IEC TR 61000-1-6:2012

IEC/TR 61000-1-6 ®
Edition 1.0 2012-07
TECHNICAL
REPORT
colour
inside
BASIC EMC PUBLICATION
Electromagnetic compatibility (EMC) –
Part 1-6: General – Guide to the assessment of measurement uncertainty

IEC/TR 61000-1-6:2012(E)
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IEC/TR 61000-1-6 ®
Edition 1.0 2012-07
TECHNICAL
REPORT
colour
inside
BASIC EMC PUBLICATION
Electromagnetic compatibility (EMC) –

Part 1-6: General – Guide to the assessment of measurement uncertainty

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
XB
ICS 33.100 ISBN 978-2-83220-204-3

– 2 – TR 61000-1-6 © IEC:2012(E)
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms, definitions, symbols and abbreviations . 8
3.1 Terms and definitions . 8
3.2 Symbols . 14
3.3 Abbreviations . 15
4 General . 16
4.1 Overview . 16
4.2 Classification of uncertainty contributions . 16
4.3 Limitations of the GUM . 17
4.4 Principles . 18
5 Measurement uncertainty budget development . 20
5.1 Basic steps . 20
5.2 Probability density functions . 24
5.2.1 Rectangular . 24
5.2.2 Triangular . 26
5.2.3 Gaussian . 28
5.2.4 U-Shape . 32
5.3 Concept of Type A and Type B evaluation of uncertainty . 35
5.3.1 General considerations . 35
5.3.2 Type A evaluation of standard uncertainty . 36
5.3.3 Type B evaluation of standard uncertainty . 40
5.4 Sampling statistics . 42
5.4.1 General considerations . 42
5.4.2 Sample mean and sample standard deviation . 42
5.4.3 Sample coefficient of variation . 43
5.4.4 Limits of sample-statistical confidence intervals . 43
5.4.5 Sampling distribution and sampling statistics of mean value . 44
5.4.6 Sampling distribution and sampling statistics of standard deviation . 47
5.5 Conversion from linear quantities to decibel and vice versa . 49
5.5.1 General considerations . 49
5.5.2 Normally distributed fluctuations . 49
5.5.3 Uniformly distributed fluctuations . 52
6 Applicability of measurement uncertainty . 52
7 Documentation of measurement uncertainty calculation . 56
Annex A (informative) Example of MU assessment for emission measurements . 57
Annex B (informative) Example of MU assessment for an immunity test level setting . 64
Bibliography . 67

Figure 1 – Classification of uncertainty components associated with the experimental
evaluation of uncertainty in EMC testing and measurement . 16

TR 61000-1-6 © IEC:2012(E) – 3 –
Figure 2 – Classification of uncertainty components associated with site uncertainty
(e.g. reverberation chambers) . 17
Figure 3 – Example of g(x’) . 19
Figure 4 – Impact of g(x) on interpretation of x’ . 19
Figure 5 – Estimate returned by the measurement system . 20
Figure 6 – Rectangular PDF . 25
Figure 7 – Triangular PDF . 27
Figure 8 – Normal PDF for standardized X . 29
Figure 9 – U-shaped PDF . 33
Figure 10 – Example of a circuit . 33
Figure 11 – Limits of 95 %, 99 % and 99,5 % confidence intervals for W as a function
of N for measurements using a rectilinear antenna or single-axis probe . 46
Figure 12 – Limits of 95 %, 99 % and 99,5 % confidence intervals for A as a function
of N for measurements using a rectilinear antenna or single-axis probe . 47
Figure 13 – 95 % confidence intervals for S as a function of N for measurements
X
using a single-axis detector . 48
Figure 14 – PDF of B for a Rayleigh distributed A at selected values of σ . 51
Figure 15 – Measurement uncertainty budget for a quantity to be realized in the test
laboratory . 53
Figure 16 – Relationship between measurement uncertainty budgets for a quantity to
be realized in the test laboratory and tolerances given for this quantity in the applicable
basic standard . 54
Figure 17 – Situations, where and how an instrument is suitable for tests and/or
measurements as specified in the applicable basic standard with tolerances . 55
Figure A.1 – Deviation of the peak detector level indication from the signal level at
receiver input for two cases, a sine-wave signal and an impulsive signal (PRF 100 Hz) . 60

