IEC 62884-4:2019

Measurement techniques of piezoelectric, dielectric and electrostatic oscillators - Part 4 : Short-term frequency stability test methods

IEC 62884-4:2019 describes the methods for the measurement and evaluation of the short-term frequency stability tests of piezoelectric, dielectric and electrostatic oscillators. Its purpose is to unify the test and evaluation methods for short-term frequency stability.

Techniques de mesure des oscillateurs piézoélectriques, diélectriques et électrostatiques - Partie 4: Méthodes d'essai de stabilité à court-terme de la fréquence

L'IEC 62884-4:2019 décrit les méthodes de mesure et d'évaluation des essais de stabilité à court terme de la fréquence des oscillateurs piézoélectriques, diélectriques et électrostatiques. Son but est d'unifier les méthodes d'essai et d'évaluation de la stabilité à court terme de la fréquence.

General Information

• Status: Published
• Publication Date: 05-May-2019
• ICS: 31.140 - Piezoelectric devices
• Technical Committee: TC 49 - Piezoelectric, dielectric and electrostatic devices and associated materials for frequency control, selection and detection
• Drafting Committee: WG 7 - TC 49/WG 7
• Current Stage: PPUB - Publication issued
• Start Date: 28-May-2019
• Completion Date: 06-May-2019

Overview

IEC 62884-4:2019 is an international standard published by the International Electrotechnical Commission (IEC) focusing on measurement techniques of piezoelectric, dielectric, and electrostatic oscillators. Specifically, Part 4 addresses short-term frequency stability test methods. This standard unifies the procedures and evaluation methods for quantifying how stable the frequency of these oscillators remains over short periods.

The stable operation of oscillators in electronics and precision applications depends heavily on short-term frequency stability. IEC 62884-4:2019 provides a comprehensive framework for the measurement and assessment of short-term frequency stability, thereby enabling manufacturers, designers, and test labs to ensure consistency and reliability in oscillator performance.

Key Topics

• Short-Term Frequency Stability Fundamentals
  The standard explains frequency fluctuations in oscillators as primarily influenced by phase noise and amplitude noise. It details how suppressing amplitude noise with a limiter sharpens frequency stability measurements. The instantaneous frequency is defined as the time derivative of the oscillator's phase, with fractional frequency deviation expressed relative to the nominal frequency.

• Statistical Measures and Variance Analysis
  IEC 62884-4 introduces statistical tools such as:

  • Allan Variance (AVAR) and Allan Deviation (ADEV) – fundamental for analyzing frequency stability over time intervals.
  • Overlapping Allan Variance (OAVAR) and Modified Allan Variance (MVAR) – advanced analyses that give improved confidence in results.
  • Hadamard Variance (HVAR) – for specific noise types and stability analysis.
    These measures provide structured, internationally accepted methods of quantifying noise and stability characteristics in oscillators.

• Measurement Methods
  The document describes five key practical measurement techniques:

  • Method 1: Using two oscillators with the same mean frequency to compare outputs.
  • Method 2: Measuring frequency offset between oscillators.
  • Method 3: Implementing time interval counters for precise time measurements.
  • Method 4: Direct frequency counter methods to measure short-term fluctuations.
  • Method 5: Calculating short-term frequency stability by integrating phase noise spectral data.

• Test Conditions and Precautions
  Guidelines on test setups cover topics like stabilization time, supply and control voltages, and the impact of environmental conditions such as temperature and humidity. These precautions ensure repeatability and accuracy of short-term stability assessments under various operational environments.

Applications

IEC 62884-4:2019 is essential for industries relying on highly accurate frequency sources, including:

• Precision Timing and Synchronization
  Used in telecommunications networks, GPS systems, and digital infrastructure where timing precision affects system integrity.

• Frequency Control Devices Manufacturing
  Assisting manufacturers in producing oscillators that meet application-specific frequency stability specifications.

• Test Laboratories and Quality Assurance
  Providing standardized methods for oscillator testing, ensuring comparability and compliance with international quality standards.

• Research and Development
  Enabling engineers and researchers to analyze noise mechanisms and improve oscillator designs for enhanced performance in electronic devices and sensors.

