection
two mated connectors
EXAMPLE Jack and plug.
3.1.3
image attenuation
wave attenuation
attenuation when a two-port is terminated by its input and output characteristic impedances with
no reflections at input and output
Note 1 to entry: The wave attenuation of cables is length scalable.
– 10 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
3.1.4
insertion loss
attenuation or loss caused by a two-port inserted into a system
3.1.5
insertion loss deviation
deviation of attenuation loss with regard to the wave attenuation due to mismatches or internal
reflections
3.1.6
operational attenuation
ratio of the square root of the maximum available power wave vector emitted by the generator
and the square root of the power wave vector absorbed by the load of the two-port
Note 1 to entry: The operational attenuation is not length scalable (see also C.3.1 and C.3.2).
Note 2 to entry: The operational attenuation is expressed in decibels (dB) and radians (rad).
3.1.7
passivity
property of an electrical system that the output power at all ports does not exceed the input
power at all ports
3.1.8
unitarity
mathematical concept for matrices to define passivity
3.1.9
operational reflection
loss due to the reflection at a junction
Note 1 to entry: See also C.3.6.
3.2 Symbols and abbreviated terms
For the purposes of this document, the symbols and abbreviated terms given in ISO/IEC 11801-
1 and the following apply.
f frequency (MHz)
RL return loss limit (dB)
ρ (rho) operational reflection transfer function, junction reflection coefficient
DRL distributed return loss (dB)
IL insertion loss limit (dB)
A operational wave attenuation (Np)
A operational wave transfer function (Np)
T
B operational phase (rad)
B operational phase transfer function (rad)
T
B random phase (rad)
RAND
NEXT operational near-end crosstalk loss limit (dB)
NEXT operational near-end crosstalk transfer function (dB)
T
FEXT operational far-end crosstalk loss limit (dB)
FEXT operational far-end crosstalk transfer function (dB)
T
ISO/IEC 2021
4 Matrix model
The model to be used is a concatenated matrix calculation as discussed in IEC TR 62152 [1]
for a 2-port system. For a 2-pair balanced cabling calculation, a 4-port differential matrix as
shown in Figure 2 shall be used.
The model assumes that all components are specified with S-parameters and these parameters
are used then to fill an S-matrix for every cabling component.
To concatenate components these S-matrices are transformed into transmission T-matrices
which can then be multiplied in the appropriate order to simulate the transmission
characteristics of the concatenated components (for details see IEC TR 62152:2009, Annex C).
To evaluate the transmission performance of the modelled channel or permanent link, the
calculated T-matrix of the cabling is transformed back into an S-matrix providing the expected
transmission parameters of the cabling system.
The matrix calculation is done mathematically with S-parameters in amplitude and phase.
a) Measured S-parameters are usually known in amplitude and phase.
b) Parameter limit lines for components and for cabling are specified in amplitude only, usually
in decibel. For modelling purposes these amplitudes shall be transformed into a linear value.
c) For the calculation of matrix terms representing limit lines, the phase is added as a random
value to simulate power sum addition (see Clause 6).
5 Matrix definition
5.1 General
In Clause 5 only the part with the balanced components is described. For the unbalanced part
see 8.2.
5.2 Quadriports
In IEC TR 62152 [1] voltage and currents of the input and output waves are specified for two
ports. In Figure 2, Figure 3, Table 1, and Formula (1), the cabling specific notation needed for
quadriports (two pairs) is detailed.
5.3 Matrix port definition for a two-pair system representative for modelling purposes
In Figure 2, a 4-port matrix is presented. The definition is one line per port per twisted pair.
______________
Numbers in square brackets refer to the Bibliography.
– 12 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
Key
a designates a wave entering the quadriport
b designates a wave leaving the quadriport
Figure 2 – Matrix definition of a 4-port two twisted pair system
5.4 Operational scattering matrix
In Figure 3, the S-parameters for a source at port 2 are shown. For all definitions, see 5.5.