Table 1 – Basic steps for calculating MU . 20
Table 2 – Expressions used to obtain standard uncertainty . 23
Table 3 – Examples of circuit parameters . 35
Table 4 – Values of the expansion coefficient η(ν) which transforms the standard
deviation to the Type A standard uncertainty . 39
Table A.1 – Radiated disturbance measurements from 1 GHz to 18 GHz in a FAR at a
distance of 3 m . 58
Table B.1 – Uncertainty budget of the radiated immunity test level (80 MHz –
1 000 MHz) . 65

– 4 – TR 61000-1-6 © IEC:2012(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTROMAGNETIC COMPATIBILITY (EMC) –

Part 1-6: General –
Guide to the assessment of measurement uncertainty

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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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 61000-1-6, which is a technical report, has been prepared by the IEC technical committee
77: Electromagnetic compatibility in corporation with CISPR (International Special Committee
on Radio Interference).
It forms Part 1-6 of IEC 61000. It has the status of a basic EMC publication in accordance
with IEC Guide 107, Electromagnetic compatibility – Guide to the drafting of electromagnetic
compatibility publications.
TR 61000-1-6 © IEC:2012(E) – 5 –
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
77/397/DTR 77/409/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 the parts of the IEC 61000 series, published under the general title
Electromagnetic compatibility (EMC) 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 web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.
The contents of the corrigendum of October 2014 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.
– 6 – TR 61000-1-6 © IEC:2012(E)
INTRODUCTION
IEC 61000 is published in separate parts, according to the following structure:
Part 1: General
General considerations (introduction, fundamental principles)
Definitions, terminology
Part 2: Environment
Description of the environment
Classification of the environment
Compatibility levels
Part 3: Limits
Emission limits
Immunity limits (in so far as they do not fall under the responsibility of the product
committees)
Part 4: Testing and measurement techniques
Measurement techniques
Testing techniques
Part 5: Installation and mitigation guidelines
Installation guidelines
Mitigation methods and devices
Part 6: Generic standards
Part 9: Miscellaneous
Each part is further subdivided into several parts, published either as international standards
or as technical specifications or technical reports, some of which have already been published
as sections. Others will be published with the part number followed by a dash and a second
number identifying the subdivision (example: IEC 61000-6-1).

