ETSI ETR 028 ed.2 (1994-03)

Radio Equipment and Systems (RES); Uncertainties in the measurement of mobile radio equipment characteristics

RTR/RES-02-10

Radijska oprema in sistemi (RES) - Negotovosti pri meritvah karakteristik mobilne radijske opreme

General Information

• Status: Published
• Publication Date: 30-Mar-1994
• Technical Committee: RES 2 - Land Mobile
• Current Stage: 12 - Completion
• Due Date: 01-Nov-1993
• Completion Date: 31-Mar-1994
• Ref Project: PSIST ETR 028:1998 - Radio Equipment and Systems (RES); Uncertainties in the measurement of mobile radio equipment characteristics

Standards Content (Sample)

SLOVENSKI STANDARD
01-avgust-1998
Radijska oprema in sistemi (RES) - Negotovosti pri meritvah karakteristik mobilne
radijske opreme
Radio Equipment and Systems (RES); Uncertainties in the measurement of mobile radio
equipment characteristics
Ta slovenski standard je istoveten z: ETR 028 Edition 2
ICS:
33.060.20 Sprejemna in oddajna Receiving and transmitting
oprema equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

ETSI ETR 028
TECHNICAL March 1994
REPORT Second Edition
Source: ETSI TC-RES Reference: DTR/RES 02-10
ICS: 33.020
Key words: Mobile radio, testing, measurement uncertainty, analogue, data, conducted measurements
Radio Equipment and Systems (RES);
Uncertainties in the measurement of
mobile radio equipment characteristics
ETSI
European Telecommunications Standards Institute
ETSI Secretariat
Postal address: F-06921 Sophia Antipolis CEDEX - FRANCE
Office address: 650 Route des Lucioles - Sophia Antipolis - Valbonne - FRANCE
X.400: c=fr, a=atlas, p=etsi, s=secretariat - Internet: [e-mail]
Tel.: [phone] - Fax: [phone]
Copyright Notification: No part may be reproduced except as authorized by written permission. The copyright and the
foregoing restriction extend to reproduction in all media.
© European Telecommunications Standards Institute 1994. All rights reserved.

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ETR 028:1994
Whilst every care has been taken in the preparation and publication of this document, errors in content,
typographical or otherwise, may occur. If you have comments concerning its accuracy, please write to
"ETSI Editing and Committee Support Dept." at the address shown on the title page.

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Contents
Foreword .7
Introduction.7
1 Scope .13
2 References.13
3 Definitions, symbols and abbreviations.13
3.1 Definitions .13
3.2 Symbols .15
3.3 Abbreviations .16
4 General requirements .16
4.1 Test environment .16
4.2 Calibration.16
5 Calculation of measurement uncertainty.16
5.1 General .16
5.1.1 Confidence level.17
5.1.2 Error distributions and standard deviations.17
5.1.3 Combining standard deviations.17
5.1.4 Combining uncertainties of different parameters, where their influence on
each other is dependant on the device under test (influence quantities) .19
5.1.5 Estimate of standard deviation of random errors .21
5.2 Specific to radio equipment .22
5.2.1 Uncertainty in measuring attenuation.22
5.2.2 Mismatch uncertainty and mismatch loss .24
5.3 Noise behaviour in receivers.26
5.3.1 Possible front ends of receivers .26
5.3.2 Uncertainties in measuring sensitivity in a receiver.27
5.4 Uncertainty in measuring third order intermodulation rejection .28
5.4.1 Third order intermodulation mechanisms.28
5.4.2 Measurement of third order intermodulation rejection.28
5.4.3 Uncertainties involved in the measurement .29
5.4.3.1 Uncertainty due to the signal level uncertainty of the two
unwanted signals.29
5.4.3.2 Error caused by level uncertainty of the wanted signal.30
5.4.3.3 Error caused by SINAD measurement uncertainty.30
5.5 Uncertainty in measuring continuous bit streams.31
5.5.1 General.31
5.5.2 Statistics involved in the measurement.31
5.5.3 Uncertainty caused by BER resolution.32
5.5.4 BER dependency functions .32
5.5.4.1 Coherent data communications.32
5.5.4.1.1 Coherent data communications (direct
modulation) .33
5.5.4.1.2 Coherent data communications (sub
carrier modulation).34
5.5.4.2 Non coherent data communication.35
5.5.4.2.1 Non coherent data communications
(direct modulation) .35
5.5.4.2.2 Non coherent data communications
(sub carrier modulation).36
5.5.5 Effect of BER on the RF level uncertainty .37
5.6 Uncertainty in measuring messages.40
5.6.1 General.40

