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.

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Status
Published
Publication Date
05-May-2019
Current Stage
PPUB - Publication issued
Completion Date
06-May-2019
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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
IEC 62884-4:2019-05(en-fr)
---------------------- Page: 1 ----------------------
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---------------------- Page: 2 ----------------------
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

Warning! Make sure that you obtained this publication from an authorized distributor.

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® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
---------------------- Page: 3 ----------------------
– 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

---------------------- Page: 4 ----------------------
IEC 62884-4:2019 © IEC 2019 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC, DIELECTRIC AND
ELECTROSTATIC OSCILLATORS –
Part 4: Short-term frequency stability test methods
FOREWORD

1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising

all national electrotechnical committees (IEC National Committees). The object of IEC is to promote

international co-operation on all questions concerning standardization in the electrical and electronic fields. To

this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,

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in the subject dealt with may participate in this preparatory work. International, governmental and non-

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with the International Organization for Standardization (ISO) in accordance with conditions determined by

agreement between the two organizations.

2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international

consensus of opinion on the relevant subjects since each technical committee has representation from all

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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.

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.

---------------------- Page: 5 ----------------------
– 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

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.
---------------------- Page: 6 ----------------------
IEC 62884-4:2019 © IEC 2019 – 5 –
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:
---------------------- Page: 7 ----------------------
– 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;
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.
= = =
---------------------- Page: 8 ----------------------
IEC 62884-4:2019 © IEC 2019 – 7 –
Figure 2 – Phasor diagram after suppression of amplitude noise
( )
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.
---------------------- Page: 9 ----------------------
– 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
Sf

Usually, short-term stability is considered over time intervals of > 0,001 to 1 000 seconds.

t +τ
11 1
y = y(t)dt= ⋅[φt( +τ)−φt()]= ⋅[x(t +τ)−x()t ]
k k k k k
τ 2πFτ τ
φt()
y =
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:
( ) ( )
---------------------- Page: 10 ----------------------
IEC 62884-4:2019 © IEC 2019 – 9 –
d(xt( ))
yt( ) =

The classical variance and the standard deviation at samples of is represented

σ σ M y
2 2
σ ()yy−
∑ i
M −1
i=1
Using the mean value y .
y = y
i=1

The y from small sampling of y is not suitable for the analysis of frequency stability,

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.
( )

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

systematic dead time between measurements;
is the sample time over which measurement is averaged;
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
measurement intervals τ :
M −2
σ (τ,M) (2x−⋅x+x )
y ∑ i++21ii
2⋅(M −⋅2)τ
i=1
---------------------- Page: 11 ----------------------
– 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,

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
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
( )
u = ±

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).
---------------------- Page: 12 ----------------------
IEC 62884-4:2019 © IEC 2019 – 11 –
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

( )

all possible fully overlapping samples at each averaging time . It can be estimated from a

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

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

distiguish between flicker PM noise, which appears with a slope of and white PM, which

( )
---------------------- Page: 13 ----------------------
– 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

( )
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
===
---------------------- Page: 14 ----------------------
IEC 62884-4:2019 © IEC 2019 – 13 –
= 1, 2, … M −1 = averaging factor;
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

telecommunication industry. It is calculated by moving an n-point window (with n = )

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 .

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.
---------------------- Page: 15 ----------------------
– 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 sampl
...

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