Related Standards

For a comprehensive understanding and compliance in frequency control and oscillator measurement, IEC 62884-4:2019 relates closely to:

• IEC 62884-1 – Basic measurement methods for piezoelectric, dielectric, and electrostatic oscillators.
• IEC 60679-1 – Generic specification for piezoelectric, dielectric, and electrostatic oscillators.
• IEC 60027 – Letter symbols in electrical technology for consistent notation.
• IEC 60050-561 – International electrotechnical vocabulary for devices used in frequency control.
• ISO 80000-1 – Quantities and units to standardize measurement units and symbols.
• IEC 60469 & IEC 60617 – Terms, definitions, and graphical symbols relevant to electrical diagrams and waveforms.

By applying IEC 62884-4:2019, professionals can ensure adherence to internationally recognized best practices for the short-term frequency stability measurement of oscillators, promoting quality, precision, and compatibility in electronic frequency control components.

---

Keywords: IEC 62884-4, short-term frequency stability, piezoelectric oscillators, dielectric oscillators, electrostatic oscillators, Allan variance, frequency stability test methods, oscillator noise measurement, phase noise, amplitude noise, frequency control standards, measurement techniques.

Standards Content (Sample)

IEC 62884-4 ®
Edition 1.0 2019-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Measurement techniques of piezoelectric, dielectric and electrostatic oscillators –
Part 4: Short-term frequency stability test methods

Techniques de mesure des oscillateurs piézoélectriques, diélectriques
et électrostatiques –
Partie 4: Méthodes d'essai de stabilité à court-terme de la fréquence

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IEC 62884-4 ®
Edition 1.0 2019-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Measurement techniques of piezoelectric, dielectric and electrostatic oscillators –

Part 4: Short-term frequency stability test methods

Techniques de mesure des oscillateurs piézoélectriques, diélectriques

et électrostatiques –
Partie 4: Méthodes d'essai de stabilité à court-terme de la fréquence

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 31.140 ISBN 978-2-8322-6876-6

– 2 – IEC 62884-4:2019 © IEC 2019
CONTENTS
FOREWORD . 3
1 Scope . 5
2 Normative references . 5
3 Terms and definitions, units and symbols . 5
3.1 Terms and definitions . 5
3.2 Units and symbols. 5
4 Short-term frequency stability . 6
5 Allan variance (AVAR) . 9
6 Allan deviation (ADEV), RMS fractional frequency fluctuations . 10
7 Overlapping Allan variance (OAVAR) and overlapping Allan deviation (OADEV) . 11
8 Modified Allan variance (MVAR) and modified Allan deviation (MDEV) . 11
9 Hadamard Variance (HVAR) . 12
10 Time interval error (e ) . 12
(n)
11 Maximum time interval error (e ) . 13
m(n)
12 Measurement of short-term frequency stability . 13
12.1 General . 13
12.2 Method 1: The two oscillators having exactly the same mean frequency . 14
12.3 Method 2: frequency offset measurement . 15
12.4 Method 3: time interval counter . 15
12.5 Method 4: direct frequency counter method . 16
12.6 Method 5: short-term stability computed by integration of phase noise data . 16
12.7 Test conditions and precautions . 17
12.7.1 Considerations for the test setup . 17
12.7.2 Stabilization time . 17
12.7.3 Supply voltage and control voltage . 18
12.7.4 Impact of ambient conditions . 19
Bibliography . 20

Figure 1 – Phasor diagram of carrier and non-correlated amplitude and phase noise . 6
Figure 2 – Phasor diagram after suppression of amplitude noise . 7
Figure 3 – Various noise mechanisms over time . 8
Figure 4 – Chart of Allan deviation (ADEV) as a function of τ . 11
Figure 5 – Test circuit for method 1 . 14
Figure 6 – Test circuit for method 2 . 15
Figure 7 – Time interval counter measurement method . 16
Figure 8 – Impact of a frequency drift to the measured Allan deviation . 18

Table 1 – Relation between the areas of different slopes of phase noise and Allan
deviation . 17

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC, DIELECTRIC AND
ELECTROSTATIC OSCILLATORS –
Part 4: Short-term frequency stability test methods

FOREWORD
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International Standard IEC 62884-4 has been prepared by IEC technical committee 49:
Piezoelectric, dielectric and electrostatic devices and associated materials for frequency
control, selection and detection.
The text of this International Standard is based on the following documents:
CDV Report on voting
49/1277/CDV 49/1292/RVC
Full information on the voting for the approval of this International Standard can be found in
the report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.

