IEC TR 61282-14:2016

IEC TR 61282-14 ®
Edition 1.0 2016-01
TECHNICAL
REPORT
colour
inside
Fibre optic communication system design guides –
Part 14: Determination of the uncertainties of attenuation measurements in fibre
plants
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IEC TR 61282-14 ®
Edition 1.0 2016-01
TECHNICAL
REPORT
colour
inside
Fibre optic communication system design guides –

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

plants
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.180.01 ISBN 978-2-8322-3111-1

– 2 – IEC TR 61282-14:2016 © IEC 2016

CONTENTS
FOREWORD . 5

INTRODUCTION . 7

1 Scope . 8

2 Normative references . 8

3 Terms, definitions and abbreviations . 8

3.1 Terms and definitions . 8

3.2 Abbreviations . 10
4 Overview of uncertainty . 10
4.1 What is uncertainty? . 10
4.2 Origin of uncertainties . 10
4.3 What may not be considered as uncertainty? . 10
5 Fibre cabling attenuation measurement . 11
5.1 Measurement 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 measurement 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 . 18
7 General representation of the equation using sensitivity coefficients . 19
8 Calculation . 22
8.1 Combined standard uncertainty . 22
8.2 Expanded uncertainty . 22
8.3 Determination of the coverage factor k . 22
8.3.1 General approach . 22
8.3.2 Discussion . 22

8.3.3 Typical values of degree of freedom . 23
Annex A (normative) Mathematical basis . 24
A.1 General . 24
A.2 Type A evaluation of uncertainty . 24
A.3 Type B evaluation of uncertainty . 24
A.4 Determining the combined standard uncertainty . 25
A.5 Reporting . 26
Annex B (informative) Measurement methods . 27
B.1 Measurement methods as per IEC 61280-4-1 and 61280-4-2 . 27
B.1.1 General . 27
B.1.2 Measurement configuration . 27
B.1.3 One-cord reference configuration . 27
B.1.4 Two-cord reference configuration . 28
B.1.5 Three-cord reference configuration . 28

B.2 Measurement methods as per ISO/IEC 14763-3:2014 . 28

B.2.1 General . 28

B.2.2 Channels . 29

B.2.3 Links. 30

Annex C (normative) Uncertainties evaluation . 31

C.1 Type A uncertainties . 31

C.1.1 General . 31

C.1.2 Evaluation of optical source instability and associated uncertainties . 31

C.2 Type B uncertainties . 31

C.2.1 General . 31
C.2.2 Evaluation of the power meter noise . 31
C.2.3 Elements to be considered for power meter stability analysis . 32
C.2.4 Evaluation of the centre wavelength dependence . 32
C.2.5 Spectral width dependence . 34
C.2.6 Evaluation of the uncertainties due to MM launch conditions . 34
C.2.7 Evaluation of the PDL . 35
C.2.8 Uncertainty of absolute power measurement . 36
Annex D (normative) Typical values of uncertainties . 37
Annex E (informative) Linear to dB scale conversion of uncertainties . 38
E.1 Definition of decibel . 38
E.2 Conversion of relative uncertainties . 38
Bibliography . 39

Figure 1 – Fish bone analysis . 13
Figure 2 – Measurement model . 17
Figure B.1 – Measurement configuration . 27
Figure B.2 – One-cord reference measurement . 27
Figure B.3 – Two-cord reference measurement . 28
Figure B.4 – Three-cord reference measurement . 28
Figure B.5 – Measurement on channel . 29
Figure B.6 – Channel reference measurement . 29
Figure B.7 – Link measurement configuration . 30
Figure B.8 – Link reference measurement . 30

Figure C.1 – Typical spectral response of a fibre . 33
Figure C.2 – Uncertainties due to the launch conditions for a given loss . 35

Table 1 – Source of uncertainty (raw list) . 11
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 . 20
Table 6 – Sensitivity coefficients for ISO/IEC 14763-3:2014 methods. 21
Table 7 – Values of k for different values of n . 23
Table 8 – Typical values of n . 23
i
Table C.1 – Spectral attenuation coefficients . 33

– 4 – IEC TR 61282-14:2016 © IEC 2016

Table C.2 – Sensitivity coefficients . 33

Table D.1 – Typical values of uncertainties . 37

INTERNATIONAL ELECTROTECHNICAL COMMISSION

____________
FIBRE OPTIC COMMUNICATION SYSTEM DESIGN GUIDES –

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
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2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
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3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
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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.

