IEC TR 61282-14:2019

IEC TR 61282-14 ®
Edition 2.0 2019-07
TECHNICAL
REPORT
colour
inside
Fibre optic communication system design guidelines –
Part 14: Determination of the uncertainties of attenuation measurements in fibre
plants
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IEC TR 61282-14 ®
Edition 2.0 2019-07
TECHNICAL
REPORT
colour
inside
Fibre optic communication system design guidelines –

Part 14: Determination of the uncertainties of attenuation measurements in fibre

plants
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.180.01 ISBN 978-2-8322-7069-1

– 2 – IEC TR 61282-14:2019 © IEC 2019
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 8
2 Normative references . 8
3 Terms, definitions and abbreviated terms . 8
3.1 Terms and definitions . 8
3.2 Abbreviated terms . 10
4 Overview of uncertainty . 10
4.1 What is uncertainty? . 10
4.2 Origin of uncertainties . 11
4.3 What may not be considered as uncertainty? . 11
5 Fibre cabling attenuation measurement . 11
5.1 Test methods . 11
5.2 Sources of uncertainty to be considered . 11
5.2.1 Analysis . 11
5.2.2 Uncertainties due to the environment . 14
5.2.3 Uncertainties due to operator skills . 14
5.2.4 Uncertainties due to test methods . 14
5.2.5 Uncertainties due to measuring instruments . 14
5.2.6 Uncertainties due to the setup . 16
5.2.7 Uncertainties due to cabling. 16
6 Uncertainties estimation . 17
6.1 Measurement model. 17
6.2 Accumulation of uncertainties . 19
7 General representation of the equation using sensitivity coefficients . 19
8 Calculation . 23
8.1 Combined standard uncertainty . 23
8.2 Expanded uncertainty . 23
8.3 Determination of the coverage factor k . 23
8.3.1 General approach . 23
8.3.2 Discussion . 23
8.3.3 Typical values of degree of freedom . 24
Annex A (informative) Mathematical basis. 25
A.1 General . 25
A.2 Type A evaluation of uncertainty . 25
A.3 Type B evaluation of uncertainty . 25
A.4 Determining the combined standard uncertainty . 26
A.5 Reporting . 27
Annex B (informative) Test methods . 28
B.1 Test methods as per IEC 61280-4-1 and 61280-4-2 . 28
B.1.1 General . 28
B.1.2 Measurement configuration . 28
B.1.3 One-cord reference configuration . 28
B.1.4 Two-cord reference configuration . 29
B.1.5 Three-cord reference configuration . 29

B.2 Test methods defined in ISO/IEC 14763-3:2014 . 29
B.2.1 General . 29
B.2.2 Channels . 30
B.2.3 Links. 31
Annex C (informative) Uncertainties evaluation . 32
C.1 Type A uncertainties . 32
C.1.1 General . 32
C.1.2 Evaluation of optical source instability and associated uncertainties . 32
C.2 Type B uncertainties . 32
C.2.1 General . 32
C.2.2 Evaluation of the power meter noise . 32
C.2.3 Elements to be considered for power meter stability analysis . 33
C.2.4 Evaluation of the centre wavelength dependence . 33
C.2.5 Spectral width dependence . 35
C.2.6 Evaluation of the uncertainties due to MM launch conditions . 35
C.2.7 Evaluation of the PDL . 36
C.2.8 Uncertainty of absolute power measurement . 37
Annex D (informative) Typical values of uncertainties . 38
Annex E (informative) Linear to dB scale conversion of uncertainties . 40
E.1 Definition of decibel . 40
E.2 Conversion of relative uncertainties . 40
Bibliography . 41