– 4 – IEC 62884-4:2019 © IEC 2019
A list of all parts in the IEC 62884 series, published under the general title Measurement
techniques of piezoelectric, dielectric and electrostatic oscillators, can be found on the IEC
website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
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colour printer.
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC, DIELECTRIC AND
ELECTROSTATIC OSCILLATORS –
Part 4: Short-term frequency stability test methods

1 Scope
This part of IEC 62884 describes the methods for the measurement and evaluation of the
short-term frequency stability tests of piezoelectric, dielectric and electrostatic oscillators. Its
purpose is to unify the test and evaluation methods for short-term frequency stability.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their
content constitutes requirements of this document. For dated references, only the edition
cited applies. For undated references, the latest edition of the referenced document (including
any amendments) applies.
IEC 60027 (all parts), Letter symbols to be used in electrical technology
IEC 60050-561, International electrotechnical vocabulary – Part 561: Piezoelectric, dielectric
and electrostatic devices and associated materials for frequency control, selection and
detection. Available at www.electropedia.org
IEC 60469, Transitions, pulses and related waveforms – Terms, definitions and algorithms
IEC 60617, Graphical symbols for diagrams, available at http://std.iec.ch/iec60617
IEC 60679-1, Piezoelectric, dielectric and electrostatic oscillators of assessed qualify – Part 1:
Generic specification
IEC 62884-1, Measurement techniques of piezoelectric, dielectric and electrostatic oscillators
– Part 1: Basic methods for the measurement
ISO 80000-1, Quantities and units – Part 1: General
3 Terms and definitions, units and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60679-1 apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses.
• IEC Electropedia: available at http://www.electropedia.org
• ISO Online browsing platform: available at http://www.iso.org/obp
3.2 Units and symbols
Units, graphical symbols, letter symbols and terminology shall, wherever possible, be taken
from the following standards:
– 6 – IEC 62884-4:2019 © IEC 2019
• IEC 60027;
• IEC 60050-561;
• IEC 60469;
• IEC 60617;
• ISO 80000-1.
4 Short-term frequency stability
The random fluctuations of the frequency of an oscillator over short periods of time
[IEV 561-03-16]. In general, the output voltage of the oscillator is expressed by the following
equation:
vt( )=U+⋅ε t cosφ t=U+⋅ε t cos 2π⋅F⋅t+φt 
( ) ( ) ( ) ( )
00  0 
where
is the nominal output voltage;
U
ε (t) is the amplitude noise;
F  is the average oscillator frequency;
ϕ t is the phase fluctuation.
( )
For the measurement of the short-term frequency stability, the amplitude noise ε(t) is
supressed by a limiter, thus the output voltage of oscillator simplifies as follows:
jtφ( )
vt( ) U⋅cosφ (t) U⋅cos 2π⋅F⋅+t φ(t) Re(U⋅e )
0 00 0

where
Re X means the real part of the complex number X .
( )
This can be presented in a phasor diagram (see Figure 1 below).

Figure 1 – Phasor diagram of carrier and non-correlated amplitude and phase noise
For the measurement of short-term stability, the amplitude noise ε(t) is suppressed by a limiter,
thus the phasor diagram simplifies as shown in Figure 2.
= = =
Figure 2 – Phasor diagram after suppression of amplitude noise
ft
( )
The instantaneous frequency  is the time derivative of the phase function.
φ(t) 2π⋅F⋅+t φt( )
i.e.

1 dtφ( ) 1 dφt( )
f (t)= = F⋅ 1+ ⋅ = F⋅+1 yt( )
( )

