IEC 62884-2:2017

Measurement techniques of piezoelectric, dielectric and electrostatic oscillators - Part 2: Phase jitter measurement method

IEC 62884-2:2017 specifies the methods for the measurement and evaluation of the phase jitter measurement of piezoelectric, dielectric and electrostatic oscillators, including dielectric resonator oscillators (DROs) and oscillators using a thin-film bulk acoustic resonator (FBAR) (hereinafter referred to as an "Oscillator") and gives guidance for phase jitter that allows the accurate measurement of RMS jitter.
In the measurement method, phase noise measurement equipment or a phase noise measurement system is used.
NOTE Dielectric resonator oscillators (DROs) and oscillators using FBAR are under consideration.

Techniques de mesure des oscillateurs piézoélectriques, diélectriques et électrostatiques - Partie 2 : Méthode de mesure de la gigue de phase

L'IEC 62884-2:2017 spécifie les méthodes de mesure et d'évaluation du mesurage de la gigue de phase des oscillateurs piézoélectriques, diélectriques et électrostatiques, y compris les oscillateurs à résonateur diélectrique (DRO - dielectric resonator oscillators) et les oscillateurs utilisant un résonateur à ondes acoustiques de volume à couches fines (FBAR - film bulk acoustic resonator) (appelés ici « oscillateur ») et donne des recommandations relatives à la gigue de phase permettant de mesurer avec exactitude la gigue efficace.
Dans la méthode de mesure, un matériel ou système de mesure du bruit de phase est utilisé.
NOTE Les oscillateurs à résonateur diélectrique (DRO - dielectric resonator oscillator) et les oscillateurs utilisant un FBAR sont à l'étude.

General Information

• Status: Published
• Publication Date: 29-Aug-2017
• 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: 29-Sep-2017
• Completion Date: 30-Aug-2017

Overview

IEC 62884-2:2017 - Measurement techniques of piezoelectric, dielectric and electrostatic oscillators: Part 2: Phase jitter measurement method - defines standard methods to measure and evaluate phase jitter of oscillators (including crystal, dielectric resonator oscillators (DROs) and FBAR-based oscillators). The standard prescribes using phase noise measurement equipment or a phase-noise measurement system and gives guidance to obtain accurate RMS jitter values and other jitter metrics.

Key topics

• Scope and targets
  • Measurement procedures specifically for piezoelectric, dielectric and electrostatic oscillators, with guidance for DROs and thin-film bulk acoustic resonator (FBAR) oscillators.
• Measurement domains
  • Procedures for measuring phase jitter in the time domain, data domain, and frequency domain (phase-noise-based methods).
• Equipment and setup
  • Use of phase noise analyzers, sampling oscilloscopes, and jitter/wander analysers (e.g., block diagrams referenced to ITU-T practices).
  • Requirements on input/output impedances, output waveform, output voltage, and jitter floor of measurement systems.
• Test procedures and environment
  • Pre-test setup and configuration, measurement under reference temperature, temperature-characteristics testing, measurement under vibration, impact, and accelerated ageing.
• Calculation and analysis
  • Normative Annex A: calculation methods linking phase noise (SSB phase noise) to phase jitter metrics - RMS jitter, peak-to-peak, random vs deterministic jitter, and total jitter.
• Measurement integrity
  • Guidance on test fixtures, cables, instruments, error sources, and factors affecting measurement uncertainty.
• Document structure
  • Normative references and terminology aligned with related IEC and ISO vocabularies.

Applications

IEC 62884-2:2017 is useful for:

• Oscillator manufacturers validating phase jitter performance for product datasheets and customer delivery.
• Test laboratories standardizing measurement procedures and reporting reproducible RMS jitter and phase-noise-derived metrics.
• RF and system engineers designing communications, satellite, automotive, EV control and timing systems where low jitter/phase noise is critical.
• Quality and compliance teams performing environmental and ageing tests (temperature, vibration, impact, accelerated ageing) to assess long-term oscillator stability.

Related standards

• IEC 62884-1:2017 - Basic measurement methods for oscillators
• IEC 60679-1:2017 - Generic specifications for oscillators of assessed quality
• IEC 60027, IEC 60050-561, IEC 60469, ISO 80000-1 - referenced terminology and units

Keywords: IEC 62884-2:2017, phase jitter measurement, phase noise, oscillator testing, DRO, FBAR, RMS jitter, jitter measurement methods.

Standards Content (Sample)

IEC 62884-2 ®
Edition 1.0 2017-08
INTERNATIONAL
STANDARD
colour
inside
Measurement techniques of piezoelectric, dielectric and electrostatic
oscillators –
Part 2: Phase jitter measurement method

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
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IEC 62884-2 ®
Edition 1.0 2017-08
INTERNATIONAL
STANDARD
colour
inside
Measurement techniques of piezoelectric, dielectric and electrostatic

oscillators –
Part 2: Phase jitter measurement method

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 31.140 ISBN 978-2-8322-4762-4