TR 61000-1-6 © IEC:2012(E) – 7 –
ELECTROMAGNETIC COMPATIBILITY (EMC) –

Part 1-6: General –
Guide to the assessment of measurement uncertainty

1 Scope
This part of IEC 61000 provides methods and background information for the assessment of
measurement uncertainty. It gives guidance to cover general measurement uncertainty
considerations within the IEC 61000 series.
The objectives of this Technical Report are to give advice to technical committees, product
committees and conformity assessment bodies on the development of measurement
uncertainty budgets; to allow the comparison of these budgets between laboratories that have
similar influence quantities; and to align the treatment of measurement uncertainty across the
EMC committees of the IEC.
Any contributing factor to measurement uncertainty that is mentioned within this Technical
Report shall be treated as an example: the technical committee responsible for the
preparation of a basic immunity standard is responsible for identifying the factors that
contribute to the measurement uncertainty of their basic test method.
It gives a description for
– a method for the assessment of measurement uncertainty (MU),
– mathematical formulas for probability density functions,
– analytical assessment of statistical evaluations,
– correction of measured data,
– documentation.
This Technical Report is not intended to summarize all measurement uncertainty influence
quantities nor is it intended to define how measurement uncertainty is to be taken into
account in determining compliance with an EMC requirement.
NOTE Some of the examples given in this report are taken from IEC publications other than the IEC 61000 series
that have already implemented the evaluation procedure presented here. These examples are used to illustrate the
principles.
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 60050-161, International Electrotechnical Vocabulary (IEV) – Chapter 161: Electro-
magnetic compatibility
CISPR 16-1-1, Specification for radio disturbance and immunity measuring apparatus and
methods – Part 1-1: Radio disturbance and immunity measuring apparatus – Measuring
apparatus
– 8 – TR 61000-1-6 © IEC:2012(E)
CISPR 16-4-2, Specification for radio disturbance and immunity measuring apparatus and
methods – Part 4-2: Uncertainties, statistics and limit modelling – Uncertainty in EMC
measurements
ISO/IEC Guide 98-3:2008, Uncertainty of measurement – Part 3: Guide to the expression of
st
uncertainty in measurement (GUM:1995), corrected 1 edition, 2008
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-161, as well
as the following apply.
NOTE Several of the most relevant terms and definitions from IEC 60050-161 are included among the terms and
definitions below.
3.1.1
combined standard uncertainty
standard measurement uncertainty that is obtained using the individual standard
measurement uncertainties associated with the input quantities in a measurement model
[SOURCE: ISO/IEC Guide 99:2007, definition 2.31, modified – Admitted term became the
preferred (and only) term.]
3.1.2
confidence level
probability, generally expressed as a percentage, that the true value of a statistically
estimated quantity falls within a pre-established interval about the estimated value
[SOURCE: IEC 60050-393:2003, 393-18-31]
3.1.3
coverage factor
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain
an expanded uncertainty
[SOURCE: ISO/IEC Guide 98-3:2008, definition 2.3.6, modified – NOTE was deleted.]
3.1.4
coverage interval
interval containing the set of quantity values of a measurand with a stated probability, based
on the information available
[SOURCE: ISO/IEC Guide 99:2007, definition 2.36, modified – True quantity values was
changed to quantity values.]
3.1.5
coverage probability
probability that the set of quantity values of a measurand is contained within a specified
coverage interval
[SOURCE: ISO/IEC Guide 99:2007, definition 2.37, modified – True quantity values was
changed to quantity values.]
TR 61000-1-6 © IEC:2012(E) – 9 –
3.1.6
distribution function
function giving, for every value ξ, the probability that the random variable X be less than or
equal to ξ:
G(ξ ) = Pr(X ≤ ξ )
[SOURCE: ISO/IEC Guide 98-3, Supplement 1:2008, definition 3.2]
3.1.7
error
measured quantity value minus a reference quantity value
[SOURCE: ISO/IEC Guide 99:2007, definition 2.16, modified – Second admitted term became
the preferred (and only) term.]
3.1.8
expanded uncertainty
quantity defining an interval about the result of a measurement that may be expected to
encompass a large fraction of the distribution of values that could reasonably be attributed to
the measurand
[SOURCE: ISO/IEC Guide 98-3:2008, definition 2.3.5, modified – Notes 1 to 3 were deleted.]
3.1.9
electromagnetic compatibility
EMC
ability of an equipment or system to function satisfactorily in its electromagnetic environment
without introducing intolerable electromagnetic disturbances to anything in that environment
[SOURCE: IEC 60050-161:1990, 161-01-07]
3.1.10
emission
phenomenon by which electromagnetic energy emanates from a source
[SOURCE: IEC 60050-161:1990, 161-01-08, modified – The addition "electromagnetic" in the
term was deleted.]
3.1.11
emission level
emission level of a disturbing source
level of a given electromagnetic disturbance emitted from a particular device, equipment or
system
[SOURCE: IEC 60050-161:1990, 161-03-11]
3.1.12
emission limit
emission limit from a disturbing source
specified maximum emission level of a source of electromagnetic disturbance
[SOURCE: IEC 60050-161:1990, 161-03-12]

– 10 – TR 61000-1-6 © IEC:2012(E)
3.1.13
immunity
immunity to a disturbance
ability of a device, equipment or system to perform without degradation in the presence of an
electromagnetic disturbance
[SOURCE: IEC 60050-161:1990, 161-01-20]
3.1.14
immunity limit
specified minimum immunity level
[SOURCE: IEC 60050-161:1990, 161-03-15]
3.1.15
immunity test level
level of a test signal used to simulate an electromagnetic disturbance when performing an
immunity test
[SOURCE: IEC 60050-161:1990, 161-04-41]
3.1.16
indication
quantity value provided by a measuring instrument or a measuring system
[SOURCE: ISO/IEC Guide 99:2007, definition 4.1, modified – Notes 1 and 2 were deleted.]
3.1.17
influence quantity
quantity that is not the measurand but that affects the result of the measurement
[SOURCE: IEC 60050-394:2007, 394-40-27, modified – Note was deleted.]
3.1.18
instrumentation uncertainty
IU
measurement instrumentation uncertainty
MIU
parameter, associated with the disturbance quantity generated during an emission
measurement or applied during an immunity test that characterizes the dispersion of the
values that could reasonably be attributed to the measurand, induced by all relevant influence
quantities that are related to the measurement instrumentation and the test facility
Note 1 to entry: This term is intended to be applicable to both emission measurements and immunity tests. The
CISPR 16 series of documents also employs the term ‘measurement instrumentation uncertainty’ (MIU).
Note 2 to entry: Based on IEC 60359:2001, definition 3.1.4.
3.1.19
intrinsic uncertainty of the measurand
minimum uncertainty that can be assigned in the description of a measured quantity
Note 1 to entry: In theory, the intrinsic uncertainty of the measurand would be obtained if the measurand was
measured using a measurement system having a negligible measurement instrumentation uncertainty.
Note 2 to entry: No quantity can be measured with continually lower uncertainty, inasmuch as any given quantity
is defined or identified at a given level of detail. If one tries to measure a given quantity at an uncertainty lower
than its own intrinsic uncertainty one is compelled to redefine it with higher detail, so that one is actually measuring
another quantity. See also ISO/IEC Guide 98-3:2008, D.1.1.
Note 3 to entry: The result of a measurement carried out with the intrinsic uncertainty of the measurand may be
called the best measurement of the quantity in question.