22π dt πF dt
0
1 dφt( )
yt( ) ⋅
2πF dt
where
yt is the fractional frequency deviation to the average oscillator frequency F .
( )
The phase and frequency fluctuations can be distinguished according to their appearances
over time as shown in Figure 3.
=
=
– 8 – IEC 62884-4:2019 © IEC 2019

a) White frequency noise (α = 0)

b) Flicker frequency noise (α = −1)

c) Random walk frequency noise (α = −2)

d) Flicker walk frequency noise (wander) (α = −3)
Figure 3 – Various noise mechanisms over time
with α being the exponent of the fractional frequency fluctuation, i.e. the slope in the double-
logarithmic phase noise response
α
Sf
y
Usually, short-term stability is considered over time intervals of > 0,001 to 1 000 seconds.
t +τ
11 1
k
y = y(t)dt= ⋅[φt( +τ)−φt()]= ⋅[x(t +τ)−x()t ]
k k k k k
∫
t
τ 2πFτ τ
k
φt()
k
y =
k
2πF
xt is the phase-time fluctuation, that is, the random phase fluctuation converted into time
( )
and measured in seconds.
The relation of xt and y t is represented as follows:
( ) ( )
d(xt( ))
yt( ) =
dt
The classical variance and the standard deviation at samples of is represented
σ σ M y
i
as
M
2 2
σ ()yy−
∑ i
M −1
i=1
Using the mean value y .
M
y = y
∑
i
M
i=1
The y from small sampling of y is not suitable for the analysis of frequency stability,
i
because of lack of convergence for some common types of clock noise. Their value depends
on the number of samples taken.
5 Allan variance (AVAR)
The Allan variance στ is the most common measure for time domain stability.
( )
y
It is an unbiased estimate of the preferred definition in the time domain of the short-term
stability characteristics of the oscillator output frequency:
M −1
(yy− )
k+1 k
στ =
( )
y ∑
M −12
k=1
where
y  are the average fractional frequency fluctuations obtained sequentially, with no
k
systematic dead time between measurements;
is the sample time over which measurement is averaged;
τ
M is the number of measurements.
The confidence on the estimate improves as M increases.
AVAR can be alternatively derived from phase measurement samples x taken in
i
measurement intervals τ :
M −2
σ (τ,M) (2x−⋅x+x )
y ∑ i++21ii
2⋅(M −⋅2)τ
i=1
=
=
– 10 – IEC 62884-4:2019 © IEC 2019
6 Allan deviation (ADEV), RMS fractional frequency fluctuations
In detail specifications, instead of the variance AVAR, usually its square root is used,
σ
which is called Allan deviation (ADEV). It has the same order of magnitude as the relative
frequency fluctuations that are to be characterized.
It is a measure in the time domain of the short-term frequency stability of an oscillator, based
on the statistical properties of a number of frequency measurements, each representing an
average of the frequency over the specified sampling interval τ .
M −1
σ ()τ,M (y−y )
y ∑ i+1 i
2⋅−(M 1)
i=1
ADEV can be alternatively derived from phase measurement samples taken in
x
i
measurement intervals τ .
M −2
σ ()τ,M (x−⋅2 x+x )
y ∑ i++21ii
2⋅(M −⋅2)τ
i=1
NOTE In IEC 60679-1:1997, 2.2.24, ADEV was called RMS fractional frequency fluctuation.
M shall be sufficiently large in order to achieve a satisfactory confidence interval. A simple
approximation for the confidence interval u for ±1 σ error (with no consideration of the noise
type) is
στ
( )
y
u = ±
M
The confidence interval u is usually depicted as error bars in the ADEV chart. If not, the
number of samples M should be indicated in the test report.
ADEV is either defined for certain discrete values of τ or it is displayed graphically as a
function of the sample interval τ (Sigma-Tau diagram) with the confidence interval for each
value shown as error-bars. This presentation allows for the identification of the various
underlying noise types (see Figure 4).
=
=
Figure 4 – Chart of Allan deviation (ADEV) as a function of τ
7 Overlapping Allan variance (OAVAR) and overlapping Allan deviation
(OADEV)
A form of the normal Allan variance στ , that makes maximum use of a data set by forming
( )
y
all possible fully overlapping samples at each averaging time . It can be estimated from a
τ
set of M frequency measurements for averaging time τ mt⋅ , where m is the averaging
factor and t is the basic measurement interval.
Mm−+21 jm+−1