– 2 – IEC 62884-2:2017 © IEC 2017
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Test and measurement procedures . 8
4.1 General . 8
4.2 Test methods of phase jitter . 8
4.2.1 General . 8
4.2.2 Measurement in the time domain . 8
4.2.3 Measurement in the data domain . 9
4.2.4 Measurement in the frequency domain . 9
4.3 Input and output impedances of the measurement system . 13
4.4 Measurement equipment . 13
4.4.1 General . 13
4.4.2 Jitter floor . 13
4.4.3 Output wave form . 13
4.4.4 Output voltage . 14
4.5 Test fixture. 14
4.6 Cable, tools and instruments, and so on . 14
5 Measurement and the measurement environment . 14
5.1 Set-up before taking measurements . 14
5.2 Points to be considered and noted at the time of measurement . 14
5.3 Treatment after the measurement . 14
6 Measurement . 15
6.1 Reference temperature . 15
6.2 Measurement of temperature characteristics . 15
6.3 Measurement under vibration . 15
6.4 Measurement at the time of impact . 15
6.5 Measurement in accelerated ageing . 15
7 Other points to be noted . 15
8 Miscellaneous . 15
Annex A (normative)  Calculation method for the amount of phase jitter . 16
A.1 General . 16
A.2 Explanation . 16
A.3 Relations between phase noise and phase jitter . 16
A.4 Commentary on theoretical positioning of phase jitter . 18
A.5 Description . 18
A.5.1 General . 18
A.5.2 RMS jitter . 19
A.5.3 Peak-to-peak jitter . 19
A.5.4 Random jitter . 20
A.5.5 Deterministic jitter . 20
A.5.6 Period (periodic) jitter . 20
A.5.7 Data-dependent jitter . 20
A.5.8 Total jitter . 21

A.6 Points to be considered for measurement . 21
A.6.1 Measurement equipment . 21
A.6.2 Factors of measurement errors . 22
Bibliography . 24

Figure 1 – Phase jitter measurement with sampling oscilloscope . 9
Figure 2 – Block diagram of a jitter and wander analyser according to ITU-T O.172 . 11
Figure 3 – Equivalent block diagram . 13
Figure A.1 – Concept diagram of SSB phase noise . 18
Figure A.2 – Voltage versus time . 19
Figure A.3 – Explanatory diagram of the amount of jitter applied to RMS jitter . 21
Figure A.4 – Explanatory diagrams of random jitter, deterministic jitter, and total jitter . 22

Table 1 – Fourier frequency range for phase noise test . 10
Table 2 – Standard bit rates for various applications . 12

– 4 – IEC 62884-2:2017 © IEC 2017
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC,
DIELECTRIC AND ELECTROSTATIC OSCILLATORS –

Part 2: Phase jitter measurement method

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 62884-2 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
49/1212/CDV 49/1243/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.

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.
A bilingual version of this publication may be issued at a later date.

IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – IEC 62884-2:2017 © IEC 2017
INTRODUCTION
A crystal oscillator as a highly efficient and highly precise source of a frequency oscillation is
widely used for fields such as the electronic equipment, communication equipment,
measurement equipment and a clock. Also recently, digitalization of these equipments is
advancing rapidly. In this situation, the frequency of crystal oscillator requires high precision
and high stability and reduction of noise with oscillating phenomenon. A phase jitter is one of
the noise characteristic in oscillation characteristic and precise measurement which is needed
when shipping a component to a customer.
For advance application in electronic information and communication technology,
(e.g. advanced satellite communications, control circuits for electric vehicle (EV)), necessity
arises for the measurement method for common guidelines of phase jitter. In these days,
measurement method of phase jitter also becomes more important from the electromagnetic
influence (EMI) point of view.
This document has been restructured from IEC 60679-1:2007 (third edition) and
IEC 60679-6:2011 (first edition). The test methods for oscillators have been separated from
IEC 60679-6:2011 into IEC 62884 (all parts). This document covers the phase jitter
measurement.
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC,
DIELECTRIC AND ELECTROSTATIC OSCILLATORS –

Part 2: Phase jitter measurement method

1 Scope
This part of IEC 62884 specifies the methods for the measurement and evaluation of the
phase jitter measurement of piezoelectric, dielectric and electrostatic oscillators, including
dielectric resonator oscillators (DROs) and oscillators using a thin-film bulk acoustic resonator
(FBAR) (hereinafter referred to as an "Oscillator") and gives guidance for phase jitter that
allows the accurate measurement of RMS jitter.
In the measurement method, phase noise measurement equipment or a phase noise
measurement system is used.
NOTE Dielectric resonator oscillators (DROs) and oscillators using FBAR are under consideration.
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
IEC 60679-1:2017, Piezoelectric, dielectric and electrostatic oscillators of assessed quality –
Part 1: Generic specification
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 62884-1:2017, 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
For the purposes of this document, the terms and definitions given in IEC 60027 (all parts),
IEC 60050-561, IEC 60469, IEC 60617, IEC 60679-1 and ISO 80000-1 apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/