Figure 1 – Fishbone analysis . 13
Figure 2 – Measurement model . 17
Figure B.1 – Measurement configuration . 28
Figure B.2 – One-cord reference measurement . 28
Figure B.3 – Two-cord reference measurement . 29
Figure B.4 – Three-cord reference measurement . 29
Figure B.5 – Measurement on channel . 30
Figure B.6 – Channel reference measurement . 30
Figure B.7 – Link measurement configuration . 31
Figure B.8 – Link reference measurement . 31
Figure C.1 – Typical spectral response of a fibre . 34
Figure C.2 – Uncertainties due to the launch conditions for a given loss . 36

Table 1 – Source of uncertainty (raw list) . 12
Table 2 – Uncertainties due to measuring instruments . 15
Table 3 – Uncertainties due to the setup . 16
Table 4 – Uncertainties due to cabling . 16
Table 5 – Sensitivity coefficients for IEC 61280-4-1 and IEC 61280-4-2 methods . 21
Table 6 – Sensitivity coefficients for ISO/IEC 14763-3:2014 methods. 22
Table 7 – Values of k for different values of ν . 24
Table 8 – Typical values of ν . 24
i
Table C.1 – Spectral attenuation coefficients . 34

– 4 – IEC TR 61282-14:2019 © IEC 2019
Table C.2 – Sensitivity coefficients . 35
Table D.1 – Typical values of uncertainties . 39

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION
SYSTEM DESIGN GUIDELINES –
Part 14: Determination of the uncertainties
of attenuation measurements in fibre plants

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 this end and
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6) All users should ensure that they have the latest edition of this publication.
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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 61282-14, which is a Technical Report, has been prepared by subcommittee 86C: Fibre
optic systems and active devices, of IEC technical committee 86: Fibre optics.
This publication contains an attached file titled "Supplemental Data for Section 8" in the form
of an Excel spread sheet. This file is intended to be used as a complement and does not form
an integral part of the standard.
This second edition cancels and replaces the first edition published in 2016. This edition
constitutes a technical revision.

– 6 – IEC TR 61282-14:2019 © IEC 2019
This edition includes the following significant technical changes with respect to the previous
edition:
a) in the title: replacement of "guide" by "guidelines";
b) text adaptation to allow both standard grade B and reference grade connectors for
termination of test cords;
c) addition of values needed for calculation of uncertainties, when standard grade connectors
are used, to Annex D;
d) correction of minor inconsistencies in Equation (18) and after.
The text of this Technical Report is based on the following documents:
Enquiry draft Report on voting
86C/1572/DTR 86C/1584/RVDTR
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 document has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 61282 series, published under the general title Fibre optic
communication system design guides, can be found on the IEC website.
Future standards in this series will carry the new general title as cited above. Titles of existing
standards in this series will be updated at the time of the next edition.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific document. At this date, the document 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.

INTRODUCTION
The determination of the uncertainty of every measurement is a key activity, which should be
performed by applying dedicated methods as extensively presented in reference documents
such as ISO/IEC Guide 98-3:2008, Guide to the uncertainty of measurement (GUM).
This document shows a practical application of these methods for the determination of the
measurement uncertainty of the attenuation of fibre optic cabling using optical light sources and
power meters as defined in IEC 61280-4-1 and IEC 61280-4-2.
It includes the review of all contributing factors to uncertainty (such as launch conditions,
spectral width, stability of source, power meter polarization, resolution, linearity, quality of test
cord connectors) to determine the overall measurement uncertainty. This part of IEC 61282
applies to the measurement of single mode or multimode fibres without restrictions to the fibre
parameters, including mode field diameter, core diameter and numerical aperture. However,
numerical values given in Clause C.2 and typical values given in Annex D are not valid for
multimode fibres types A2, A3 and A4.
The list of uncertainties presented in this document is related to this particular application and
should be reconsidered if measurement conditions are not compliant to measurement
requirements defined by IEC 61280-4-1 and IEC 61280-4-2.
The reference document for general uncertainty calculations is ISO/IEC Guide 98-3:2008, and
this document does not intend to replace it; it only represents an example and should be used
in conjunction with ISO/IEC Guide 98-3:2008. A brief introduction to the determination of
measurement uncertainty according to ISO/IEC Guide 98-3:2008 is given in Annex A.
This document is associated with a calculation spreadsheet (Excel) containing practical
calculations.
– 8 – IEC TR 61282-14:2019 © IEC 2019
FIBRE OPTIC COMMUNICATION
SYSTEM DESIGN GUIDELINES –
Part 14: Determination of the uncertainties
of attenuation measurements in fibre plants