στ( ) (y−y )
y ∑∑ im+ i
2mM⋅ −+21m 
( )
j 1 ij

Derived from phase data:
Mm−2
στ x−⋅2 x+x
( ) ( )
y ∑ i++2m im i
22⋅−Mm ⋅τ
( )
i=1
Usually the square root σ (τ ) of these expressions is used, which is called overlapping Allan
y
deviation (OADEV).
The Overlapping Allan Deviation OADEV is the most widely used general purpose measure of
frequency short-term stability (even if it is often erroneously named Allan deviation).
The confidence interval of OADEV is better than that of a normal ADEV.
8 Modified Allan variance (MVAR) and modified Allan deviation (MDEV)
The modified Allan variance (MVAR) and the modified Allan deviation (MDEV) allow to
−1
distiguish between flicker PM noise, which appears with a slope of and white PM, which
τ
( )
=
==
=
=
– 12 – IEC 62884-4:2019 © IEC 2019

−
has a slope of τ in the MDEV-chart. It is estimated from a set of M frequency


measurements for averaging time ττm⋅ , where m is the averaging factor and τ is the
0 0
basic measurement interval.
jm+−1
M −32m+  im+−1 

Mod _στ  y−y 
( ) ( )
y ∑ ∑∑ km+ k
 
2mM⋅ −+32m 
( )
j 1 i j ki
 
Derived from phase data:
Mm−+31 jm+−1


Mod _στ( ) (x−⋅2 x+x )
y ∑∑ i++2m im i
2mM⋅ − 31m +⋅τ 
( )
i 1 ij

The results are usually expressed by their square roots Mod σ t , the modified Allan
( )
y
deviation (MDEV).
For m = 1 , the modified Allan variance (deviation) is equal to the normal Allan variance
(deviation).
The estimate for the confidence interval of MDEV is the same as that of ADEV.
9 Hadamard Variance (HVAR)
The Hadamard variance (HVAR) is a 3-sample variance version of the Allan variance. It
examines the second difference of the fractional frequencies.
M −2
στ( ) (y−+2y y )
H ∑ i++21ii
62⋅−M
( )
i=1
Derived from phase data:
M −3
στ x− 33x+ x−x
( ) ( )
H ∑ i++3 i 21i+ i
63⋅(M −⋅) τ
j=1
The Hadamard variance (HVAR) rejects the linear frequency drift.
10 Time interval error (e )
(n)
The time interval error is a common stability statistic used in the telecommunications industry.
It is defined by
Mn−
e x−x
( )
∑
()n in+ i
M − n
i=1
where
=
=
=
==
=
===
=
=
= 1, 2, … M −1 = averaging factor;
n
M = number of phase data points.
In the case of no frequency drift, e is approximately equal to the Allan deviation (ADEV)
(n)
multiplied by the averaging time.
11 Maximum time interval error (e )
m(n)
The maximum time interval error is a commonly used measure of clock error in the
τ
telecommunication industry. It is calculated by moving an n-point window (with n = )
τ
through the phase (time error) data and finding the difference between the maximum and the
minimum values at each window position. The maximum time interval error is the overall
maximum of this time interval error over the entire data set.

e MAX MAX x−MIN x
( ) ( )
mn() i i
1≤k≤(M −n) k≤≤i (k+n) k≤≤i (k+n)

where
n = 1, 2, … M −1 = averaging factor;
k = 1 … ( M − n) = index of the n-point window, that moves through the N phase data
points X .
i
The maximum time interval error is a measure of the peak time deviation of a clock and is
therefore very sensitive to single extreme values, transients or outliers.
12 Measurement of short-term frequency stability
12.1 General
The test and measurement procedures shall be carried out in accordance with the relevant
detail specification.
Where any discrepancies occur for any reason, documents shall rank in the following order of
precedence:
– detail specification;
– sectional specification;
– generic specification;
– any other international documents (for example of the IEC) to which reference is made.
The same order of precedence shall apply to equivalent national documents.
In principle, time domain stability measurements are made with respect to a reference source
having much better stability than the unit under test.
In general practice, however, comparisons are commonly made between two oscillators of
similar design, and it is usually assumed that the probability densities and distribution
functions of their random noise processes are nearly the same. Since the noise processes
combine on a power basis, the fractional frequency fluctuations between the two similar
oscillators shall be divided by 2 to arrive at an estimate of the fluctuation due to one of the
oscillators alone.
=
– 14 – IEC 62884-4:2019 © IEC 2019
This is reflected in the formulae derived for each of the two methods.
12.2 Method 1: The two oscillators having exactly the same mean frequency
The two oscillators should be connected as shown in Figure 5