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ETR 028:1994
5.6.2 Statistics involved in the measurement . 40
5.6.3 Analysis of the situation where the up down method results in a shift
between two levels. 41
5.6.4 Detailed example of uncertainty in measuring messages . 42
5.7 Detailed example of the calculation of measurement uncertainty (Carrier power) . 46
5.7.1 Power meter and sensor module uncertainty . 46
5.7.2 Matching network and mismatch uncertainties. 47
5.7.2.1 Calculations based on available data. 47
5.7.2.2 Calculations based on measured data. 47
5.7.3 Uncertainty caused by influence quantities. 48
5.7.4 Random uncertainty. 49
5.7.5 Total uncertainty . 49
6 Transmitter measurement examples. 51
6.1 Frequency error. 51
6.2 Carrier power. 52
6.3 Frequency deviation .55
6.3.1 Maximum frequency deviation. 55
6.3.2 Modulation frequencies above 3 kHz. 56
6.4 Adjacent channel power. 57
6.4.1 Adjacent channel power method 1 (Using an adjacent channel power
meter) . 57
6.4.2 Adjacent channel power method 2 (Using a spectrum analyser) . 58
6.5 Conducted spurious emissions . 61
6.6 Cabinet radiation . 64
6.7 Intermodulation attenuation. 66
6.8 Transmitter attack/release time. 68
6.8.1 Frequency behaviour (applicable to attack time measurement). 68
6.8.2 Power level behaviour (applicable to attack and release time
measurements). 69
6.9 Transient behaviour of the transmitter . 70
6.9.1 Uncertainty in measuring frequency error. 70
6.9.2 Uncertainty in measuring power level slope . 71
7 Receiver measurement examples. 72
7.1 Maximum usable sensitivity. 72
7.1.1 Maximum usable sensitivity (analogue speech) . 72
7.1.2 Maximum usable sensitivity (bit stream). 74
7.1.3 Maximum usable sensitivity (messages). 78
7.2 Amplitude characteristic . 80
7.3 Two signal measurements . 82
7.3.1 Two signal measurements (analogue speech). 82
7.3.1.1 In band measurements . 82
7.3.1.2 Out of band measurements . 84
7.3.2 Two signal measurements (bit stream) . 87
7.3.2.1 In band measurements . 87
7.3.2.2 Out of band measurements . 90
7.3.3 Two signal measurements (messages). 92
7.3.3.1 In band measurements . 92
7.3.3.2 Out of band measurements . 94
7.4 Intermodulation response. 96
7.4.1 Intermodulation response (analogue speech) . 96
7.4.2 Intermodulation response (bit stream). 100
7.4.3 Intermodulation response (messages) . 104
7.5 Conducted spurious emissions . 107
7.6 Cabinet radiation . 109
8 Duplex operation measurements. 109
8.1 Receiver desensitisation . 109
8.1.1 Desensitisation (analogue speech). 109
8.1.2 Desensitisation (bit stream) . 112
8.1.3 Desensitisation (messages) . 115
8.2 Receiver spurious response rejection. 117

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8.2.1 Spurious response rejection (analogue speech).117
8.2.2 Spurious response rejection (bit stream) .119
8.2.3 Spurious response rejection (messages).121
Annex A: Maximum accumulated measurement uncertainty .123
Annex B: Interpretation of the measurement results.124
Annex C: Influence quantity dependency functions.125
Annex D: Bibliography .127
History.128