1 Scope
This part of IEC 61282, which is a Technical Report, establishes the detailed analysis and
calculation of the uncertainties related to the measurement of the attenuation of both multimode
and single mode optical fibre cabling using optical light sources and power meters.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 61280-4-1:2009, Fibre-optic communication subsystem test procedures – Part 4-1:
Installed cable plant – Multimode attenuation measurement
IEC 61280-4-2:2014, Fibre-optic communication subsystem test procedures – Part 4-2:
Installed cable plant – Single-mode attenuation and optical return loss measurement
ISO/IEC Guide 98-3:2008, Uncertainty of measurement – Part 3: Guide to the expression of
uncertainty in measurement (GUM:1995)
3 Terms, definitions and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1.1
attenuation
L
reduction of optical power induced by transmission through a medium such as cabling
L = 10 × log (P /P )
dB 10 in out
where
P and P are the power, typically measured in mW, into and out of the cabling
in out
Note 1 to entry: Attenuation is expressed in dB.

3.1.2
calibration
set of operations that establish, under specified conditions, the relationship between the values
of quantities indicated by a measuring instrument and the corresponding values realized by
standards
3.1.3
encircled flux
EF
fraction of the radial-weighted cumulative near field power to the total radial-weighted output
power as a function of radial distance from the optical centre of the core
3.1.4
measurement repeatability
measurement precision under a set of repeatability conditions of measurement
3.1.5
measurement reproducibility
reproducibility
measurement precision under reproducibility conditions of measurement
3.1.6
polarization dependent loss
PDL
maximum variation of attenuation to a variation of the state of polarization (SOP) over all the
SOPs
Note 1 to entry: PDL is expressed in dB.
3.1.7
nonlinearity
NL
relative difference, for a power meter, between the response at a given power P and the
response at a reference power P :
rP( )
nl −1
P/ P
rP
( )
If expressed in decibels, the nonlinearity is:
rP
( )
NL 10×log (dB)
PP/ 10
rP
( )
Note 1 to entry: The nonlinearity is equal to zero at the reference power.
3.1.8
uncertainty of measurement
quantified doubt about the result of a measurement
3.1.9
stability
ability of a measuring instrument to keep its performance characteristics within a specified
range during a specified time interval, all other conditions being the same
=
=
– 10 – IEC TR 61282-14:2019 © IEC 2019
3.1.10
repeatability condition
condition of measurement that includes the same measurement procedure, same operators,
same measuring system, same operating conditions and same location, and replicates
measurements on the same or similar objects over a short period of time
3.1.11
reproducibility condition
condition of measurement that includes different locations, operators, measuring systems, and
replicate measurements on the same or similar objects
3.1.12
standard uncertainty
u
uncertainty of a measurement result expressed as a standard deviation
Note 1 to entry: For further information, see ISO/IEC Guide 98-3.
3.1.13
type A uncertainty
type of uncertainty obtained by a statistical analysis of a series of observations, such as when
evaluating certain random effects of measurement
Note 1 to entry: See Annex A and ISO/IEC Guide 98-3.
3.1.14
type B uncertainty
type of uncertainty obtained by means other than a statistical analysis of observations, for
example an estimation of probable sources of uncertainty, such as when evaluating systematic
effects of measurement
Note 1 to entry: See Annex A and ISO/IEC Guide 98-3.
3.2 Abbreviated terms
APC angled physical contact (description of connector style)
CW continuous wave
LSPM light source power meter
OPM optical power meter
NA numerical aperture
PC physical contact (description of connector style that is not angled)
4 Overview of uncertainty
4.1 What is uncertainty?
According to ISO/IEC Guide 98-3:2008 (GUM), the uncertainty of a measurement is the
quantified doubt that exists about the result of any measurement. For every measurement, even
the most careful, there is always a margin of doubt.
For example, when measuring the attenuation of fibre optic cabling, the operator may observe
a variation of the displayed power level on the power meter and be unable to know which value
should be recorded. This variation of the displayed value is an element of doubt regarding the
result of the measurement.
4.2 Origin of uncertainties
Uncertainties come from measurement devices, the item to be measured, the measurement
process, operator skills, references used, and the environment.
4.3 What may not be considered as uncertainty?
Unknown parameters that contribute directly or indirectly to the quantity to be measured cannot
be considered as uncertainties. For example, when measuring a cabling, mode field diameter
or numerical aperture of different fibres of cabling are unknown; however, mismatch of these
parameters causes the measured attenuation.
Also, poor knowledge of measurement conditions generates uncertainties but is not directly an
uncertainty. A common example is the wavelength of the optical source: if the wavelength of
the source is known with an uncertainty smaller than 1 nm, the measurement condition can be
specified precisely. Conversely, if the wavelength of the source is known to be within a range
of 40 nm, the possible variation of the attenuation of the device under test should be estimated
based on the typical variation of attenuation over the wavelength range for a given length of
fibre.
5 Fibre cabling attenuation measurement
5.1 Test methods
Three attenuation test methods use an optical light source and power meter (LSPM) to measure
input and output power levels of the cabling under test to determine the attenuation. These
methods are designated respectively, one-cord, three-cord and two-cord method.
The main functional difference between these methods is the way the input power level, known
as the reference power level (P ), is measured (see Annex B).
in
Refer to IEC 61280-4-1 and IEC 61280-4-2 for more details.
NOTE Test methods presented in ISO/IEC 14763-3 have different names and are slightly different. See
Clause B.2.
5.2 Sources of uncertainty to be considered
5.2.1 Analysis
An extensive analysis of the source of uncertainties to be considered has been conducted. This
resulted in the sorted source of uncertainty given in Table 1.