NOTE 1 Phase comparators are often sensitive to both phase and amplitude deviations. In order to minimize
sensitivity to amplitude, it is normal practice to use a double-balanced mixer as a quadrature detector.
NOTE 2 If the mean frequency is not exactly the same, both oscillators can be locked to each other by a PLL.
NOTE 3 The loop time constant τ limits the maximum evaluable τ of ADEV. ττ> 10 ⋅ .
loop loop ADEVmax
Figure 5 – Test circuit for method 1
In the case of method 1, the phase comparator produces an analogue signal that is directly
proportional to the instantaneous phase fluctuations between the two oscillator signals (for
Fourier frequencies below the cut-off of the low-pass filter). This signal may be examined by
analogue methods (such as continuous strip chart recorder, RMS voltmeter or spectrum
analyzer), or it can be examined by time domain methods using a sampling type A/D
converter with a controlled sample averaging time, and the repetitive measurements of the
samples are stored for analysis by a computer. Using this method, there is no dead time
introduced in the measurement system, and the RMS fractional frequency fluctuation is:
M −1
2
ΔF 11

(τ) φt(+ 2τ)(−φt+τ)−φt(+τ)(−φt )
[ ] [ ]
RMS ∑ k k kk

F 2πFτ 2(M −1)
0 0 
k=
where
M is the number of repetitive measurements;
τ  is the sample averaging time.
If, in fact, the reference oscillator used has much better stability than the unit under test, then
all of the frequency fluctuations can be attributed to the unit under test and the equation
above is multiplied by √2.
=
12.3 Method 2: frequency offset measurement
The two oscillators being compared are usually made to be essentially identical, except that
one of them is adjusted to a slightly different frequency, commonly somewhere in the range
from 100 Hz to 10 kHz. It is assumed that the small difference in oscillator adjustment will not
significantly influence the noise characteristic of the oscillators.
The two oscillators shall be connected as shown in Figure 6.

Position X or Y may be used to obtain the Allan variance and deviation. X allows determination of the standard
deviation as well
Figure 6 – Test circuit for method 2
The specified number of measurements M of the period of the beat frequency is made using
the specified averaging time ( should be an integral number of periods of the beat
τ τ
frequency). The interval between successive measurements T will usually be at least one
period of the beat frequency longer than the sample averaging time τ and may be two or
more periods greater depending upon the beat frequency and the recycling time of the
counter data acquisition system.
By this method the resolution is increased by the factor f /f .
osc beat
12.4 Method 3: time interval counter
Because time interval measurements directly at the oscillator frequency causes frequent
phase spillovers, in this measurement method the frequency of both oscillators is divided
−6
down to a very low frequency, usually to 1 Hz (1 pps). For a frequency difference of 1 × 10 ,
the phase spillover time extends to 5,8 days.

– 16 – IEC 62884-4:2019 © IEC 2019
Figure 7 shows the setup principle:

Figure 7 – Time interval counter measurement method
This method allows for the evaluation of the short-term stability only for longer than τ > 1 s.
12.5 Method 4: direct frequency counter method
Deriving short-term frequency stability data from the direct recording of a series of frequency
readings from a frequency counter leads to systematic errors, which may result in severely
erroneous results. The major causes for this are the following:
a) the impact of the counter dead time due to the data acquisition process and – if remotely
controlled – of the data transfer time through the computer interface. The error introduced
by the counter acquisition time can be considered by introducing a correction function
B ( τµ⋅ ), which was derived and tabulated by Barnes;
b) the impact of the interpolation techniques used in modern frequency counters. Owing to
this technique, the displayed frequencies are already a result of statistically weighted
averages.
Therefore, this method shall not be used without consideration of potential underlying
systematic errors.
12.6 Method 5: short-term stability computed by integration of phase noise data
Short-term stability can be computed from phase noise test data Sf by numerical
( )
y
integration according to the following equation:
f
h
sin πτf
( )
σ ()τ 2⋅ S (f) df
y y
∫
πτf
( )
f
L
The lower integration limit f is determined by the maximum τ value, and the upper
L
integration limit f is determined by the minimum τ value to be computed.
h
The relation between the areas of different slope of the phase noise responses Lf , Sf
( ) ( )
y
and the Allan deviation σ τ is summarized in Table 1.
( )
y
=
Table 1 – Relation between the areas of different slopes of
phase noise and Allan deviation
L(f) S (f) σ (τ)
y y
−4 −2 0,5
Random walk frequency noise f f
τ
−3 −1
Flicker frequency noise f f
τ
−2 0 −0,5
White frequency noise f f τ
−1 1 −1
Flicker phase noise f f τ
0 2
−1
White phase noise f f
τ
The computation of ADEV for longer τ values requires phase noise data from very close to
carrier to achieve reasonably accurate results, e.g. for valuable results at > 0,1 s, the
τ
Sf( ) data shall include a range a frequency range down to f << 1 Hz.
y
12.7 Test conditions and precautions
12.7.1 Considerations for the test setup
The following precautions shall be taken to avoid interferences and trigger errors.
– Avoid ground loops in the test setup.
– Use phase-stable cabling.
– The measured signals shall have fast rise and decay time with low added jitter and
hysteresis by the square-wave generation.
Prior to the computational analysis, the data set should be reviewed for consistency. Outliers
– i.e. phase or frequency jumps – should be identified and removed, if it is certain that these
are caused by external influences and do not originate from oscillators.
12.7.2 Stabilization time
Before starting the data acquisition, the oscillators shall be continuously operating over a
longer stabilization time. Oven-controlled crystal oscillators (OCXO) require a longer
stabilization time than the other oscillator types (SPXO, VCXO, TCXO, etc.).
The minimum stabilization time (besides the warm-up time for OCXO) can be estimated from
the targeted maximum τ , which should be characterized. The slope of the remaining
frequency drift of oscillators under test shall be small enough to have a negligible impact on
the short-term stability measure σ τ , otherwise the ADEV of oscillators under test is to be
( )
y
computed by
2 2
σ τ στ−στ
( ) ( ) ( )
y yy
osc meas D
where
στ is the Allan variance caused by the frequency drift.
( )
y
D
Figure 8 shows the Allan deviation (ADEV) στ contributed by a frequency drift (in ppb
( )
n
D
−9
[1 × 10 ] per hour) of oscillators under test.
=
– 18 – IEC 62884-4:2019 © IEC 2019

Figure 8 – Impact of a frequency drift to the measured Allan deviation
−9
If after stabilization, the oscillator under test has a remaining frequency drift of 4 × 10 /h, this
−12
contributes an error of 8·10 to the Allan deviation at τ = 10 s. Assuming that the fully
−12
stabilized oscillator would have σ (τ ) = 5·10 , the measurement would yield a value of
y
2 2 −−12 12
στ 5+⋅8 10 9,43⋅10
( )
y
meas
−9
If the stabilization time is increased until a drift of 1 × 10 /h is reached, the measurement
−12
would yield a value of σ τ of 5,38·10 , which may be close enough to the real value.
( )
y
If σ τ is determined with a maximum relative error of ± %, then the allowed ADEV of the
( ) ε
y
frequency drift στ( ) shall be
n
ε
σ τ ≤⋅στ
( ) ( )
Dy
If the impact of the frequency drift is too strong, the use of the Hadamard variance instead of
ADEV is recommended.
12.7.3 Supply voltage and control voltage
The power supply unit for the oscillators under test shall provide a low-noise DC voltage,
which does not deteriorate the short-term stability.
Especial attention has to be given that the frequency control voltage (if present) source has
no impact on the short-term stability as well.
Batteries are a preferred solution for both cases.
= =
If two oscillators are measured against each other, the power supply of both units shall be
sufficiently decoupled to avoid any injection locking. It is recommended to use two separate
power supply units.
12.7.4 Impact of ambient conditions
The ambient temperature shall be as stable as possible. Thermal isolation against the
environment and airflow is highly recommended.
Acoustic noise and vibrations shall be strictly avoided.
Electromagnetic shielding of the oscillators under test may be necessary if the
electromagnetic sensitivity of the devices is higher. Also, magnetic fields can have an impact.