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Foreword
This ETSI Technical Report (ETR) has been prepared by the Radio Equipment and Systems (RES)
Technical Committee of the European Telecommunications Standards Institute (ETSI).
In this second edition the area of data communication measurement uncertainties has been addressed
and added to the analogue measurement uncertainties in the first edition of this ETR, in addition the
diagrams have been standardised and minor editorial corrections have been carried out.
Introduction
This ETR has been written to clarify the many problems associated with the interpretation, calculation and
application of measurement uncertainty.
This ETR is intended to provide, for relevant standards, the method of calculating the measurement
uncertainty relating to type testing. This ETR is not intended to replace any test methods in the relevant
standards although Clauses 6, 7 and 8 contain brief descriptions of each measurement.
This ETR is intended for use, in particular, by accredited test laboratories performing type testing.
The basic purpose of this ETR is to:
- provide the method of calculating the total measurement uncertainty;
- provide the maximum acceptable "window" of measurement uncertainty (see Annex A, table A.1),
when calculated using the methods described in this ETR;
- provide the Equipment Under Test (EUT) dependency functions (see Annex C, table C.1) which
should be used in the calculations unless these functions are evaluated by the individual
laboratories;
- provide a recommended method of applying the uncertainties in the interpretation of the results
(see Annex B).
Exact measurement of a quantity which can vary infinitesimally is an ideal which cannot be attained in
practical work. Both science and industry assesses measurements which are always in error by an
amount that may or may not be significant for the particular purpose in hand. Examples of such errors are:
a) that the measured value will be influenced by the operators, perhaps in a scale being misread;
b) the test configuration or test method, which may result in the measured value being biased in some
way;
c) the test equipment used, which may be subject to several sources of error and may alter the value
being measured simply by making the measurement (e.g. loading);
d) the environment, for example the humidity and the temperature;
e) the equipment under tests input and output impedances, transfer characteristics, stability etc.
A method is required to calculate the error of the measured value which takes into account:
- systematic errors, which are those errors inherent in the construction and calibration of the
equipment used and in the method employed;
- random errors, which are errors due to chance events which, on average, are as likely to occur as
not to occur and are outside the engineers control; and
- influence quantity errors, whose magnitude is dependant on a particular parameter or function of
the EUT.
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Error is usually taken to mean the difference between the measured value of a quantity and the true value.
The error is something that can never be known exactly, generally the measurement would not be made if
the true value was known.
The definition of absolute error is:
Absolute error = the measured value - the true value.
The true value (which is the ideal result) is not known, only the measured value, therefore the magnitude
of the absolute error can never be known, and it is only possible to approximate the true value.
To estimate the amount of error in the approximation, a set of rules is needed to determine the value of
the error.
In practice there usually is some idea of the size of the error inherent in the components of a system. No
measuring equipment is perfect, so skill should be exercised in measurement and in the use of statistics
to assess the probable limits of error, or the uncertainty. One method is by arithmetic summation, this
method can be used to arrive at a range of values within which the result lies.
When, in a particular measurement system, the measured result is biased away from the true value, the
mean value towards which several readings tend, is in error by a specific offset value. For example, when
measuring RF power, the radio frequency attenuation of a connecting cable will consistently produce
readings that are lower than the true value. The results are in error by the value of the RF attenuation of
the cable.
This offset is a systematic error and if the attenuation is known the results can be corrected to eliminate
this error.
Systematic errors are inherent in the construction and calibration of the equipment used and in the
method employed. They cannot be measured by repeating the measurement under standard conditions.
The assessment of systematic uncertainty requires changes to be made to the measurement system. If,
at the same laboratory using the same test configuration and the same test equipment, including the set
up and breakdown of the test equipment, a measurement is repeated a number of times, assuming there
is a sufficient resolution in the measurement system, the measured value will differ from one
measurement to the next. This is known as repeatability and corresponds to random uncertainty. The
mean value of the measurements will however converge to a particular value.
Random uncertainty can only be assessed if the measurement system is sufficiently sensitive and in a
state of statistical control.
If unknown variations are occurring, the mean value of the measurement will drift and will not converge to
any particular value making the exercise pointless.
The assessment of random errors requires that no changes will be made to the measurement system.
The measured value that differs from one measurement to another (assuming there is sufficient
resolution) by using a different test equipment configuration, or different test equipment, or by comparison
with another laboratory is known as reproducibility and should not be confused with repeatability.
A further uncertainty in the measurement process is the influence from quantities which are not directly
related to the function or parameter being measured. These are known as influence quantities.
Influence quantities create errors whose magnitude is dependant on a specific parameter or function of
the particular equipment under test and will vary between identically built standard equipments.
The influence functions have no connection with the test equipment, they do not change the random or
systematic error of the measurement system but they do interact with the measurement system to
produce influence uncertainties.

