IEC 60444-11:2026

IEC 60444-11 ®
Edition 2.0 2026-04
INTERNATIONAL
STANDARD
REDLINE VERSION
Measurement of quartz crystal unit parameters -
Part 11: Standard method for the determination of the load resonance frequency
f and the effective load capacitance C using automatic network analyzer
L Leff
techniques and error correction
ICS 31.140 ISBN 978-2-8327-1234-4
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CONTENTS
FOREWORD . 3
INTRODUCTION . 5
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 6
4 General concepts . 6
4.1 Load resonance frequencies f and f . 6
Lr La
4.2 Effective load capacitance C . 8
Leff
5 Reference plane and test conditions . 8
5.1 General . 8
5.2 Principle of measurement . 8
5.3 Evaluation of errors. 12
5.3.1 General comments . 12
5.3.2 Accuracy of measurement . 12
5.3.3 Reproducibility . 13
5.3.4 Comparison with the manual method of IEC 60444-4 . 16
5.3.5 Limitations . 17
Annex A (informative) Manual measuring method of the load resonance frequency fL
and load resonance resistance RL using physical load capacitance . 18
A.1 General . 18
A.2 Measuring circuit . 18
A.2.1 The measuring circuit of a zero phase π-network system . 18
A.2.2 An outline description . 18
A.2.3 Load capacitor specification . 19
A.3 Method of measurement . 19
A.3.1 Initial adjustment . 19
A.3.2 The method for the measurement of load resonance frequency and
resistance . 19
A.4 Load capacitor design . 19
A.4.1 Mechanical features . 19
A.4.2 Insertion into π-network . 20
A.4.3 Calibration and measurement of load capacitors . 22
A.5 Measurement errors . 23
A.5.1 General . 23
A.5.2 Main sources of measurement errors . 23
A.5.3 Effects of the frequency/temperature characteristics of the crystal unit . 24
A.5.4 Accuracy of the frequency measurements . 24
A.6 Analysis of errors . 24
A.6.1 Measurement error of load resonance frequency f . 24
L
A.6.2 Measurement error of load resonance resistance R . 25
L
A.6.3 Measurement errors of C . 26
Bibliography . 29

Figure 1 – Admittance of a quartz crystal unit . 7
Figure 2 – X as a function of frequency (solid line) in the vicinity of f . 10
C L
Figure 3 – P as level of drive of a crystal in a π-network versus df/f as frequency . 11
eff nom
Figure 4 – Error of the load resonance frequency due to the inaccuracy of the
measured voltages (dashed line) and the calibration resistances (soft line) . 13
Figure 5 – C -error resulting from f error (due to inaccuracy of the measured voltages
L L
and the calibration resistances) Error of the load resonance frequency due to the
change of the setting C for the same crystal as in Figure 4 . 13
L
Figure 6 – Frequency error Error of the load resonance frequency due to noise of V
C
as the measured voltages . 14
Figure 7 – Error of load resonance frequency f at 30 pF and 10 pF
L
for typical equivalent parameters of quartz crystal units .
Figure 8 – Error of C for typical equivalent parameters of quartz crystal units .
Leff
Figure 7 – Error of load resonance frequency f at different C for typical equivalent
L L
parameters of quartz crystal units . 16
Figure A.1 – Typical load capacitor with carrier . 20
Figure A.2 – Method of insertion of load capacitor into π-network . 21
Figure A.3 – Circuit diagram of π-network including load capacitor C . 22
L
Figure A.4 – Load capacitance inaccuracy as a function of frequency, for a load
capacitance of 30 pF inclusive of calibration inaccuracy and residual inductance
effects (worst case situation) . 24
Figure A.5 – Relative measurement error of f versus crystal pulling sensitivity for
L
various frequencies at a load capacitance of 30 pF . 25
Figure A.6 – Relative measurement error of R versus frequency, for
L
various values of C . 25
L
Figure A.7 – Relative measurement error of C as a function of frequency. 26
Figure A.8 – Relative measurement error of C as a function of C for various
1 1
frequency measurement errors C = 5 pF; C = 15 pF; C = 30 pF . 27
o L1 L2
Figure A.9 – Relative measurement error of C as a function of C for various values
1 1
of quality factor Q C = 3 pF; C = 15 pF; C = 30 pF . 28
o L1 L2
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
Measurement of quartz crystal unit parameters -
Part 11: Standard method for the determination of the load resonance
frequency f and the effective load capacitance C using automatic
L Leff
network analyzer techniques and error correction

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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6) All users should ensure that they have the latest edition of this publication.
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
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9) IEC draws attention to the possibility that the implementation of this document may involve the use of (a)
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shall not be held responsible for identifying any or all such patent rights.
This redline version of the official IEC Standard allows the user to identify the changes made
to the previous edition IEC 60444-11:2010. A vertical bar appears in the margin wherever a
change has been made. Additions are in green text, deletions are in strikethrough red text.