– 12 – IEC TR 61282-14:2019 © IEC 2019
Table 1 – Source of uncertainty (raw list)
Source of uncertainty Type of origin Index
Measurement source instability (power deviation Measurement devices 01
over time)
Source wavelength Measurement devices 02
Source spectrum (spectral width) Measurement devices 03
Laser speckle Measurement devices 04
Launch condition for multimode fibres (dependent Measurement devices 05
upon the compliance or noncompliance with the
EF template and a function of the attenuation of
the measured cabling)
Power meter nonlinearity Measurement devices 06
Power meter reading resolution Measurement devices 07
Power meter spatial uniformity References used 08
Power meter polarization sensitivity Measurement devices 09
Power meter noise Measurement devices 10
Power meter stability Measurement devices 11
Power meter calibration References used 12
Test cord connector/fibre attenuation uncertainty References used 13
Connector mating repeatability (test cord or References used/item to be measured 14
cabling)
Connector PDL References used/item to be measured 15
Reflections (FP cavity) References used/item to be measured 16
Connector end face cleanliness Operator skills 17
Fibre handling Operator skills 18
Calculation errors Measurement process 19
Numerical aperture of the fibre Item to be measured 20
Core diameter of the fibre or mode filed diameter Item to be measured 21
Fibre nonlinearity Item to be measured 22
Temperature Environment 23
Humidity Environment 24
Some of the uncertainties listed in Table 1 are negligible or need to be grouped together to be
estimated; however, some of them apply to different domains. Figure 1 presents an organised
list of these uncertainties.
Environment Man: Operator skills Method: Measurement
Two cords
Connector end face
Measurement process
cleanliness (17)
Humidity (24)
Circulation errors (19)
Fibre and connectors
handling (18)
One cord Three cords
Temperature (23)
Cabling (link or channel)
The uncertainties of the attenuation measurement of a cabling
Optical power meter
calibration (12)
Reading Stability: Type A
Connectors
resolution (07) uncertainties (11)
Reflexions (16) Speckle (04)
NA (20) Nonlinearity (22)
Launch
PDL (15)
Mating
Optical power
conditions (05)
Un-stability
repeatability (14)
Fibre
meter
(01)
Ref cords
Spatial
Nonlinearity
uniformity (08)
Core
(06) Core diameter (21)
Source
diameter (21)
Polarisation
PDL (15) Reflexions (16)
Spectral
Noise (10) sensitivity (9)
width (03)
NA (20)
Central
Connectors
wavelength (02)
Fibre
Wavelength
Detector
Change
Mating repeatability (14)
connector (13)
Measurement references Machine: Measurement device Material: Cabling
IEC
Figure 1 – Fishbone analysis
– 14 – IEC TR 61282-14:2019 © IEC 2019
5.2.2 Uncertainties due to the environment
It is assumed that environmental parameters (temperature and humidity) generate negligible
variations of the attenuation of the fibre and that fibre environmental conditions are reported as
measurement conditions.
Temperature and humidity can generate source and power meter instability. This instability shall
be reported in 5.2.5 (see also C.1.2).
NOTE This corresponds to uncertainties reported as index 23 and 24.
5.2.3 Uncertainties due to operator skills
It is assumed that operators follow approved procedures for connector end face inspection and
cleaning, so the connector attenuation is as expected.
It is also assumed that operator skills do not create additional variations to those included with
connector mating repeatability.
NOTE This corresponds to uncertainties reported as index 17 and 18.