TR 61000-1-6 © IEC:2012(E) – 11 –
[SOURCE: IEC 60359:2001, definition 3.1.11, modified – An additional explanation has been
added, i.e. Note 1 to entry.]
3.1.20
level
level of a time varying quantity
value of a quantity, such as a power or a field quantity, measured and/or evaluated in a
specified manner during a specified time interval
[SOURCE: IEC 60050-161:1990, 161-03-01, modified – The NOTE was deleted.]
3.1.21
limits of error of a measuring instrument
extreme value of measurement error, with respect to a known reference quantity value,
permitted by specifications or regulations for a given measurement, measuring instrument, or
measuring system
[SOURCE: ISO/IEC Guide 99:2007, definition 4.26, modified – The term has been clarified
and Notes 1 and 2 have been deleted.]
3.1.22
measurand
particular quantity subject to measurement
[SOURCE: IEC 60050-311:2001, 311-01-03]
3.1.23
measurement accuracy
accuracy of measurement
DEPRECATED: precision of measurement
closeness of agreement between a measured quantity value and the true quantity value of a
measurand
Note 1 to entry: ‘accuracy’ is a qualitative concept.
[SOURCE: IEC 60050-311:2001, 311-06-08, modified – The term has been changed and
replaced by two terms, Note 1 has been deleted and Note 2 replaced by an explanation.]
3.1.24
measurement precision
closeness of agreement between indications or measured quantity values obtained by
replicate measurements on the same or similar objects under specified conditions
[SOURCE: ISO/IEC Guide 99:2007, definition 2.15, modified – Notes 1 to 4 have been
deleted.]
3.1.25
measurement result
set of quantity values being attributed to a measurand together with any other available
relevant information
[SOURCE: IEC 60050-311:2001, 311-01-01, modified – The term has been clarified and the
definition extended. Notes 1 to 5 have been deleted.]
3.1.26
measuring system
complete set of measuring instruments and other equipment assembled to carry out specified
measurements
[SOURCE: IEC 60050-311:2001, 311-03-06]