– 8 – IEC 62884-2:2017 © IEC 2017
• ISO Online browsing platform: available at http://www.iso.org/obp
4 Test and measurement procedures
4.1 General
The test and measurement procedures are given in Clause 4 of IEC 62884-1:2017 and shall
be applied as indicated in 4.2 to Clause 8.
4.2 Test methods of phase jitter
4.2.1 General
As the measurement method, the phase noise measurement equipment (system) or the
specially designed phase jitter measurement equipment shall be used.
Three basic methods are described:
a) measurement in the time domain by use of a digital real-time or sampling oscilloscope;
b) measurement in the data domain (BER test set);
c) measurement in the frequency domain using
1) a phase noise test set, or
2) a jitter and wander test set.
Method c) 1) using a phase noise test set is the recommended measurement method because
it allows sufficient accuracy for arbitrary oscillator output frequencies.
– In the measurement of phase jitter and wander of oscillator circuits, attention should be
paid to relative measurement reproducibility.
– A user and a manufacturer should deepen understanding through discussion about
relative measurement reproducibility.
– Measurement equipment (including software program) should be made clear between a
manufacturer and a user through a contract.
– When phase jitter and wander is calculated from phase noise, the range of frequency
deviation should be made clear between a user and a manufacturer through a contract.
4.2.2 Measurement in the time domain
Digital real-time or sampling oscilloscopes with wide bandwidth, fast sampling rates, and large
data memories are commercially available (see Figure 1), in some cases with special jitter
evaluation software.
Sampling
Delay line
scope
スコープ
Trigger
Input
Power
Oscillator
splitter
IEC
Figure 1 – Phase jitter measurement with sampling oscilloscope
The time variation of the edges of the clock signal relative to the trigger edge is displayed and
stored over a large number (typically thousands) of cycles. Instrument software allows the
determination of the peak-to-peak jitter value and a statistical evaluation of its distribution.
The sampling oscilloscope method does not allow an accurate evaluation of the spectral
content of the jitter. Also, jitter larger than one unit interval (UI) cannot be distinguished.
The measured jitter value is worse than the jitter of the device under test due to the internal
jitter of the instrument’s clock.
2 2
J = (J ) − (J )
DUT meas int
where
J is the measured jitter;
DUT
J is the jitter of the device under test;
meas
J is the internal jitter of the instrument’s clock.
int
High stability/low noise Oscillator exhibits a significantly lower jitter than the instrument’s
clock jitter and trigger stability. Therefore, this technology is currently not suitable for accurate
jitter measurement of such Oscillator.
4.2.3 Measurement in the data domain
Bit-error rate (BER) test sets are used for measuring bit-error rate to characterise the overall
system performance of a communication subsystem. It is difficult to deduct the contribution of
the Oscillator jitter to the system BER. This method also does not yield quantitative jitter
performance values for the Oscillator.
4.2.4 Measurement in the frequency domain
4.2.4.1 Methods of phase noise test set
Phase jitter can be tested in the frequency domain using the well-established phase noise test
method with a phase locked loop as described in 4.5.25 of IEC 62884-1:2017.
The range of detuned frequency shall be determined by contracts between customers and
suppliers after discussion between them. The formula for calculating the RMS jitter from a
phase noise is based on the calculation method for the amount of phase jitter shown in
Annex A.
– 10 – IEC 62884-2:2017 © IEC 2017
For given SDH/SONET applications, the Fourier frequency range (f . f ) may be
min max
selected as described in 3.2.53 of IEC 60679-1:2017. If not specified in the relevant data
sheet, the recommended Fourier frequency range is as given by f to f in Table 1.
3 4
Table 1 – Fourier frequency range for phase noise test
Oscillator output frequency f = f f = f
f
0 min 4 max
1 MHz to < 10 MHz 10 Hz 10 kHz 100 kHz
10 MHz to < 50 MHz 20 Hz 20 kHz 500 kHz
50 MHz to < 200 MHz 100 Hz 50 kHz 1,5 MHz
200 MHz to < 1 000 MHz 1,0 kHz 200 kHz 5,0 MHz
1 000 MHz to < 5 000 MHz 5,0 kHz 500 kHz 15 MHz
≥ 5 000 MHz 20 kHz 2 MHz 80 MHz

From Table 1, it can be seen that the most stringent requirement applies over the range f to
f .
Jitter performance over a frequency-band other than f to f may also be defined.
3 4
To compute the phase jitter, the phase noise data L(f) have to be integrated in the considered
frequency ranges and evaluated as follows.
Compute the spectral density of phase fluctuations S (f) from the single-sideband phase noise
φ
plot 10 log L (f):
S( f)= 2L( f)
φ
Integrate S (f) over the specified Fourier frequency range f to f to get the mean squared
φ min max
phase jitter in that bandwidth:
f
max
( ) ( )
∆ϕ f = S f df
ϕ
∫
f
min
The mean square phase jitter can be approximated by stepwise integration over the specified
Fourier frequency range f to f segmented by n, for example:
min max
∆φ( f) ≈ S( f)∆f
∑ φ i i
where
Δf = f – f (i = 1.n - 1)
i i+1 i
with
f = f and f = f
1 min n max
The square root Δφ(f) of the integral is the effective or RMS phase jitter in radians. It can be
converted into degrees, fractions of unit interval (UI), or time (in seconds) by multiplication
with the following factor k:
Degree Unit interval Time
UI s
°
k = 1/(2πf )
360/2π 1/(2π)
c
For random jitter, the peak-to-peak value is assumed to be 7 times the value computed above
(see 3.2.53 of IEC 60679-1:2017).
Accuracy:
A 1 dB error of the phase noise data 10 log L(f) over the full Fourier frequency range causes
a jitter inaccuracy of approximately 10 %.
4.2.4.2 Methods of communication analyser
Commercially available communication analyser may be used to measure jitter and wander of
clock sources with the method described in ITU-T Recommendation O.172 (see Figure 2). The
working principle is similar to the phase noise measurement technique using the quadrature
method. Softwares supplied with the test sets deliver directly all characteristic values for jitter
and wander in numeric and graphical presentation.
Jitter free
Clock with Demodulator
reference clock
output
jitter and generation
wander
ψ U ~ Δψ
Digital signal
UI
Pattern
pp
Ext.
HP
LP
U
(with jitter UI
Clock
Jitter RMS
and wander) Int. Weighting
Phase detector
filters Result
Peak-peak
evaluation
RMS
and
display
External clock
TIE
PLL
PLL LP
(wander
10 Hz
measurement)
MTIE
Internal reference
Lowpass
clock generation
IEC
Figure 2 – Block diagram of a jitter and wander analyser
according to ITU-T O.172
The advantage of these systems over the phase noise test is that a measurement of both
RMS and peak-to-peak jitter is possible. The disadvantage is that these systems require an
input signal (Oscillator frequency) according to the standard data bit rates for optical
communication systems (SONET, SDH) – see Table 2.