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For example, consider the measurement of receiver sensitivity, where a SINAD meter, connected to the
audio output is used to evaluate an RF sensitivity expressed in μV. The uncertainty in the measurement of
the SINAD on the audio side of the receiver has at some point in time to be converted into an uncertainty
in terms of μV at the RF input of the receiver. This conversion depends clearly on the characteristics of
the receiver being measured, more specifically, of the slope Signal/Noise (S/N) as a function of
Carrier/Noise (C/N) (see subclause 5.3).
The measurement conditions can also have an influence on the results. Consider, for example the heating
effect of a continuous carrier on the output stage of a power amplifier in a transmitter. Assume the
measurement system would measure carrier power to within 0,5 dB, but that the transmitter output power
fell at the rate of 1,0 dB per minute. If the carrier power was measured at the instant of stabilising at full
power (say less than one second after switching on) a particular value for the carrier power would be
recorded. If however the measurement was performed two minutes after the switching on, then the carrier
power would have been 2 dB lower than that found during the first case. Both have been measured with
an accuracy of 0,5 dB but the results are in fact separated by 2 dB, and have an apparent conflict as the
uncertainties of both measurements do not overlap.
As the time between turning on the transmitter and the measurement is not known exactly, this is an
example of an influence uncertainty and, taken to its logical conclusion, does not satisfy the requirements
of estimating for a random uncertainty as it is obvious that the mean of a series of measurements will not
converge but will drift to zero or until the transmitter is destroyed.
The characteristics of the equipment can also change in time, due, for example, to the ageing of
components e.g. crystals. The aim of the evaluation of measurement uncertainty is to ensure that at the
time when a measurement is performed the measurement is within the an expected range of values. This
does not imply, in all cases necessarily, that if the measurement was to be performed at another moment
or by another laboratory the true value of the measurement would be the same, or lie within the
measurement uncertainty of the first measurement.
Influence uncertainty is related to the parameters of the EUT, e.g. the input and output impedances,
transfer characteristics, stability, sensitivity to changes in the environment etc. The dependencies can be
evaluated for each equipment by the laboratories, or can be taken from table C.1 of this ETR. However
arrived at, the magnitudes of the influence uncertainties should be included in the calculation of the total
uncertainty for each measurement.
When estimating the measurement uncertainty by arithmetic summation, a pessimistic range of
uncertainty limits are calculated. This is because the principle of summation corresponds to the case
when all the error components act in the same direction at the same time. This approach gives the
maximum and minimum error bounds with 100 % confidence.
To overcome this very pessimistic view of the uncertainty of measurement, the guidelines given in the
reference documents (see Clause 2), have been adopted in this ETR.
These guidelines apply statistical analysis to the calculation of the overall probable error but relies on the
knowledge of the magnitude and the distribution of the individual error components.
As a first principle, the following guidelines for reducing and estimating uncertainties in measurement
should be used:
a) list the sources of error that could exist in the system;
b) separate the list into three parts: errors that are systematic errors, random (repeatability) errors, and
human errors;
NOTE: Some of the sources may appear in more than one list.
c) examine carefully the procedure for reducing the probability of human errors (a typical one might be
wrongly interpreting the manufacturers data); good documentation of results is essential;
d) make a first estimate of the uncertainties of the systematic errors; determine the distribution factors
used in the combination and arrange the lists of systematic and random errors in order of
importance;
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ETR 028:1994
e) consider the benefits of making a correction to a systematic error in order to reduce the systematic
uncertainty, in some cases a systematic error correction may not be feasible;
f) where corrections have been made, revise the list for systematic uncertainties;
g) investigate repeatability; use previous experience to decide on how many samples should be made;
the decision will depend, in part, on the relative size of the random errors and their distribution
factors;
h) consider tightening the control of influence quantities; you should first make an assessment of the
effect of each influence quantity; there is no point in making a negligible uncertainty even smaller, or
in controlling an influence quantity which has very little, if any, effect on the measured quantity;
j) state clearly and explicitly all the assumptions in your calculations of uncertainty.
For further reading see the bibliography in Annex D.
The main advantage of this ETR is in the flexible approach that has been adopted; it is based on an "error
budget" for each test. The budget is used to calculate the measurement uncertainty, which should be
compared to the relevant figure in table A.1. The values in table A.1 have been set and should not be
exceeded, but it is left to the individual as to how this is actually accomplished. More accurate test
equipment will enable a more flexible approach whilst still remaining within the appropriate value, but it
does not automatically exclude "less accurate" test equipment.
For this reason individual test equipment parameters are not specified. However, a test equipment
performance for a specific parameter should be known, and including this value in the specific example
will allow rapid assessment of the suitability for that particular task in relation to the other parameters.
When selecting equipment that is suitable for making a particular measurement some points that should
be taken into account are:
a) the test equipment measurement uncertainty is appropriate to the required uncertainty;
b) equipment resolution is appropriate to its uncertainty;
c) the overall measurement uncertainty is equal to, or better than that required by the appropriate
standard;
d) equipment resolution is at least an order of magnitude better than the limits of measurement
variation;
e) the number of measurements (n) should ideally be large enough so that the measurement (n+1)
varies the mean value by less than the equipment resolution or one tenth of the maximum
acceptable uncertainty stated by the specification.
Caution should be exercised when:
a) the measured parameter varies significantly from one measurement to the next;
b) the measurement system contains loose connections, poor loads, VSWR's or conditions which vary
during the measurement.
Summarising, if the uncertainty (or error bound) of a particular parameter of an item of test equipment is
known, and if its interaction within a test configuration is understood, the overall measurement error can
be predicted by calculation and hence controlled.
Caution should be exercised in using calibration curves or figures. For example a particular manufacturer
states an insertion loss of 6,0 ± 2 dB. The calibration curve states 6,5 dB ± 0,5 dB and the calibration
curve figures are used in the calculation.
Subsequently, the previous three calibration reports (6 months interval) should be viewed which gives
insertion losses as 6,5 dB ± 0,25 dB, 4,9 dB ± 0,25 dB and 7,2 dB ± 0,25 dB respectively. Obviously this
equipment has insufficient stability to allow the uncertainty of ± 0,25 dB to be used.