– 12 – TR 61000-1-6 © IEC:2012(E)
3.1.27
measurement trueness
closeness of agreement between the average of an infinite number of replicate measured
quantity values and the reference quantity value
[SOURCE: ISO/IEC Guide 99:2007, definition 2.14, modified – Only preferred term is given
and Notes 1 to 3 have been deleted.]
3.1.28
measurement uncertainty
MU
non-negative parameter characterizing the dispersion of the quantity values being attributed
to a measurand, based on the information used
[SOURCE: ISO/IEC Guide 99:2007, definition 2.26, modified – Only preferred term is given
and Notes 1 to 4 have been deleted.]
3.1.29
probability density function
PDF
derivative, when it exists, of the distribution function
dG(ξ )
g(ξ ) =
dξ
Note 1 to entry: g(ξ )dξ is the ‘probability element’; g(ξ )dξ = Pr(ξ < X < ξ + dξ )
[SOURCE: ISO/IEC Guide 98-3:2008, definition 3.3, modified – Equation has been changed.]
3.1.30
random error
difference between a measurement and the mean that would result from an infinitely large
number of measurements of the same measurand carried out under repeatability conditions
[SOURCE: IEC 60050-394:2007, 394-40-33, modified – Definition was changed and Notes 1
and 2 have been deleted.]
3.1.31
repeatability
repeatability of results of measurements
closeness of agreement between the results of successive measurements of the same
measurand, carried out under the same conditions of measurement, i.e.:
• by the same measurement procedure,
• by the same observer,
• with the same measuring instruments, used under the same conditions,
• in the same laboratory,
• at relatively short intervals of time
[SOURCE: IEC 60050-311:2001, 311-06-06, modified – Note has been deleted.]
3.1.32
reproducibility of measurements
closeness of agreement between the results of measurements of the same value of a
quantity, when the individual measurements are made under different conditions of
measurement:
TR 61000-1-6 © IEC:2012(E) – 13 –
• principle of measurement,
• method of measurement,
• observer,
• measuring instruments,
• reference standards,
• laboratory,
• under conditions of use of the instruments, different from those customarily used,
• after intervals of time relatively long compared with the duration of a single measurement.
Note 1 to entry: The term ‘reproducibility’ also applies to the instance where only certain of the above conditions
are taken into account, provided that these are stated.
[SOURCE: IEC 60050-311:2001, 311-06-07, modified – Note 1 has been deleted and Note 2
has been renumbered Note 1 to entry.]
3.1.33
sensitivity coefficient
relationship between a change in an output estimate, y, for a corresponding change in an
input estimate, x .
i
3.1.34
standard deviation of a single measurement in a series of measurements
parameter characterising the dispersion of the result obtained in a series of n measurements
of the same measurand
n
sq−
qq
( ) ( )
∑
jj
n −1
( )
j=1
where is the mean value of n measurements
q
[SOURCE: ISO/IEC Guide 98-3:2008, definition B.2.17, modified – Term, definition and
equation have been modified and Notes 1 to 4 have been deleted.]
3.1.35
standard deviation of the arithmetic mean of a series of measurements
parameter characterising the dispersion of the arithmetic mean of a series of independent
measurements of the same value of a measured quantity, given by the formula:
n
sq −q
( ) q
( )
∑
j
nn⋅−1
( )
j=1
Note 1 to entry: sq is the standard uncertainty for type A evaluation (see 5.3), if is used as the estimate.
( ) q
3.1.36
standard uncertainty
measurement uncertainty expressed as a standard deviation
[SOURCE: ISO/IEC Guide 99:2007, definition 2.30, modified – Admitted term became the
preferred (and only) term.]
=
=
– 14 – TR 61000-1-6 © IEC:2012(E)
3.1.37
systematic error
difference between the arithmetic mean that would result from an infinite number of
measurements of the same measurand carried out under repeatability conditions and the true
value of the measurand.
[SOURCE: IEC 60050-394:2007, 394-40-32, modified – Definition was changed and the Note
has been deleted.]
3.1.38
tolerance
maximum variation of a value permitted by specifications, regulations, etc. for a given
specified influence quantity
3.1.39
true value
actual value of the quantity being measured
Note 1 to entry: This can never be known absolutely but can be approximated (within the bounds of uncertainty)
by traceability to national standards.
[SOURCE: IEC 60050-311:2001, 311-01-04, modified – Complement to term was deleted,
definition has been changed, Notes 1 to 4 have been deleted and Note 1 to entry has been
added.]
3.1.40
type A evaluation
evaluation of a component of measurement uncertainty by a statistical analysis of measured
quantity values obtained under defined measurement conditions
[SOURCE: ISO/IEC Guide 99:2007, definition 2.28, modified – Admitted term became the
preferred (and only) term and Notes 1 to 3 have been deleted.]
3.1.41
type B evaluation
evaluation of a component of measurement uncertainty determined by means other than a
Type A evaluation of measurement uncertainty
[SOURCE: ISO/IEC Guide 99:2007, definition 2.29, modified – Admitted term became the
preferred (and only) term and Examples and Note have been deleted.]
3.2 Symbols
X Generic quantity
+
a Upper bound of quantity X
−
a Lower bound of quantity X
d Number of axes of field probe
N Number of repeated indications
ν Number of degrees of freedom, v = N – 1
ν Coefficient of variation of X
X
M Number of samples of N repeated indications
P Coverage probability
p Probability value, p = (1 – P) / 2
Q Random indication
i
Q Mean of a sample of N indications