– 20 – IEC 62884-4:2019 © IEC 2019
Bibliography
Rubiola, E., Phase Noise and Frequency Stability in Oscillators, Cambridge University Press,
(Nov. 2008)
Allan, D.W., Statistics of Atomic Frequency Standards; Proc. IEEE, Vo.54, (Feb.1966), pp.
221-230
IEC 60068-1, Environmental testing – Part 1: General and guidance
Sullivan, D.B., Allan, D.W., Howe, D.A., Walls, F.I. (Editors): Characterization of Clocks and
Oscillators; NIST Technical Note 1337, (March 1990)
Riley, W., Stable32 Frequency Stability Analysis – User Manual, Version 1.3, Hamilton
Technical Services, Beaufort (USA)
Barnes, J.A., Tables of Bias Functions B1 and B2 for Variances Based on Finite Samples of
Processes with Power Law Spectral Densities; NBS Technical Note 375, (Jan. 1969)
Riley, W.J., Handbook of Frequency Stability Analysis; NIST Special Publication 1065, (July
2008)
Vig, J.R., Quartz Crystal Resonators and Oscillators For Frequency Control and Timing
Applications – A Tutorial, US Army Communications-Electronics Research, Development &
Engineering Center Ft, Monmouth/USA, (Jan. 2004)

___________
– 22 – IEC 62884-4:2019 © IEC 2019
SOMMAIRE
AVANT-PROPOS . 23
1 Domaine d'application . 25
2 Références normatives . 25
3 Termes, définitions, unités et symboles . 25
3.1 Termes et définitions . 25
3.2 Unités et symboles. 26
4 Stabilité à court-terme de la fréquence . 26
5 Variance d'Allan (AVAR) . 29
6 Ecart-type d'Allan (ADEV), fluctuations relatives efficaces de fréquence . 30
7 Variance d'Allan avec recouvrement (OAVAR: Overlapping Allan Variance) et
écart-type d'Allan avec recouvrement (OADEV: Overlapping Allan Deviation) . 31
8 Variance d'Allan modifiée (MVAR: Modified Allan Variance) et écart-type d'Allan
modifié (MDEV: Modified Allan Deviation) . 32
9 Variance d'Hadamard (HVAR) . 32
10 Erreur d'intervalle de temps (e ) . 32
(n)
11 Erreur d'intervalle de temps maximale (e ) . 33
m(n)
12 Mesure de la stabilité à court-terme de la fréquence . 33
12.1 Généralités . 33
12.2 Méthode 1: deux oscillateurs ayant exactement la même fréquence moyenne . 34
12.3 Méthode 2: mesure du décalage de la fréquence . 35
12.4 Méthode 3: compteur d'intervalle de temps . 35
12.5 Méthode 4: méthode du compteur de fréquence directe . 36
12.6 Méthode 5: stabilité à court terme calculée par intégration des données de
bruit de phase . 36
12.7 Conditions et précautions d'essai . 37
12.7.1 Considérations sur le montage d’essai . 37
12.7.2 Temps de stabilisation . 37
12.7.3 Tension d'alimentation et tension de commande . 38
12.7.4 Effet des conditions ambiantes . 39
Bibliographie . 40

Figure 1 – Diagramme de phaseur d'une porteuse et de l'amplitude et de la phase non
corrélés du bruit . 26
Figure 2 – Diagramme de phaseur après suppression de l'amplitude du bruit . 27
Figure 3 – Différents mécanismes de bruit en fonction du temps . 28
Figure 4 – Diagramme des écarts-types d'Allan (ADEV) en fonction de τ . 31
Figure 5 – Circuit d'essai pour la méthode 1 . 34
Figure 6 – Circuit d'essai pour la méthode 2 . 35
Figure 7 – Méthode de mesure du compteur d'intervalle de temps . 36
Figure 8 – Effet d'une dérive de fréquence sur l'écart-type d'Allan mesuré . 38

Tableau 1– Relation entre les régions dont les pentes du bruit de phase et de l'écart-
type d'Allan sont différentes . 37

COMMISSION ÉLECTROTECHNIQUE INTERNATIONALE
____________
TECHNIQUES DE MESURE DES OSCILLATEURS PIÉZOÉLECTRIQUES,
DIÉLECTRIQUES ET ÉLECTROSTATIQUES –

Partie 4: Méthodes d'essai de stabilité à court-terme de la fréquence

AVANT-PROPOS
1) La Commission Electrotechnique Internationale (IEC) est une organisation mondiale de normalisation
composée de l'ensemble des comités électrotechniques nationaux (Comités nationaux de l'IEC). L’IEC a pour
objet de favoriser la coopération internationale pour toutes les questions de normalisation dans les domaines
de l'
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