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As a conclusion, calibration curves should not be used unless they can be supported by historical
evidence of the stability of the device.
This ETR has been produced, (and is to be used in conjunction with the appropriate standard, that
references this ETR), to reconcile not only the foregoing but also the interpretation of the various elements
that are required in assessing measurement uncertainty. This will ensure that there is a clear and
harmonised approach to the assessment of measurement uncertainty.
On a final note it should be remembered that no matter how carefully a measurement is made, if the EUT
is unrepresentative, the result will also be unrepresentative. Generally the EUT is a sample of one from an
undefined population size and is subject to unknown statistical fluctuations.
The definitions, symbols and abbreviations used in this report are described in Clause 3. This was
included to ensure that there shall be no other interpretation of their meaning. Measurement equipment
requirements are detailed in Clause 4.
Clause 5 covers the calculations of measurement uncertainty, particular attention is drawn to
subclause 5.1 which provides a general introduction to the calculation of measurement uncertainty, and
includes details of some of the assumptions made and expansion of some of the definitions. Subclause
5.2 details specific examples, subclause 5.3 discusses noise behaviour in receivers, subclause 5.4
examines uncertainties in third order intermodulation rejection, subclause 5.5 discusses uncertainties in
measuring continuous bit streams, subclause 5.6 discusses uncertainties in measuring messages.
Subclause 5.7 is a detailed example of the calculation of the measurement uncertainty of a transmitter
carrier power measurement.
Clause 6 contains worked examples of transmitter measurement uncertainty calculations. Clause 7
contains worked examples of receiver measurement uncertainty calculations. Clause 8 contains worked
examples of duplex operation measurement uncertainty calculations.
Finally there are four annexes:
- Annex A, contains a table of maximum accumulated measurement uncertainty values;
- Annex B, describes how to interpret the measurement result;
- Annex C, contains a table of values of influence quantities;
- Annex D, contains the bibliography.

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1 Scope
This ETSI Technical Report (ETR) provides a method to be applied to all applicable European
Telecommunication Standards (ETSs) and ETRs, and supports ETR 027 [1]. The following aspects relate
to the measurements:
- the calculation of the total uncertainty for each of the measured parameters;
- recommended maximum acceptable uncertainties for each of the measured parameters;
- a method of applying the uncertainties in the interpretation of the results.
This ETR provides the methods of evaluating and calculating the measurement uncertainties and the
required corrections on measurement conditions and results. These corrections are necessary in order to
remove the errors caused by certain deviations of the test system due to its known characteristics (e.g.
the RF signal path attenuation and mismatch loss, etc.).
2 References
Within this ETR the following references apply:
[1] ETR 027: "Methods of measurement for private mobile radio equipment".
[2] ETS 300 086: "Radio Equipment and Systems (RES); Land mobile service
Technical characteristics and test conditions for radio equipment with an internal
or external RF connector intended primarily for analogue speech".
[3] I-ETS 300 113: "Radio Equipment and Systems (RES); Land mobile service
Technical characteristics and test conditions for non-speech and combined
analogue speech/non-speech equipment with an internal or external antenna
connector intended for the transmission of data".
[4] CEPT Recommendation T/R 24-01: "Specifications for equipments for use in
the Land Mobile Service".
3 Definitions, symbols and abbreviations
3.1 Definitions
For the purpose of this ETR the following definitions apply.
Measurand: a quantity subjected to measurement.
Accuracy of measurement: the closeness of the agreement between the result of a measurement and
the true value of the measurand.
Repeatability of measurements: the closeness of the agreement between the results of successive
measurements of the same measurand carried out subject to all the following conditions:
- the same method of measurement;
- the same observer;
- the same measuring instrument;
- the same location;
- the same conditions of use;
- repetition over a short period of time.