Key
Definition of S-parameters: S
output, input
S = operational near-end crosstalk transfer function (NEXT )
12 T
S = operational reflections coefficient (ρ)
S = operational far-end crosstalk transfer function (FEXT )
32 T
S = operational forward transfer function (A )
42 T
Figure 3 – Operational scattering parameters example from port 2
5.5 General naming convention
The naming convention for the four ports is given in Table 1.
Table 1 – All four ports operational scattering parameter definition
From Port 1: From Port 2: From Port 3: From Port 4:
S NEXT S NEXT S NEXT S NEXT
21 T 12 T 43 T 34 T
S ρ S ρ S ρ S ρ
11 22 33 44
S FEXT S FEXT S FEXT S FEXT
41 T 32 T 23 T 14 T
S A S A S A S A
31 T 42 T 13 T 24 T
ISO/IEC 2021
5.6 S-matrix
For each cabling component (for cables for each length and type involved, for connections for
each type) an S-matrix needs to be developed, see Formula (1). The matrix numbering starts
with 1 to be compatible with scattering parameters and generally used definitions (see 5.5) and
IEC TR 62152.
SS S S
11 12 13 14
SS S S
21 22 23 24
S=
(1)
SS S S
31 32 33 34
SS S S
41 42 43 44
The following transmission parameters can be substituted into the matrix in Formula (1).
ρ: S , S , S , S
11 22 33 44
NEXT : S , S
T 12 34
FEXT : S , S
T 14 23
A : S , S
T 13 24
The equal scattering coefficient due to symmetrical nature of component parameters results in
the set of equalities in Table 2.
Table 2 – Equal S-parameters for real components
Parameter Equality For pair number(s)
A S = S 1
T 13 31
A S = S 2
T 24 42
FEXT S = S 1 and 2
T 14 41
FEXT S = S 1 and 2
T 23 32
NEXT S = S 1 and 2
T 21 12
NEXT S = S 1 and 2
T 34 43
The equalities provided in Table 2 apply to the component scattering matrix in Formula (1).
5.7 Passivity
There is a general assumption that all transmission parameter loss values, e.g. NEXT and
FEXT, are much less than one, in linear value, or much greater than 0, in dB.
At higher frequencies this needs to be taken care of. Otherwise, the output power at ports in
total can be calculated as being higher than the input power.
This is defined as passivity and should be implemented. An example is shown in 5.8.
– 14 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
5.8 Operational reflection loss matrix
To account for the impedance mismatch between two cabling segments a reflection matrix is
defined. Unitarity should be taken care of especially when phase randomization is applied. As
in the cabling matrix only the wave attenuation is inserted, it is important to add this operational
reflection transfer function to get the operational attenuation as defined, see Formula (2), see
C.3.6.
ρρ01− 0
2
0 ρρ01−
S =
(2)
ρ
2
10−ρρ 0
01−ρρ0
where
S is the operational reflection loss, transfer function matrix;
ρ
ρ (rho) is the operational reflection transfer function, junction reflection coefficient.
The reflection loss between two cabling sections is defined as ρ, reflection transfer function
(rho), where:
ρ is constant over frequency (for similar cable types);
ρ is a function of frequency, e.g. at the end of cables (cabling) and connectors;
ρ is a real function assuming the reflected wave is in phase, or
ρ is a complex function taking a phase shift of the reflected wave into account.
5.9 Transmission matrix (T-matrix)
The component S-matrices are transformed into component transmission matrices (for an
example mathematical transform see Annex A) which can then be multiplied in the appropriate
order to calculate a chain of cabling elements forming a cable assembly channel; see the
example illustration in Figure 4.
Key
T T-matrix of a connection
CO
T T-matrix of a cable
C
Figure 4 – Transmission matrix concatenation showing
an example of a 2-connector permanent link
5.10 S-matrix of cabling
The resulting concatenated T-matrix is then transformed back to an S-matrix. The derived S-
parameters describe the parameters of the cascaded components, i.e. of the cabling.