5.2.4 Uncertainties due to test methods
Test methods do not affect the uncertainties directly, as different numbers of connectors are
used depending on the method used. The accumulation of uncertainties takes into account the
correct amount of uncertainties related to the connectors.
Calculation errors due to truncation of results may exist in this type of measurement, especially
if measurements are controlled by an external computer. However, most of the time, users
simply calculate the attenuation by an embedded dBr (decibel relative) function that can be
assumed to have no more error than the rounding error of the optical power meter (OPM) – see
5.2.5.
NOTE This corresponds to uncertainty reported as index 19.
5.2.5 Uncertainties due to measuring instruments
Table 2 provides a list of the uncertainties to be taken into account for the measurement devices
group.
Table 2 – Uncertainties due to measuring instruments
Reference/ Index Description Concerned Apply to Apply to Other
Symbol element P P condition
in out
5.2.5.1 01 Relative uncertainty arising from the Source Yes Yes
instability of the optical source and
u
Pstat any other instabilities (assumed to
include instability due to multiple
reflections)
5.2.5.2 02 Relative attenuation uncertainty Source No Yes If unknown
arising from the uncertainty of the
u
λs optical source wavelength. See C.2.4
and C.2.5.
5.2.5.3 05 Relative uncertainty due to the Source and No Yes MM
multimode launch condition. cabling
u
MMLC
See C.2.6.
5.2.5.4 06 Relative uncertainty arising from the
Power No Yes One power
nonlinearity of the power meter. This meter meter
u
Lin contribution will only be considered
when using the same power meter for
the measurement of P and of P .
in out
5.2.5.5 07 Relative uncertainty arising from the Power Yes Yes
finite display resolution of power meter meter
u
i
Displ
i
5.2.5.6 08 Relative uncertainty arising from Power Yes Yes If APC and
power meter spatial uniformity. Only meter PC
u
Pspace significant for single mode connectors
measurement and when using a are used
different type of connector for P and
in
One power
of P and using the same power
out
meter
meter for the measurement of P and
in
P .
out
5.2.5.7 09 Relative uncertainty arising from the Power Yes Yes SM
polarization dependency of power meter
u meter i (see C.2.7)
PDR
i
5.2.5.8 10 Relative uncertainty arising from Power Yes Yes
power meter noise becomes negligible meter
u
if power level remains 30 dB over the
Pnoise
power meter noise level (see C.2.2).
5.2.5.9 11 Relative uncertainty arising from Power Yes Yes
power meter instability (see C.2.3) meter
u
PM
stabin
u
PM
stabout
5.2.5.10 12 Relative uncertainties of the absolute Power Yes Yes If two
power measurements of P and of meter different
in
u
power
abs P . These uncertainties need to be
P
out
in
meters are
considered only when performing
u used
abs
P measurements of P and P using
out
in out
two different power meters. The use of
two different power meters is not
recommended (see also C.2.8).
When measuring fibre optic cabling, and assuming the spectrum of the sources used is
symmetrical, the variation of the spectral width does not cause variation of the attenuation of
the cabling. Hence, uncertainties due to the spectral width are assumed to be negligible.
NOTE This corresponds to uncertainty reported as index 03.
The speckle due to a laser source used to measure a multimode cabling may affect the stability
of the power meter measurements. However, this would occur only if the power meter detector