– 12 – IEC 62884-2:2017 © IEC 2017
Table 2 – Standard bit rates for various applications
SDH SONET Bit rate Allowed oscillator frequencies

Mbit/s
- OC-1 51,84 25,92 MHz，51,84 MHz
STM-1 OC-3 155,52 77,76 MHz，155,52 MHz
STM-4 OC-12 622,08 311,04 MHz，622,08 MHz
STM-16 OC-48 2488,32 1 244,16 MHz，2 488,32 MHz
STM-64 OC-192 9953,28 4 976,64 MHz，9 953,28 MHz

An Oscillator with other output frequencies cannot be tested, which limits the area of
application.
NOTE Other applications can have different requirements.
4.2.4.3 Methods of the specially designed measurement equipment
4.2.4.3.1 General
The measurement equipment and system shall be the specially designed SONET/SDH
measurement equipment using a time interval analyser.
4.2.4.3.2 Measurement items
The measurement items shall be the RMS jitter and the period (periodic) jitter.
4.2.4.3.3 Number of measurements
The measurement times shall be determined by contracts between customers and suppliers
after discussion between them. The target measurement times shall be 20 000 times or more.
Attention is needed because this device may not meet the requirements of the Oscillator for
the follo
...

IEC 62884-2 ®
Edition 1.0 2017-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Measurement techniques of piezoelectric, dielectric and electrostatic
oscillators –
Part 2: Phase jitter measurement method

Techniques de mesure des oscillateurs piézoélectriques, diélectriques
et électrostatiques –
Partie 2: Méthode de mesure de la gigue de phase

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International Standards for all electrical, electronic and related technologies.

About IEC publications
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latest edition, a corrigendum or an amendment might have been published.

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IEC 62884-2 ®
Edition 1.0 2017-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Measurement techniques of piezoelectric, dielectric and electrostatic

oscillators –
Part 2: Phase jitter measurement method

Techniques de mesure des oscillateurs piézoélectriques, diélectriques

et électrostatiques –
Partie 2: Méthode de mesure de la gigue de phase

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 31.140 ISBN 978-2-8322-7553-5

– 2 – IEC 62884-2:2017 © IEC 2017
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Test and measurement procedures . 8
4.1 General . 8
4.2 Test methods of phase jitter . 8
4.2.1 General . 8
4.2.2 Measurement in the time domain . 8
4.2.3 Measurement in the data domain . 9
4.2.4 Measurement in the frequency domain . 9
4.3 Input and output impedances of the measurement system . 13
4.4 Measurement equipment . 13
4.4.1 General . 13
4.4.2 Jitter floor . 13
4.4.3 Output wave form . 13
4.4.4 Output voltage . 14
4.5 Test fixture. 14
4.6 Cable, tools and instruments, and so on . 14
5 Measurement and the measurement environment . 14
5.1 Set-up before taking measurements . 14
5.2 Points to be considered and noted at the time of measurement . 14
5.3 Treatment after the measurement . 14
6 Measurement . 15
6.1 Reference temperature . 15
6.2 Measurement of temperature characteristics . 15
6.3 Measurement under vibration . 15
6.4 Measurement at the time of impact . 15
6.5 Measurement in accelerated ageing . 15
7 Other points to be noted . 15
8 Miscellaneous . 15
Annex A (normative)  Calculation method for the amount of phase jitter . 16
A.1 General . 16
A.2 Explanation . 16
A.3 Relations between phase noise and phase jitter . 16
A.4 Commentary on theoretical positioning of phase jitter . 18
A.5 Description . 18
A.5.1 General . 18
A.5.2 RMS jitter . 19
A.5.3 Peak-to-peak jitter . 19
A.5.4 Random jitter . 20
A.5.5 Deterministic jitter . 20
A.5.6 Period (periodic) jitter . 20
A.5.7 Data-dependent jitter . 20
A.5.8 Total jitter . 21

A.6 Points to be considered for measurement . 21
A.6.1 Measurement equipment . 21
A.6.2 Factors of measurement errors . 22
Bibliography . 24

Figure 1 – Phase jitter measurement with sampling oscilloscope . 9
Figure 2 – Block diagram of a jitter and wander analyser according to ITU-T O.172 . 11
Figure 3 – Equivalent block diagram . 13
Figure A.1 – Concept diagram of SSB phase noise . 18
Figure A.2 – Voltage versus time . 19
Figure A.3 – Explanatory diagram of the amount of jitter applied to RMS jitter . 21
Figure A.4 – Explanatory diagrams of random jitter, deterministic jitter, and total jitter . 22

Table 1 – Fourier frequency range for phase noise test . 10
Table 2 – Standard bit rates for various applications . 12

– 4 – IEC 62884-2:2017 © IEC 2017
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC,
DIELECTRIC AND ELECTROSTATIC OSCILLATORS –

Part 2: Phase jitter measurement method

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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governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
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
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
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misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
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 62884-2 has been prepared by IEC technical committee 49:
Piezoelectric, dielectric and electrostatic devices and associated materials for frequency
control, selection and detection.
This bilingual version (2019-11) corresponds to the monolingual English version, published in
2017-08.
The text of this International Standard is based on the following documents:
CDV Report on voting
49/1212/CDV 49/1243/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.