– 6 – IEC TR 61282-14:2016 © IEC 2016

The text of this technical report is based on the following documents:

Enquiry draft Report on voting

86C/1339/DTR 86C/1351/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.

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.

This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC website 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.
The contents of the corrigendum of April 2016 have been included in this copy.
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 Technical Report 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 reference connectors, etc.) to determine the overall measurement uncertainty. The
Technical Report 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 Technical Report 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 61280-4-2.
The reference document for general uncertainty calculations is ISO/IEC Guide 98-3:2008, and
this report 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 Technical Report is associated with a calculation spreadsheet (Excel) containing
practical calculations.
– 8 – IEC TR 61282-14:2016 © IEC 2016

FIBRE OPTIC COMMUNICATION SYSTEM DESIGN GUIDES –

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, 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.
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 abbreviations
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1.1
attenuation
L
reduction of optical power induced by transmission through a medium such as cabling, given
as L (dB)
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
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 insertion loss due to a variation of the state of polarization (SOP) over
all the SOPs
3.1.7
nonlinearity
NL
for a power meter, the relative difference between the response at a given power P and the
response at a reference power P :
r(P)
nl = − 1
P/P
r(P )
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

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.

– 10 – IEC TR 61282-14:2016 © IEC 2016

3.1.13
uncertainty type A
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
uncertainty type B
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 Abbreviations
For the purposes of this document, the following acronyms apply.
APC angled physical contact (description of connector style)
CW continuous wave
LSPM light source power meter
OPM optical power meter
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 cause 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 Measurement methods
Three attenuation measurement 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 measurement methods are designated respectively, one-cord, three-cord

and two-cord reference 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 61280-4-2 for more details.
NOTE Measurement 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.
Table 1 – Source of uncertainty (raw list)
Source of uncertainty Type of origin Index
Measurement source instability (power deviation Measurement devices
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
upon the compliance or noncompliance with the
EF template and a function of the attenuation of
the measured cabling)
Power meter non linearity 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
Reference connector / fibre attenuation uncertainty References used 13
References used/ item to be measured
Connector mating repeatability (Reference or
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 non linearity Item to be measured 22
Temperature Environment 23
Humidity Environment 24
– 12 – IEC TR 61282-14:2016 © IEC 2016

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.
Man: Operator skills Method: Measurement
Environment
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
Power meter calibration (12)
Reading Stability: Type A
Connectors
resolution (07) uncertainties (11)
Speckle (04)
Reflexions (16)
NA (20) Non linearity (22)
Launch
PDL (15)
Mating
conditions (05)
Un-stability
repeatability (14)
Fibre
Power metre
(01)
Ref cords
Spatial
Non linearity
uniformity (08)
Core
(06) Core diameter (21)
Source
diameter (21)
Polarisation
PDL (15) Reflexions (16)
Spectral
sensitivity (9)
Noise (10)
width (03)
NA (20)
Central
Connectors
wavelength (02)
Fibre
wavelength
Detector
Change
Mating repeatability (14)
connector (13)
Measurement references Material: Cabling
Machine: Measurement device
IEC
Figure 1 – Fish bone analysis
– 14 – IEC TR 61282-14:2016 © IEC 2016

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 measurement methods
Measurement 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
(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 / Concerned Apply to Apply to Other
Index Description
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 any other instabilities (assumed to

Pstab
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 optical source wavelength. See C.2.4
λs
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
non-linearity 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 meter
u
negligible if power level remains 30 dB
Pnoise
over the 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
P . These uncertainties need to be power
u
out
abs
P
in
considered only when performing meters are

u measurements of P and P using used
abs in out
P
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

– 16 – IEC TR 61282-14:2016 © IEC 2016

detector 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 / Concerned Apply to Apply to Other

Index Description
Symbol element P P 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
upon the
repeatability of the reference
u
connector mating method
Mating
used
5.2.6.3 15 Relative uncertainty related to the Ref cords Yes Yes SM and
PDL of the reference APC APC
u
connectors
CPDL
Mismatch of reference cord fibre parameters like core diameter (or mode field diameter) and
numerical aperture may generate variation of the connector attenuation. Uncertainty due to
reference cord fibre parameters is assumed to be included in the relative uncertainty of the
attenuation of the reference 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 reference 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