– 16 – IEC TR 61282-14:2019 © IEC 2019
is not spatially uniform; hence, uncertainties due to laser source speckle are assumed to be
negligible.
NOTE This corresponds to uncertainty reported as index 04.
5.2.6 Uncertainties due to the setup
Table 3 provides a list of the uncertainties to be taken into account for the setup group.
Table 3 – Uncertainties due to the setup
Reference / Index Description Concerned Apply to Apply to Other
P P
Symbol element condition
in out
5.2.6.1 13 Mating reproducibility (setup) Ref cords Yes No
u
Mreprod
5.2.6.2 14 Relative uncertainty related to the Ref cords Yes No Dependent
repeatability of the test cord on method
u
connector mating used
Mating
5.2.6.3 15 Relative uncertainty related to the Ref cords Yes Yes SM and
PDL of the test cord APC APC
u
connectors
CPDL
Mismatch of test cord fibre parameters like core diameter (or mode field diameter) and
numerical aperture may generate variation of the connector attenuation. Uncertainty due to test
cord fibre parameters is assumed to be included in the relative uncertainty of the attenuation of
the test cord connectors.
NOTE 1 This corresponds to uncertainties reported as index 20 and 21.
Reflections may exist between the optical input port of the power meter and the cabling
connector. Multiple reflections may exist in all optical connectors causing variation of the source
and/or higher loss. Uncertainty due to multiple reflections is assumed to be included in the
relative stability of the source and in the attenuation of the test cord connectors.
NOTE 2 This corresponds to uncertainty reported as index 16.
5.2.7 Uncertainties due to cabling
Table 4 provides the list of the uncertainties to be taken into account for the cabling group.
Table 4 – Uncertainties due to cabling
Reference Index Description Concerned Apply to Apply to Other
element P P condition
in out
5.2.7.1 13 Mating reproducibility (cabling) Ref cords No Yes
u
Mreproduc
5.2.7.2 14 Relative uncertainty related to the Cabling No Yes Quantity of
repeatability of the test cord connector connectors
u
mating to cabling connectors depends on
Mating
method
used
5.2.7.3 15 Relative uncertainty related to the PDL of Cabling No Yes SM and APC
the cabling APC connectors
u
CPDL
Mismatch of test cord fibre parameters such as core diameter (or mode field diameter) and
numerical aperture may generate variation of the connector attenuation. Uncertainty due to test