The French version of this standard has not been voted upon.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.
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.
– 6 – IEC 62884-2:2017 © IEC 2017
INTRODUCTION
A crystal oscillator as a highly efficient and highly precise source of a frequency oscillation is
widely used for fields such as the electronic equipment, communication equipment,
measurement equipment and a clock. Also recently, digitalization of these equipments is
advancing rapidly. In this situation, the frequency of crystal oscillator requires high precision
and high stability and reduction of noise with oscillating phenomenon. A phase jitter is one of
the noise characteristic in oscillation characteristic and precise measurement which is needed
when shipping a component to a customer.
For advance application in electronic information and communication technology,
(e.g. advanced satellite communications, control circuits for electric vehicle (EV)), necessity
arises for the measurement method for common guidelines of phase jitter. In these days,
measurement method of phase jitter also becomes more important from the electromagnetic
influence (EMI) point of view.
This document has been restructured from IEC 60679-1:2007 (third edition) and
IEC 60679-6:2011 (first edition). The test methods for oscillators have been separated from
IEC 60679-6:2011 into IEC 62884 (all parts). This document covers the phase jitter
measurement.
MEASUREMENT TECHNIQUES OF PIEZOELECTRIC,
DIELECTRIC AND ELECTROSTATIC OSCILLATORS –

Part 2: Phase jitter measurement method

1 Scope
This part of IEC 62884 specifies the methods for the measurement and evaluation of the
phase jitter measurement of piezoelectric, dielectric and electrostatic oscillators, including
dielectric resonator oscillators (DROs) and oscillators using a thin-film bulk acoustic resonator
(FBAR) (hereinafter referred to as an "Oscillator") and gives guidance for phase jitter that
allows the accurate measurement of RMS jitter.
In the measurement method, phase noise measurement equipment or a phase noise
measurement system is used.
NOTE Dielectric resonator oscillators (DROs) and oscillators using FBAR are under consideration.
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
IEC 60679-1:2017, Piezoelectric, dielectric and electrostatic oscillators of assessed quality –
Part 1: Generic specification
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 62884-1:2017, 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
For the purposes of this document, the terms and definitions given in IEC 60027 (all parts),
IEC 60050-561, IEC 60469, IEC 60617, IEC 60679-1 and ISO 80000-1 apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/

– 8 – IEC 62884-2:2017 © IEC 2017
• ISO Online browsing platform: available at http://www.iso.org/obp
4 Test and measurement procedures
4.1 General
The test and measurement procedures are given in Clause 4 of IEC 62884-1:2017 and shall
be applied as indicated in 4.2 to Clause 8.
4.2 Test methods of phase jitter
4.2.1 General
As the measurement method, the phase noise measurement equipment (system) or the
specially designed phase jitter measurement equipment shall be used.
Three basic methods are described:
a) measurement in the time domain by use of a digital real-time or sampling oscilloscope;
b) measurement in the data domain (BER test set);
c) measurement in the frequency domain using
1) a phase noise test set, or
2) a jitter and wander test set.
Method c) 1) using a phase noise test set is the recommended measurement method because
it allows sufficient accuracy for arbitrary oscillator output frequencies.
– In the measurement of phase jitter and wander of oscillator circuits, attention should be
paid to relative measurement reproducibility.
– A user and a manufacturer should deepen understanding through discussion about
relative measurement reproducibility.
– Measurement equipment (including software program) should be made clear between a
manufacturer and a user through a contract.
– When phase jitter and wander is calculated from phase noise, the range of frequency
deviation should be made clear between a user and a manufacturer through a contract.
4.2.2 Measurement in the time domain
Digital real-time or sampling oscilloscopes with wide bandwidth, fast sampling rates, and large
data memories are commercially available (see Figure 1), in some cases with special jitter
evaluation software.
Sampling
Delay line
scope
スコープ
Trigger
Input
Power
Oscillator
splitter
IEC
Figure 1 – Phase jitter measurement with sampling oscilloscope
The time variation of the edges of the clock signal relative to the trigger edge is displayed and
stored over a large number (typically thousands) of cycles. Instrument software allows the
determination of the peak-to-peak jitter value and a statistical evaluation of its distribution.
The sampling oscilloscope method does not allow an accurate evaluation of the spectral
content of the jitter. Also, jitter larger than one unit interval (UI) cannot be distinguished.
The measured jitter value is worse than the jitter of the device under test due to the internal
jitter of the instrument’s clock.
2 2
J = (J ) − (J )
DUT meas int
where
J is the measured jitter;
DUT
J is the jitter of the device under test;
meas
J is the internal jitter of the instrument’s clock.
int
High stability/low noise Oscillator exhibits a significantly lower jitter than the instrument’s
clock jitter and trigger stability. Therefore, this technology is currently not suitable for accurate
jitter measurement of such Oscillator.
4.2.3 Measurement in the data domain
Bit-error rate (BER) test sets are used for measuring bit-error rate to characterise the overall
system performance of a communication subsystem. It is difficult to deduct the contribution of
the Oscillator jitter to the system BER. This method also does not yield quantitative jitter
performance values for the Oscillator.
4.2.4 Measurement in the frequency domain
4.2.4.1 Methods of phase noise test set
Phase jitter can be tested in the frequency domain using the well-established phase noise test
method with a phase locked loop as described in 4.5.25 of IEC 62884-1:2017.
The range of detuned frequency shall be determined by contracts between customers and
suppliers after discussion between them. The formula for calculating the RMS jitter from a
phase noise is based on the calculation method for the amount of phase jitter shown in
Annex A.
– 10 – IEC 62884-2:2017 © IEC 2017
For given SDH/SONET applications, the Fourier frequency range (f . f ) may be
min max
selected as described in 3.2.53 of IEC 60679-1:2017. If not specified in the relevant data
sheet, the recommended Fourier frequency range is as given by f to f in Table 1.
3 4
Table 1 – Fourier frequency range for phase noise test
Oscillator output frequency f = f f f = f
0 min 3 4 max
1 MHz to < 10 MHz 10 Hz 10 kHz 100 kHz
10 MHz to < 50 MHz 20 Hz 20 kHz 500 kHz
50 MHz to < 200 MHz 100 Hz 50 kHz 1,5 MHz
200 MHz to < 1 000 MHz 1,0 kHz 200 kHz 5,0 MHz
1 000 MHz to < 5 000 MHz 5,0 kHz 500 kHz 15 MHz
≥ 5 000 MHz 20 kHz 2 MHz 80 MHz