ISO/IEC 2021
6 Calculation with matrices using limit lines
For the calculation of matrix terms representing limit lines, the phase is added as a random
value to simulate power sum addition.
For the components a random uniform phase distribution from −π to +π is added to the scalar
amplitude; see Formula (3).
This is done by multiplying the scalar amplitude by a complex rotation factor with the
randomized phase in its imaginary exponent. Clause 10 indicates to which parameters this
operation is applied.
B BB+
(3)
T RAND
where
B is the operational phase transfer function, expressed in (rad);
T
B is the operational phase, expressed in (rad);
B is the random phase, expressed in (rad).
RAND
The calculation of the random phase term is shown in Formula (4).
jxRAND 2π−π
( ( )( ) )
(4)
B = e
RAND
where
B is the random phase, expressed in (rad);
RAND
RAND(x) is the random function used in Formula (4); example RAND(), which returns an evenly
distributed random real number greater than or equal to 0 and less than 1.
7 Extracting limit lines
Due to the randomized phase of the components, the cabling calculation results in values which
can change randomly within a range of total constructive and total destructive interferences.
To derive the requested limit curve, a least mean square curve-fit of these values shall be
determined.
A calculation sweep with more than five calculation points per megahertz sweep should be
applied (e.g. sweep 1 MHz to 2 000 MHz, more than 10 000 calculation points).
Logarithmic sweep is advisable to get sufficient data points at low frequencies. Additionally, the
frequency sweep should be extended to higher frequencies by about 20 % to improve stability
at the high end of interest.
The limit lines are derived by a least mean square curve-fit using specific formulas for each of
IL, NEXT, FEXT, and RL; see 9.2.
A graphical example of a near-end crosstalk (NEXT) calculation in decibel over frequency is
shown in Figure 5. The red dots represent the statistical matrix calculation and the blue line
represents the fitted curve.
=
– 16 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
Figure 5 – Graphical example of a NEXT calculation showing
statistical results (red) and final calculation (blue)
8 General case using mixed-mode matrices
8.1 General
S-parameters can only be used for differential mode analysis. In the general case the
parameters are called M-parameters
8.2 M-parameters
Figure 6 shows the M-matrix in its general form in an example of one pair.
Figure 6 – One pair M-matrix showing the submatrices
In this case the submatrices are 2×2. For the two-pair simulation the structure remains, just the
submatrices grow to 4×4. To compare it to practical components each submatrix is given a
special name.
a) DD – differential (in) differential (out) submatrix. This submatrix includes values of insertion
loss, return loss, near-end crosstalk and far-end crosstalk, as known.
b) CD – differential (in) common mode (out) submatrix. This submatrix includes the transverse
conversion loss (TCL) and the transverse conversion transfer loss (TCTL) values.
c) DC – common mode (in) differential (out) submatrix. This submatrix includes the longitudinal
conversion loss (LCL) and longitudinal conversion transfer loss (LCTL) values.
d) CC – common mode (in) common mode (out) submatrix: This submatrix includes the same
values as the DD submatrix but for the common mode.
As done with the DD submatrix and S-parameters for all submatrices, the cabling components
need to be inserted. The component parameter symmetry stays as shown in 5.6.
ISO/IEC 2021
9 Submatrix DD
9.1 General
Submatrix DD contains the following parameters:
RL NEXT IL FEXT
dd11 dd12 dd13 dd14
NEXT RL FEXT IL
dd21 dd22 dd23 dd24
DD=
IL FEXT RL NEXT
dd31 dd32 dd33 dd34
FEXT IL NEXT RL
dd41 dd42 dd43 dd44
9.2 Equations to extract the cabling limit lines
9.2.1 General
Limit lines are normally given in decibel values.