cord fibre parameters is assumed to be included in the relative uncertainty of the attenuation of
the test cord connectors.
NOTE 1 This corresponds to uncertainties reported as index 20 and 21.
Fibre cabling nonlinearities such as Raman scattering or Brillouin scattering should be
considered if a high power source is used. However, when using common sources having a
maximum output power lower than 1 mW (0 dBm), fibre cabling nonlinearity is negligible.
NOTE 2 This corresponds to uncertainty reported as index 22.
6 Uncertainties estimation
6.1 Measurement model
The attenuation L is expressed as the ratio of the input power to the output power level of the
cabling under test as shown in Figure 2.
P (W) P (W)
in Fibre out
plant
IEC
Figure 2 – Measurement model
Ldb = 10 ×log10(P / P ) (1)
in out
where
P is the input power;
in
P is the output power.
out
L = P / P (2)
in out
The relative uncertainty of the power ratio is calculated according to Equation (13) of
ISO/IEC Guide 98-3:2008 as follows:
N NN−1
 
∂L ∂∂LL
u ×u+×2 ××u P ,P (3)
 
L P ( ij )
∑ ∑ ∑
i
∂P ∂∂P Pj
ii
 
i= 1 i= 11ji= +
where
u are the uncertainties related to the measurements of power levels;
P
i
P and u(P ,P ) are the covariance.
i i j
For the purposes of this document, it is supposed that uncertainties that may be correlated, like
the stability of the source and the effect of multiple reflections, are grouped together.
This does not apply to P and P when read from a single power meter. To avoid analysis of
in out
the covariance of these two strongly correlated readings, the following measurement model is
used:
=
– 18 – IEC TR 61282-14:2019 © IEC 2019
P = k × P
in c in-read
= k × K × P (4)
P
out c lin out-read
where
k is the power meter calibration factor;
c
k is the deviation created on P by the nonlinearity.
lin out
Applying this model to the attenuation measurement L shows that the calibration factor should
not be taken into account, while the nonlinearity shall be considered for P only.
out
kP× P
c in-read in-read
L (5)
in
k ××k P k × P
c lin out-read lin out-read
Therefore, Equation (3) yields the following simplified equation:
N
 
∂L
uu×
(6)
 
LP∑
i
∂P
 i 
i=1
By calculating the partial derivatives using the previous equation, one gets:
2 22
N

       
∂∂LL ∂L 1 −P
2 22 2 2 2
in
 (7)
u ×uu×+ ×u ×+u ×u
       
L PP P P P
∑
i in out in out

∂∂PP ∂P P
P
 i   in   out   out 
i=1 out
It is common to express the uncertainties and in a relative form, namely:
u u
P P
in out
u u /P and u u /P
nP in n P out
PPin out
in out
.
This can be achieved by dividing Equation (7) by L , namely:

2 2
 u u
  
P  P
 uP 1 − P P
L out 22out in in out
× ×+u ××u + (8)
  
  
  PP
in 2 out   

LP P P P P
  P
in out in in out
out   

This can be finally written as:
u
 
L
(9)
uu+
  nn
P P
in out
L
 
=
= =
==
= = =
=
==
6.2 Accumulation of uncertainties
The relative uncertainties and can be expressed as the accumulation of the
u u
n n
P P
in out
previously defined relative uncertainties.
As there are many possible measurement configurations, the accumulation of uncertainties can
only be analytically presented for a particular example. The calculation reported below applies
to the measurement of a single mode link having PC connectors, using the one cord method
with a single power meter and a single set of test cables.
NOTE Calculation results for the other configurations are provided in Table 6.
2 22 2 2 2 2
uu + u ++u u + u + u + u (10)
n P Displ PDR P PM Mreprodin Matingin
P stabin in in noisein stabin
in
22 2 2 2 2 2
uu++ u + uu+ + u + u
P λs Lin Displ PDR Pnoiseout PM
stabout out out stabout
(11)
u =
n
P
out 22
++uu
Mreprodout Matingout
This leads to the following formula:
2 2 2 2 2 2 2 22
u + u + u + u + u + u + u + u + u
PPDispl PDR Pnoisein PM Mreprodin Matingin λs
u
stabin in in stabin stabout
L
= (12)
2 22 2 2 2 2
L
++uu + u + u + u + u + u
Lin Displ PDR Pnoiseout PM Mreprodout
...