From Table 1, it can be seen that the most stringent requirement applies over the range f to
f .
Jitter performance over a frequency-band other than f to f may also be defined.
3 4
To compute the phase jitter, the phase noise data L(f) have to be integrated in the considered
frequency ranges and evaluated as follows.
Compute the spectral density of phase fluctuations S (f) from the single-sideband phase noise
φ
plot 10 log L (f):
S( f)= 2L( f)
φ
Integrate S (f) over the specified Fourier frequency range f to f to get the mean squared
φ min max
phase jitter in that bandwidth:
f
max
( ) ( )
∆ϕ f = S f df
ϕ
∫
f
min
The mean square phase jitter can be approximated by stepwise integration over the specified
Fourier frequency range f to f segmented by n, for example:
min max
∆φ( f) ≈ S( f)∆f
∑ φ i i
where
Δf = f – f (i = 1.n - 1)
i i+1 i
with
f = f and f = f
1 min n max
The square root Δφ(f) of the integral is the effective or RMS phase jitter in radians. It can be
converted into degrees, fractions of unit interval (UI), or time (in seconds) by multiplication
with the following factor k:
Degree Unit interval Time
° UI s
k =
360/2π 1/(2π) 1/(2πf )
c
For random jitter, the peak-to-peak value is assumed to be 7 times the value computed above
(see 3.2.53 of IEC 60679-1:2017).
Accuracy:
A 1 dB error of the phase noise data 10 log L(f) over the full Fourier frequency range causes
a jitter inaccuracy of approximately 10 %.
4.2.4.2 Methods of communication analyser
Commercially available communication analyser may be used to measure jitter and wander of
clock sources with the method described in ITU-T Recommendation O.172 (see Figure 2). The
working principle is similar to the phase noise measurement technique using the quadrature
method. Softwares supplied with the test sets deliver directly all characteristic values for jitter
and wander in numeric and graphical presentation.
Jitter free
Demodulator
Clock with
reference clock
output
jitter and
generation
wander
ψ U ~ Δψ
Digital signal
UI
Pattern pp
Ext.
HP
LP
U
(with jitter UI
Clock
RMS
Jitter
and wander) Int. Weighting
Phase detector
filters Result
Peak-peak
evaluation
RMS
and
display
External clock
TIE
PLL
PLL LP
(wander
10 Hz
measurement)
MTIE
Internal reference
Lowpass
clock generation
IEC
Figure 2 – Block diagram of a jitter and wander analyser
according to ITU-T O.172
The advantage of these systems over the phase noise test is that a measurement of both
RMS and peak-to-peak jitter is possible. The disadvantage is that these systems require an
input signal (Oscillator frequency) according to the standard data bit rates for optical
communication systems (SONET, SDH) – see Table 2.

– 12 – IEC 62884-2:2017 © IEC 2017
Table 2 – Standard bit rates for various applications
SDH SONET Bit rate Allowed oscillator frequencies

Mbit/s
- OC-1 51,84 25,92 MHz，51,84 MHz
STM-1 OC-3 155,52 77,76 MHz，155,52 MHz
STM-4 OC-12 622,08 311,04 MHz，622,08 MHz
STM-16 OC-48 2488,32 1 244,16 MHz，2 488,32 MHz
STM-64 OC-192 9953,28 4 976,64 MHz，9 953,28 MHz