IEC 60444-11 has been prepared by IEC technical committee 49: Piezoelectric, dielectric and
electrostatic devices and associated materials for frequency control, selection and detection. It
is an International Standard.
This second edition cancels and replaces the first edition published in 2010. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) key content of withdrawn IEC TR 60444-4 is reproduced as Annex A;
b) some formulae in the first edition have been corrected.
The text of this International Standard is based on the following documents:
Draft Report on voting
49/1489/CDV 49/1515/RVC
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
A list of all parts in the IEC 60444 series, published under the general title Measurement of
quartz crystal unit parameters, 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 webstore.iec.ch in the data related to the
specific document. At this date, the document will be
– reconfirmed,
– withdrawn, or
– revised.
INTRODUCTION
This part of IEC 60444 defines the measuring method of load resonance frequency f using
L
automatic network analyzer techniques.
At the same time, even though IEC TR 60444-4 [8] specifying the manual measuring method
has been withdrawn, the main contents of the manual measuring method remain as Annex A
for the user's convenience. However, in case of dispute, the standard method as described
below should be used as reference.
The figure of merit M, according to IEC 60122-1:2002, Table 1, is expressed in the following
formula:
Q 1
M
(1)
r ωC R
This gives good results in a frequency range up to 200 MHz. This method allows the calculation
of load resonance frequency offset ∆f , frequency pulling range ∆f ∆f and pulling sensitivity
L L1, L2
S as described in IEC 60122-1:2002, 2.2.31. In contrary to the simple method of IEC 60444-4,
This measurement technique avoids the use of physical load capacitors, and allows higher
accuracy, better reproducibility and correlation to the application. It extends the upper
frequency limit from 30 MHz by the manual method of IEC 60444-4 to 200 MHz approximately.
This method is based on the error-corrected measurement technique of IEC 60444-5:1995 [9]
and therefore allows the measurement of f and C together with the determination of the
L Leff
equivalent crystal parameters in one sequence without changing the test fixture.
With this method the frequency f is searched where the reactance X of the crystal has the
L C
opposite value of the reactance of the load capacitance.
XX=−=
(2)
C CL
ωC
LL
Furthermore, this method allows to determine the effective load capacitance C at the nominal
Leff
frequency f
nom.
___________
Numbers in square brackets refer to the Bibliography.
= =
1 Scope
This part of IEC 60444 defines the standard method of measuring load resonance frequency f
L
at the nominal value of C , and the determination of the effective load capacitance C at the
L Leff
nominal frequency for crystals with the figure of merit M > 4.
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 60122-1:2002, Quartz crystal units of assessed quality - Part 1: Generic specification
IEC 60122-1:2002/AMD1:2017
IEC 60444-1:1986, Measurement of quartz crystal unit parameters by zero phase technique in
a pi-network - Part 1: Basic method for the measurement of resonance frequency and resonance
resistance of quartz crystal units by zero phase technique in a pi-network
IEC 60444-1:1986/AMD1:1999
IEC/TR 60444-4, Measurement of quartz crystal unit parameters by zero phase technique in a
π-network – Part 4: method for the measurement of the load resonance frequency f , load
L
resonance resistance R and the calculation of other derived values of quartz crystal units, up
L
to 30 MHz
IEC 60444-5:1995, Measurement of quartz crystal units parameters – Part 5: Methods for the
determination of equivalent electrical parameters using automatic network analyzer techniques
and error correction
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60122-1 apply.
ISO and IEC maintain terminology databases for use in standardization at the following
addresses:
– IEC Electropedia: available at https://www.electropedia.org/
– ISO Online browsing platform: available at https://www.iso.org/obp
4 General concepts
4.1 Load resonance frequencies f and f
Lr La
, f with
As can be seen in Figure 1, there are two intersection frequencies where XX= −
C CL Lr
high admittance (low impedance) and f with low admittance (high impedance).
La
The load resonant frequency f is one of the two frequencies of a crystal unit in association with
L
a series or with a parallel load capacitance, at which the electrical admittance (respectively
impedance) of the combination is resistive. The load resonance frequency f is the lower of the
L
two frequencies.
In a first approximation f can be calculated by:
L
1 LC ()C + C
11 0 L
≈π2 (3)
f CC++ C
L 1 0 L
f =
S (3)
2π LC
 