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Reproducibility of measurements: the closeness of agreement between the results of measurements of
the same measurand, where the individual measurements are carried out changing conditions such as:
- method of measurement;
- observer;
- measuring instrument;
- location;
- conditions of use;
- time.
Uncertainty of measurement: an estimate characterising the range of values within which the true value
of a measurand lies.
Part uncertainty: an estimate characterising one of the parts of a combination of individual uncertainties.
(Absolute) error of measurement: the result of a measurement minus the (conventional) true value of
the measurand.
Random error: a component of the error of measurement which, in the course of a number of
measurements of the same measurand, varies in an unpredictable way.
Systematic error: a component of the error of measurement which, in the course of a number of
measurements of the same measurand remains constant or varies in a predictable way.
A systematic error is unchanged when a measurement is repeated under the same conditions, but it may
become evident whenever the test configuration is changed. Thus, before a systematic error can be
determined and afterwards corrected, it should be identified; that is, related to some part of the
measurement apparatus or procedure. Then, a modification of the method or the apparatus may be made
that will reveal the error, so that a correction can be applied. Often, it is not possible to determine a
systematic error precisely. In these cases a systematic uncertainty is estimated.
An example of systematic error is the cable loss which may be measured at the relevant frequencies and
allowed for in the measurements. Thus a signal generator output may be set 1 dB higher than the required
level, if the connecting cable loss is known to be 1 dB.
However, the error in measuring the cable loss should be allowed for.
Correction: the value which, added algebraically to the uncorrected result of a measurement,
compensates for assumed systematic error.
Correction factor: the numerical factor by which the uncorrected result of a measurement is multiplied to
compensate for an assumed systematic error.
Measuring system: a complete set of measuring instruments and other equipment assembled to carry
out a specified measurement task.
Accuracy of a measuring instrument: the ability of a measuring instrument to give indications
approaching the true value of a measurand.
Limits of error of a measuring instrument: the extreme values of an error permitted by specifications,
regulations etc. for a given measuring instrument.
NOTE 1: This term is also known as "tolerance".
Error of a measuring instrument: the indication of a measuring instrument minus the (conventional) true
value.
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Standard deviation of a single measurement in a series of measurements: the parameter
characterising the dispersion of the result obtained in a series of n measurements of the same measured
quantity, given by the formula:
n
xx−
()
∑ i
i=1
σ=
n−
x being the ith result of measurement (i=1,2,3, .,n) and x the arithmetic mean of the n results
i
considered.
Bit error ratio: the ratio of the number of bits in error to the total number of bits.
Standard deviation of the arithmetic mean of a series of measurements: the 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:
σ
σ =
r
n
where σ is an estimate of the standard deviation of a single measurement of the series and n the number
of measurements in the series.
Confidence level: the probability of the accumulated error of a measurement being within the stated
range of uncertainty of measurement.
Range of uncertainty (confidence interval) of measurement: the value expressed by the formula 2kσ
for a single measurement and by 2kσ for the arithmetic mean of a series of measurements. This
r
corresponds to the statistical term "confidence interval".
NOTE 2: In this ETR the range of uncertainty is expressed as ± U .
x
Stochastic (random) variable: a variable whose value is not exactly known, but is characterised by a
distribution or probability function, or a mean value and a standard deviation (e.g. a measurand and the
related measurement uncertainty).
Quantity (measurable): an attribute of a phenomenon or a body which may be distinguished qualitatively
and determined quantitatively.
Influence quantity: a quantity which is not the subject of the measurement but which influences the value
of the quantity to be measured or the indications of the measuring instrument or the value of the material
measure reproducing the quantity.
Influence function: a function defining the influence of the "influence quantity" on the measurand.
Noise gradient of EUT: a function characterising the relationship between the RF input signal level and
the performance of the EUT, e.g., the SINAD of the AF output signal.
3.2 Symbols
k a factor from Student's t distribution
M Mismatch uncertainty
iu
R Reflection coefficient of the generator part of a connection
g
R Reflection coefficient of the load part of the connection
l
σ standard deviation
n
σ the standard deviation of the n'th part uncertainty
σ the standard deviation of the mean value of a series of measurements
r
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σ the standard deviation of the total accumulated error
t
σ if the standard deviation consists of two figures (one for the positive (or upper)
n+
part of the uncertainty and one for the negative (or lower) part the abbreviation
has a sign, e.g. the standard deviation of the 5 part uncertainty is characterised
by two figures: σ and σ
5+ 5-
U the uncertainty figure for the accumulated uncertainty corresponding to a
x
confidence level of x %: U = k x σ
x t
SNR Signal to Noise Ratio per bit
b
SNR * SNR at a specific Bit Error Ratio
b
C cross correlation coefficient
cross
Pe Probability of error n
(n)
Pp Probability of position n
(n)
3.3 Abbreviations
a assumed
AF Audio Frequency
BER Bit Error Ratio
BIPM the International Bureau of Weights and Measures
(Bureau International des Poids et Mesures)
c calculated on the basis of given and measured data
d derived from a measuring equipment specification
EUT Equipment Under Test
FSK Frequency Shift Keying
GMSK Gaussian Minimum Shift Keying
GSM Global System for Mobile telecommunication (Pan European digital
telecommunication system)
m measured
p power level value
r indicates rectangular distribution
RF Radio Frequency
RSS Root-Sum-of-the-Squares
t indicates triangular distribution
u indicates U-distribution
VSWR Voltage Standing Wave Ratio.
4 General requirements
4.1 Test environment
Measuring equipment should not be operated outside the manufacturer's stated temperature and humidity
range.
4.2 Calibration
Measuring instruments and their associated components should be calibrated by an accredited calibration
laboratory.
5 Calculation of measurement uncertainty
5.1 General
The method of calculating the total uncertainty of a measurement is to calculate the standard deviation for
the distribution of the accumulated error. This method is known as the BIPM-method proposed by the
International Bureau of Weight and Measures (IBWM).