TR 61000-1-6 © IEC:2012(E) – 15 –
Q Mean of the j-th sample of N indications
j
Q Mean of M samples of N indications
s(Q ) Experimental standard deviation
i
s()Q Experimental standard deviation of the mean, s(Q) = s(Q )/ N
i
u(Q ) Type A (evaluation of the) standard uncertainty, u(Q ) =η(v)∙s(Q )
i i i
η(v) Coefficient which transforms the experimental standard deviation to the Type A
standard uncertainty
Type A (evaluation of the) standard uncertainty of the mean,
uQ() uQ( ) = uQ( )/ N
i
t (v) Upper critical value of the Student’s t PDF with v degrees of freedom corresponding to
p
probability p in one tail
X Lower value of a (specification, tolerance, coverage) interval for quantity X
min
X Upper value of a (specification, tolerance, coverage) interval for quantity X
max
ˆ ˆ
G(X) Distribution function of quantity X, G( X ) = Pr(X ≤ X), where Pr(∙) stands for
“probability that”
g(X) Probability density function (PDF) of quantity X, g(X) = dG(X) / dX
X Expected value of quantity X, X = X ⋅ g(X )dX
∫
x Best estimate of quantity X, x = X
2 2 2
σ Variance of quantity X, σ = (X − X ) = (X − x) ⋅ g(X )dX
X
X
∫
u(x) Type B (evaluation of the) standard uncertainty, u(x) = σ
X
X Influence quantity to a mathematical measurement model
i
x Best estimate of the influence quantity to a mathematical measurement model
i
δX Correction for influence quantity X
i i
Y Output quantity from a mathematical measurement model
y Best estimate of the measurand, corrected for all recognized and significant
systematic effects
c Sensitivity coefficient, partial derivative, with respect to X , of the measurement model,
i i
evaluated at the best estimates x of the input quantities X
i i
u(x ) Standard uncertainty of the best estimate of the influence quantity X
i i
u (y) Combined standard uncertainty of the best estimate of the measurand
c
k Coverage factor
U(y) Expanded uncertainty of the best estimate of the measurand, U(y) = k∙u (y)
c
3.3 Abbreviations
CLT Central Limit Theorem
EM Electromagnetic
EMC Electromagnetic Compatibility
EME Electromagnetic Environment
EUT Equipment Under Test
FAR Fully Anechoic Room
GUM Guide to the expression of Uncertainty in Measurement
IEC International Electrotechnical Commission
IFU Intrinsic Field Uncertainty

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IUM Intrinsic Uncertainty of the Measurand
LPU Law of Propagation of Uncertainty
MIU Measurement Instrumentation Uncertainty
MU Measurement Uncertainty
OATS Open Area Test Site
PDF Probability Density Function
RSS Root of the Sum of Squares
SAC Semi-Anechoic Chamber
SCU Standards Compliance Uncertainty
VSWR Voltage Standing Wave Ratio
4 General
4.1 Overview
This Technical Report presents background material on the principles of Measurement
Uncertainty (MU) and guidelines on the calculation and application of MU values. The
Technical Report is intended as an aid to those preparing EMC standards under the
IEC 61000 series.
4.2 Classification of uncertainty contributions
An estimated value of an electrical or electromagnetic (EM) quantity becomes more
meaningful when a quantitative statement of uncertainty and confidence is reported together
with this value. Further discussion is focused here on the experimental evaluation of
uncertainty, rather than evaluation through numerical calculation (e.g. Monte Carlo methods
or simulation) that may provide an alternative or additional method for the evaluation of
uncertainty.
MU can be subdivided into different components (see Figure 1).

measurement uncertainty (MU)
measurement
intrinsic
instrumentation uncertainty of the
uncertainty (MIU)
measurand (IUM)
IEC  1303/12
Figure 1 – Classification of uncertainty components associated with
the experimental evaluation of uncertainty in EMC testing and measurement