If necessary, the equations to extract the resulting limit lines are applied to the parameters'
calculated linear values, before transforming them back to decibel values, when averaging the
decibel values overemphasizes high values.
9.2.2 Operational attenuation
The limit line is averaged in decibel because the deviations from the expected formula are
minor.
The result will depend strongly on connector attenuation specification and how it is specified
therefore in the connector matrix.
1) No reflections included in connector attenuation (wave attenuation): Model result will be the
addition of component operational attenuations.
2) Return loss is included in connector attenuation (operational attenuation): Model result will
be the insertion loss deviation.
The curve-fit formula for operational attenuation values in decibel is given in Formula (5).
c
A a f+ bf+
(5)
f
9.2.3 Near-end crosstalk
The curve-fit formula for operational NEXT transfer function in linear values is given in
T
Formula (6).
NEXT=a+ bf+ cf+ df (6)
T
9.2.4 Attenuation to far-end crosstalk ratio
The curve-fit formula for operational FEXT transfer function in linear values is given in
T
Formula (7).
=
– 18 – ISO/IEC TS 11801-9903:2021
ISO/IEC 2021
NOTE Components and cabling normally define far-end crosstalk as attenuation-to-crosstalk-ratio-far end (ACR-F);
ACR is the decibel sum of attenuation and crosstalk, thus FEXT = ACR-F − IL.
b
FEXT af+
(7)
T
f
9.2.5 Reflection (RL)
9.2.5.1 High frequency
The curve-fit formula for operational RL transfer function in linear values is given in Formula (8).
ρ=a+bf+cf+df (8)
9.2.5.2 Low frequency
At frequencies below ~50 MHz, as no randomization is applied to connections, the calculation
shows the phase impact on return loss.
The reflection from 5.8 is applied until it intercepts the curve from Formula (8). If only higher
frequencies are of interest this can be neglected.
10 Component values to be used as input to the model
10.1 General
All limit lines shall be in value (not in decibels) to be used in matrix operations.
B is the definition for random phase, from Clause 6; it can be applied independently to
RAND
cables and connectors.
B is the definition for operational phase transfer function; it defines the length of the
T
component.
The operational phase transfer function, in free air, is calculated according to Formula (9):
j(2π)( fl)()//(300 NVP)
(9)
B= e
where
B is the operational phase, expressed in radians (rad);
f is the frequency, expressed in megahertz (MHz);
l is the length, expressed in metres (m);
NVP is the nominal velocity of propagation, fraction of the speed of light.
NOTE 300 m is the wavelength at 1 MHz in free air, with relative permittivity = 1, corresponding to NVP = 1; this
can be scaled up, in dielectric, with relative permittivity > 1, corresponding to NVP < 1; see B.5.1.
The component parameter limit is the component linear limit value (not in decibel).
=
ISO/IEC 2021
10.2 Cable
10.2.1 General
For each cable segment, length and type, a unique S-matrix shall be obtained.
The component parameter limits are length scaled values and thus a function of length, see
IEC TR 61156-1-3 [2].
10.2.2 Wave attenuation
The operational wave attenuation transfer function is calculated according to Formula (10):
A IL l× Bl
() () (10)
T
where
IL(l) is the insertion loss limit, given in Table B.2;
B(l) is the operational phase, expressed in radians (rad), Formula (9).
To calculate operational attenuation the reflections shall be added; see 10.2.5.
10.2.3 Near-end crosstalk
The operational near-end crosstalk transfer function is calculated according to Formula (11):
NEXT NEXT lB××lB
() () (11)
T RAND
where
NEXT(l) is the near-end crosstalk loss limit, given in Table B.2;
B(l) is the operational phase, expressed in radians (rad), Formula (9);
B is the random phase, expressed in radians (rad), see Clause 6.
RAND
10.2.4 Far-end crosstalk
The operational far-end crosstalk transfer function is calculated according to Formula (12):
FEXT FEXT lB××lB
() () (12)
T RAND
where
FEXT(l
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.