An Oscillator with other output frequencies cannot be tested, which limits the area of
application.
NOTE Other applications can have different requirements.
4.2.4.3 Methods of the specially designed measurement equipment
4.2.4.3.1 General
The measurement equipment and system shall be the specially designed SONET/SDH
measurement equipment using a time interval analyser.
4.2.4.3.2 Measurement items
The measurement items shall be the RMS jitter and the period (periodic) jitter.
4.2.4.3.3 Number of measurements
The measurement times shall be determined by contracts between customers and suppliers
after discussion between them. The target measurement times shall be 20 000 times or more.
Attention is needed because this device may not meet the requirements of the Oscillator for
the following reasons.
a) The measurable range of the measurement equipment may not meet the frequency of the
Oscillator to be measured.
b) The output voltage of the Oscillator is lower as compared with this device. For this reason,
an amplifier is required, and the necessity of evaluating the phase jitter of the amplifier
arises.
c) The realization of square waves, such as CMOS, LVDS, and LVPECL, is difficult because
harmonics components decrease in the frequency bands exceeding 300 MHz. For this
reason, the signal waveforms become sine waves, clipped-sine waves and the like. It is
difficult to analyse them by the specially designed SONET/SDH measurement equipment,
and thus a decrease in measurement accuracy is possible.
4.2.4.3.4 Block diagram of the measurement
A representative block diagram is shown in Figure 3. A practical block diagram is utilized as
modified forms of Figure 1.
Measurement
Test fixture
equipment
load
Sample
Power supply
oscillator
IEC
Figure 3 – Equivalent block diagram
4.3 Input and output impedances of the measurement system
The load impedance of the Oscillator widely ranges from 5 Ω to 100 MΩ. The parts to be
applied are the types shown below. However, since numerous demands are made by
customers, the values of this load impedance are infinite.
a) capacitor only;
b) resistor only;
c) both capacitor and resistor;
d) compliment output with bias.
Here, since the measurement system is unified into 50 Ω, the input-output impedances of
measurement systems shall be 50 Ω. For this reason, the load impedance of the Oscillator
shall also be 50 Ω.
The oscillation output voltage changes depend on the load impedance of the Oscillator. For
this reason, the thermal noise of load circuits also changes.
As a result, since the amount of phase jitter changes, a recommendation is presented to
suppliers and customers, when adopting any load impedance other than 50 Ω, to conduct a
detailed study and examination and to determine the impedance by contract.
4.4 Measurement equipment
4.4.1 General
The specification required for the measurement equipment is described in 4.4.2 to 4.6 without
any necessity of adhering to this document. The adoption of measurement equipment which
satisfies sufficiently the requirements of the Oscillator is important.
4.4.2 Jitter floor
The jitter floor shall take values smaller by one digit as compared with the phase jitter
demanded for the Oscillator.
4.4.3 Output wave form
The output waveforms shall be CMOS, LVDS, LVPECL, clipped-sine waves, sine waves, etc.
NOTE CMOS, LVDS, and LVPECL originally refer to the type of devices and not a waveform per se. However,
they are also used as the terms showing the waveforms and are, therefore, described as the type of output
waveforms in this document.
– 14 – IEC 62884-2:2017 © IEC 2017
4.4.4 Output voltage
The output voltage shall be 350 mV or more.
4.5 Test fixture
The specification demanded for measurement implements is shown below.
a) Connection between the Oscillator to be measured and measurement implements
The application of sockets, connectors, screws, clips, and the like may be allowed. In
addition, the Oscillator to be measured and the measurement implements shall be ensured
to be mechanically and electrically connectable.
b) Compatibilization of oscillators to be measured and measurement implements
The Oscillator to be measured and the measurement implements shall be capable of being
earthed.
c) Although the load impedance may not be built in, a recommendation is presented to use
measurement implements having the load impedance built therein in order to reduce
influences on the phase jitter of the Oscillator to be measured from a thermal noise or the
like from the load impedance.
4.6 Cable, tools and instruments, and so on
As for a cable, the double-shield type of a 50 Ω system shall be used. The cable shall be as
short as possible. As connectors, the 50 Ω system shall be used. It is recommended that SMA
or N-type connectors be used.
NOTE This measurement system is a 50 Ω system. This is the definition of the viewpoint of a measuring method.
The actual load impedance of the Oscillator cannot say it as a 50 Ω system. When a measurement system is not a
50 Ω system, user and supplier permit mutually use of the measurement system which is not a 50 Ω system. User
and supplier can define a new measurement system by a contract.
5 Measurement and the measurement environment
5.1 Set-up before taking measurements
Attention should be paid to the following matters.
a) The entire measurement system and the Oscillator to be measured shall be installed in a
measurement chamber at least 2 h previously.
b) The measurement equipment shall be set to operate for 2 h or more.
c) The frequency stability of clock signals in the measurement equipment shall be verified to
be smaller than, or equivalent to, the frequency stability of the Oscillator to be measured.
d) The power supply voltage of the Oscillator to be measured and the measurement
equipment shall be verified to be set to the AC voltage and the DC voltage as requested.
e) Restrictions shall be provided for the operation of surrounding electronic devices so as not
to produce an electronic noise from the surrounding.
5.2 Points to be considered and noted at the time of measurement
No vibration of the measurement system shall be caused. No movement shall be caused. No
shifting of the cable position shall be made.
5.3 Treatment after the measurement
It is preferable not to disassemble the measurement system after performing measurements.
Periodical inspection and calibration of the measurement equipment should be ensured.

6 Measurement
6.1 Reference temperature
The reference temperature shall be +25 °C ± 5 °C.
6.2 Measurement of temperature characteristics
Only the Oscillator to be measured shall be immobilized in the precisely variable temperature
bath as appropriately selected, and the temperature characteristics shall be measured. No
vibration shall be caused.
6.3 Measurement under vibration
Only the Oscillator to be measured shall be fixed to the shaker as appropriately selected and
caused to vibrate. No vibration of the measurement equipment shall be caused.
6.4 Measurement at the time of impact
Only the Oscillator to be measured shall be fixed to the impact machine as appropriately
selected to apply impact thereto. Moreover, no shock wave or no vibration accompanied with
the impact shall be provided for the measurement equipment.
In addition, this testing is not realistic because the impact period of time is shorter than the
measurement period of time. If this testing is performed, a recommendation is given to
suppliers and customers to conduct a detailed study and examination and to determine the
measurement by contract.
6.5 Measurement in accelerated ageing
Only the Oscillator to be measured shall be set to the temperature and time based on the
specification in the temperature bath as appropriately selected, and then caused to immobilize,
and thus the accelerated ageing shall be measured.
7 Other points to be noted
Consideration shall be taken so as to obtain the measurement results understandable to
suppliers and customers by eliminating any possibility that an electronic noise can be involved
in the measurement system from the supply source line through paying attention also to the
phase jitter of the devices applied to the measurement system, or to be applied around the
system.
8 Miscellaneous
With regard to the amount of phase jitter of the Oscillator, as well as modules that have a
multiplication function or a division function based on these oscillators, customers and
suppliers shall conduct a detailed study and examination, and determine this by contract.