TR 61000-1-6 © IEC:2012(E) – 17 –

site uncertainty (SU)
intrinsic field site imperfection
uncertainty
uncertainty
(SIU)
(IFU)
IEC  1304/12
Figure 2 – Classification of uncertainty components associated
with site uncertainty (e.g. reverberation chambers)
Figure 1 shows a classification of contributions to the MU, which consists of two components:
a) measurement instrumentation uncertainty (MIU), which represents the contribution by the
instrumentation (e.g., antennas/probes, analyzers, cables, test facility) and
b) the intrinsic uncertainty of the measurand (IUM), which represents the contribution by the
EUT (e.g. instability, setup, lack of definition of the setup).
Figure 2 shows a classification of contributions to the site uncertainty for e.g. reverberation
chambers, which consists of two components:
c) intrinsic field uncertainty (IFU), which represents the contribution inherent to the
complexity (IFU for radiated phenomena, where applicable) and
d) imperfections of the test site (SIU).
NOTE Site uncertainty and site imperfection uncertainty are the same in the case of a semi-anechoic chamber or
a fully anechoic room.
MU thus contributes only if a process of measurement (i.e. quantification of an EM quantity)
actually takes place. By contrast, SU is always present whenever an EM excitation has been
generated because the EM quantity of interest is then physically existent and fluctuating,
irrespective of whether or not a process of measurement takes place. For example, the wall
reflections generated by an ideal calibrated reference radiator placed in a test site produce
random spatial fluctuations of the field included in the SU. These reflections can be residual
(as e.g. in a FAR) or intentional (as e.g. in a reverberation chamber) and are present
irrespective whether any additional monitoring antenna or probe is present or not.
The process of calibration/validation of the test site verifies that the level of site imperfections
is within acceptable bounds, but it does neither influence nor eliminate the contribution of the
SU. Measurement uncertainty may consist of a MIU contribution and the site imperfection
contribution (e.g. NSA measurement in a FAR).
NOTE 1 In this classification, the term “instrumentation” is more restricted than in other documents, e.g.,
CISPR 16-4-1. In a FAR, the site uncertainty is caused solely by site imperfections and is incorporated within MIU
in CISPR 16-4-1 and CISPR 16-4-2. For other test sites (including multi-path EM environments, e.g., reverberation
chambers and more general fading channels), even the idealized site may exhibit inherent field uncertainty as an
additional component to site imperfections. An explicit model and example of IFU is described in 5.2.3.4.
NOTE 2 In an anechoic environment, the MU of the complete test is also known as the standards compliance
uncertainty (SCU) in CISPR 16-4-1. In ISO/IEC Guide 99:2007, the IUM is referred to as the definitional uncertainty
(DU).
4.3 Limitations of the GUM
The “Guide to the expression of uncertainty in measurement” (GUM), see ISO/IEC 98-3:2008,
provides the theoretical framework within which this Technical Report was developed. The
GUM uncertainty approach has, however, fundamental limitations. If these limitations are

– 18 – TR 61000-1-6 © IEC:2012(E)
exceeded the results produced are no longer valid. Essentially, the theoretical framework of
the GUM is based on (see [1]):
a) the Law of Propagation of Uncertainties (LPU), and
b) the Central Limit Theorem (CLT).
To insure that an uncertainty evaluation made according to the procedure described in
ISO/IEC 98-3 may be correct, the assumptions required for the validity of both LPU and CLT
shall be satisfied. The Supplement 1 to ISO/IEC 98-3 describes a numerical technique aimed
at extending the validity of the uncertainty evaluations to cases where the application of
ISO/IEC 98-3 does not produce reliable results.
CLT applies when
a) the measurement model is linear or quasi-linear, that is, it should be verified, at least to
an approximation consistent with fitness for purpose, that the measurand can be
expressed as
Y = c + c X + c X + … + c X
0 1 1 2 2 n n
b) input quantities are independent,
c) |c u(x )| have comparable magnitude,
i i
d) n is sufficiently large (say n ≥ 3).
If the requirements a) through d) are satisfied then Y approximately follows a normal PDF
having an expected value y and a standard uncertainty u(y), where
y = c + c x + c x + … + c x
0 1 1 2 2 n n
and
2 2 2 1/2
u(y) = [(c u(x )) + (c u(x )) + … (c u(x )) ]
1 1 2 2 n n
4.4 Principles
When performing either an emission measurement or an immunity test, a measurement
instrumentation chain is required. The MIU is a fundamental property of this instrumentation
chain.
At the most fundamental level, the act of measurement involves the acquisition of the
numerical value of some measurand. The true value of the measurand is written hereafter
simply as x.
To perform a measurement, some form of measurement instrumentation chain (forming the
measurement system) is required. A measurem
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