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It is assumed, that all errors are stochastic and the total error is Gaussian distributed. This is correct,
when the total error is a combination of many individual errors, where the individual errors are not
necessarily Gaussian distributed. Therefore it is possible to calculate the measurement uncertainty for a
given confidence level. Calculating the standard deviation of the accumulated error is achieved by
combining the standard deviations of the individual errors that contribute to the measurement uncertainty.
Therefore the distribution functions of the individual errors should be known or assumed.
The standard deviation for the total accumulated error distribution corresponds to a confidence level of
68 %. It is then possible by means of Student's t function to calculate the measurement uncertainty for
other confidence levels.
Both the standard deviation and Student's t factor and the confidence level should be stated in the test
report to make it possible for the user of the measured results to calculate other uncertainty figures
corresponding to other confidence levels.
5.1.1 Confidence level
Given that the distribution function of the accumulated error is a Gaussian function, the confidence level
corresponding to the standard deviation is 68 %.
Calculating the measurement uncertainty corresponding to greater confidence levels is done by
multiplying the standard deviation by Student's t factor, e.g. the factor corresponding to 95 % is 1,96, and
the factor corresponding to 99 % is 2,58.
5.1.2 Error distributions and standard deviations
Systematic errors are, unless the actual distribution is known, assumed to have a rectangular distribution,
which means, that the error can be anywhere between the error limits with equal probability. If the limits
are ± a the standard deviation is a/√3 (r).
Random errors, e.g. noise, are normally Gaussian distributed. The Gaussian distribution is characterised
by the standard deviation alone. This is known or calculated by means of repetitive measurements.
Mismatch errors and errors caused by temperature deviations around a mean temperature have a 'U'
shaped distribution, which means that the error is more likely to be near the limits than to be small or zero.
If the limits are ± a the standard deviation is a/√2 (u).
Some errors are triangularly distributed. If the limits are ± a the standard deviation is a/√6 (t).
All the measured results
...