Concerned Apply Apply Other
Reference Index Description
element to P to P condition
in out
5.2.7.1
13 Mating reproducibility (cabling) Ref cords No Yes
u
Mreproduc
Quantity of
connectors
5.2.7.2 Relative uncertainty related to the
14 repeatability of the reference connector Cabling No Yes depends on
u
mating to cabling connectors method
Mating
used.
5.2.7.3
Relative uncertainty related to the PDL of SM and
15 Cabling No Yes
the cabling APC connectors APC
u
CPDL
Mismatch of reference cord fibre parameters such as core diameter (or mode field diameter)
and numerical aperture may generate variation of the connector attenuation. Uncertainty due

to reference cord fibre parameters is assumed to be included in the relative uncertainty of the

attenuation of the reference connectors.

NOTE 1 This corresponds to uncertainties reported as index 20 and 21.

Fibre cabling non-linearities 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 non linearity 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
L = 10 ⋅log (P / P ) (1)
dB 10 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 Formula 13 of
ISO/IEC Guide 98-3:2008 as follows:
N N −1 N
 ∂L  ∂L ∂L
2 2
 
u = ⋅ u + 2 ⋅ ⋅ ⋅ u(P , P ) (3)

L P i j
∑ ∑ ∑
  i
∂P ∂P ∂Pj
i i
 
i=1 i=1 j=i+1
where
are the uncertainties related to the measurements of power levels, and
u
Pi
P , and u(P ,P ) are the covariance.
i i j
For the purposes of this Technical Report, it is supposed that uncertainties that may be
correlated, like the stability of the source and the effect of multiple reflections, were 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 61282-14:2016 © IEC 2016

P = k P
in c in−read
(4)
P = k k P
out c lin out−read
• where
• k is the power meter calibration factor, and
c
• k is the deviation created on P by the non-linearity.
lin out
Applying this model to the attenuation measurement L shows that the calibration factor should

not be taken into account, while the non-linearity shall be considered for P only.
out
k P P
c in−read in−read
(5)
L = =
in
k k P k P
c lin out −read lin out −read
Therefore, Equation (3) yields the following simplified equation:
N
 
∂L
2 2
 
u = ⋅ u
(6)
L ∑ P
  i
∂P
 i 
i =1
By calculating the partial derivatives using the previous equation, one gets:
2 2 2 2
N
 
       
∂L ∂L ∂L 1 − P
2 2 2 2 2 2
in
 
     
u = ⋅u =   ⋅u + ⋅u = ⋅u + ⋅u (7)
L ∑ P P P P P
       
i in out in out
 
∂P ∂P ∂P P
i in out out P
       
i =1  out 
u u
P P
in out
It is common to express the uncertainties and in a relative form, namely:

u = u / P u = u / P
n P in n P out
in out
P P
in out
and .
This can be achieved by dividing Equation (7) by L , namely:

2 2
2 2 2
 
u u
   
u  P     P  − P
  1 P P
2 2
L out out in in out
 
   
     
  = ⋅ ⋅ u + ⋅ ⋅ u = + (8)
P
     
in    
 2  P
L P P P P P
out
  P
 in   out   in  in out
   
 out 
This can be finally written as:
 u 
L 2 2
= u + u (9)
 
n n
P P
L in out
 
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 reference cables.

NOTE Calculation results for the other configurations are provided in Table 6.

2 2 2 2 2 2 2
(10)
u = u + u + u + u + u + u + u
n P Displ PDR Pnoisein PM Mreprodin Matingin
stabin in in stabin
P
in
2 2 2 2 2 2 2
u + u + u + u + u + u + u
P λs Lin Displ PDR Pnoiseout PM
stabout out out stabout
(11)
u =
n
P
2 2
out
+ u + u
Mreprodout Matingout
This leads to the following formula:

2 2 2 2 2 2 2 2 2
u + u + u + u + u + u + u + u + u
u P Displ PDR Pnoisein PM Mreprodin Matingin P λs
stabin in in stabin stabout
L
= (12)
2 2 2 2 2 2 2
L
+ u + u + u + u + u + u + u
Lin Displ PDR Pnoiseout PM Mreprodout Matingout
out out stabout
Assuming the P and P related terms
...