– 16 – IEC 62884-2:2017 © IEC 2017
Annex A
(normative)
Calculation method for the amount of phase jitter
A.1 General
Annex A gives the method of calculating the amount of phase jitter from phase noise
measurement results.
A.2 Explanation
When the amount of phase jitter is calculated from the phase noise measurement results, the
RMS jitter can be obtained. The details are described below.
If a spectrum analyser or a phase noise measurement system is used, the phase jitter can be
analysed as to the frequency components which can be used for the cause analysis of the
phase jitter. According to the measurement of the phase jitter by the phase noise
measurement system, the ultra-low amount of phase jitter, which cannot be measured by
other jitter measurement methods, can be measured, and thus the phase noise measurement
system is suitable for evaluating highly stable devices such as the Oscillator. With regard to
the signals of the Oscillator, various types of signal waveforms such as sine waves and
square waves are requested by customers. Among them, as for the sine wave signals, the
application of the phase noise measurement system is theoretical and appropriate. However,
as for the square wave signals, although error-increasing factors are involved, since any other
method capable of firmly measuring the ultra-low amount of phase jitter has not yet been
found, the phase noise measurement system shall be applied.
In general, when the measurement results of an SSB phase noise of the Oscillator are viewed,
the offset frequency in the horizontal axis is described such as 10 Hz to 1 MHz, 1 Hz to 1 MHz,
and 1 Hz to 10 MHz in many cases. In particular, for the offset frequency of 10 kHz or more
as the floor level, the offset frequency is described as 1 MHz or 10 MHz. Such offset
frequency is obtained because filters are provided in the measurement equipment.
On the other hand, as for the phase jitter, since such filters are not required, the
measurement values can be obtained regardless of the offset frequency. Therefore, no
complete coincidence can be maintained to be provided for the phase noise measurement
values and the phase jitter measurement values. However, in the case of the Oscillator having
the ultra-low amount of phase jitter, the phase noise measurement values and the phase jitter
need to be correlated, and, therefore, the phase noise and the phase jitter are used for
convenience.
A.3 Relations between phase noise and phase jitter
When phase modulations are demodulated by a phase detector (converting phase fluctuations
into voltage fluctuations), the relationship between phase and voltage can be expressed by
Formula (A.1), wherein K is a constant, and the unit is K (V/rad).
ϕ ϕ
ΔV = K ×∆φ
(A.1)
out φ
When the converted phase fluctuations are measured by a spectrum analyser, the relationship
can be expressed by Formula (A.2):
∆V ( f)= K ×∆φ ( f)[V] (A.2)
rms φ rms
wherein, if S ( f) is defined as the spectral density function of the voltage fluctuations
v
rms
(output fluctuations of the phase detector) as measured, the spectral density function of the
phase fluctuations can be expressed by Formula (A.3):
(∆φ ( f))
rms
S ( f)=
φ
B
(∆V ( f))
rms
= (A.3)
Kφ × B
S ( f)
V
rms 2
= [rad / Hz]
Kφ
where
B is the bandwidth of the spectrum analyser.
When the results are converted into the SSB phase noise as shown below, the SSB phase
noise can be expressed by Formula (A.4):
S ( f)
φ
(A.4)
( )
L f =
where
S (f) is a dB value relative to 1 radian, and also the power spectral density function of the
φ
phase fluctuations;
L(f) is the single sideband (SSB) phase noise.
A total phase deviation in the designated band, namely, the phase jitter, can be expressed by
Formulae (A.5) and (A.6):
B
Φ= S ( f)⋅ df [rad] (A.5)
φ
∫
A
B
Φ= 2⋅ L( f)⋅ df [rad] (A.6)
∫
A
Therefore, the shaded parts (area of SSB phase noise) shown in Figure A.1 can be referred to
as the phase jitter. This area accords with the square of the RMS jitter. Here, if the offset
frequency range is different, the phase jitter calculation value becomes different. Since the
fact is a shortcoming of this method, attention should be paid when calculating the phase jitter
from the SSB phase noise.
– 18 – IEC 62884-2:2017 © IEC 2017
Offset frequency from carrier
IEC
Figure A.1 – Concept diagram of SSB phase noise
A.4 Commentary on theoretical positioning of phase jitter
Frequency stability was compiled into a single work by IEEE in 1966 [3]. Then, the definition
is applied to atomic oscillators, crystal oscillators, as well as electronic systems for
telecommunication, information, audio-visual, and the like.
The conventional crystal oscillators and electronic systems have analogue systems with
exception of a part, and the signal waveforms are sine waves. Therefore, the short-term
frequency stability as one field of the frequency stability is measured as the phase noise or
Allan variance. Recently, digitization of electronic systems is progressing. Under such
circumstances, the short-term frequency stability has been measured as the phase jitter.
On the other hand, Oscillators are analogue-type electronic devices. For the Oscillator, the
signals having square waves or waveforms similar thereto are demanded by users for
facilitating to be assembled into the electronic systems. Naturally, for the short-term
frequency stability, the measurement as the
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