C
ff≈+ 1
  (4)
L S
 
2 CC+
( )
0L
 
NOTE f is the load resonance frequency that is commonly expressed as f .
Lr L
Figure 1 – Admittance of a quartz crystal unit
4.2 Effective load capacitance C
Leff
C is defined by the reactance of the crystal at the nominal frequency:
Leff
C =
(5)
Leff
ω Xω
( )
nom C nom
5 Reference plane and test conditions
5.1 General
Reference plane: as in IEC 60444-5:1995 [9], 8.4.
Test conditions: crystal case not grounded.
Level of drive: the output level of the generator is set, such that at its (series) resonance
frequency, the crystal under test is measured at the nominal drive level.
The measurement at the load resonance frequency using the method described below leads to
a level of drive, which is remarkably lower than at the (series) resonance frequency due to the
relative high reactance value. Therefore, a correction measurement is performed; for details
see 5.2.
5.2 Principle of measurement
The principles of measurement are the following.
a) Calibration
Due to the high impedance measurements with this method special care has to be taken in
the calibration of the test set-up.
As specified in IEC 60444-5:1995 [9], use the following three known calibration elements:
1) short-circuit (0 Ω) or resistor with low resistance;
2) resistor of 25 Ω or 50 Ω nominal;
3) open circuit (infinite resistance) or capacitor of 10 pF nominal.
b) Calibration with three known calibration elements:
1) short-circuit calibration;
2) calibration load (25 Ω or 50 Ω);
3) open circuit calibration (or calibration capacitor of 10 pF)
Z Z V V + ZZ V −+V ZZ V −V
( ) ( ) ( )
1 2 1− 22 3 2 33 1 3 1
R =
(6)
T
Z V −V + ZV −V + ZV −V
( ) ( ) ( )
12 3 2 3 1 3 1 2
VZ Z (V V ) +−V Z Z (V V ) +−VZ Z (V V )
3 12 1− 2 12 3 2 3 2 3 1 3 1
V =
(7)
s
Z Z V −+V ZZ V −+V ZZ V −V
( ) ( ) ( )
1 2 1 22 3 2 33 1 3 1
Z V V V + ZV V −V + ZV V −V
( ) ( ) ( )
1 1 2− 3 22 3 1 33 1 2
V =
(8)
o
Z V −V + ZV −V + ZV −V
( ) ( ) ( )
12 3 2 3 1 3 1 2
where
Z is the impedance of calibration element 1;
Z is the impedance of calibration element 2;
Z is the impedance of calibration element 3;
V is the measured voltage with calibration element 1;
V is the measured voltage with calibration element 2;
V is the measured voltage with calibration element 3.
The following parameters are then used for the measurement of quartz crystal units:
R is the termination impedance of the π-network;
T
is the error-corrected "short" voltage;
V
s
V is the error-corrected "open" voltage.
o
NOTE 1 If Z is taken as infinite number (ideal open circuit), the result of Formulae (6), (7) and (8) is not allowed
divisions of infinite by infinite applied.
c) Measurement of a quartz crystal unit impedance Z
c
From the measured voltage with a quartz crystal unit V , the impedance Z of the quartz
c c
crystal unit is calculated with:
(VV− )
SC
ZR=
(9)
cT
VV−
( )
C0
d) Measurement procedure for f
L
At load resonance frequency, the impedance of a quartz crystal unit is
Z R+ jX
(10)
CL L C
For the determination of the load resonance frequency, the frequency f the lower frequency
L
is searched for which Formula (2) is fulfilled, i.e.
XX+=0
(11)
C CL
With network analyzers, the frequency f is easily determined by using «marker search».
L
functions.
=
e) Evaluation of R
L
The computation of the load resonance resistance R from the real part of Z at the load
L c
resonance frequency f by the formula:
L
RR ω RZ ω
( ) ( ( )) (12)
L CL e c L
may can result in excessive inaccuracy, because – especially for low frequency crystals –
the angle of the voltage V is close to 90°.
c
X
CL
Only for < 10 this method yields reasonable results.
R
L
should be computed from the formula given in IEC 60122-1:
In all other cases, the R
L
C
RR 1+ (13)

L1
C
L
f) Measurement procedure for C
Leff
The reactance X (ω ) is measured at the nominal frequency and the effective load
C nom
capacity C is then calculated with the following formula:
Leff
C =
(14)
Leff
ω Xω( )
nom C nom
Figure 2 shows X as a function of frequency (solid line) in the vicinity of f
C L.
Figure 2 – X as a function of frequency (solid line) in the vicinity of f
C L
=
==
g) Level of drive
At the resonance frequency f , the level of drive P of a quartz crystal unit in a π-network is
r
given by the voltage V across the crystal
xr
as level of drive of a crystal in a π-network versus df/f as frequency
Figure 3 – P
eff nom
with
V
xr
P = (15)
R
r
and
VR
gr
V =
(16)
xr
RR+
rT
where
V is the voltage with measured element.
g
RR+
r T
V = PR
(17)
gr
R
r
At load resonance frequency f , the impedance Z of a quartz crystal unit is given by the
L L
load resonance resistance R and the modulus of the reactance of the load capacitor X :
L L
(18)
Z RX+
L LL
=
and, therefore, the drive level is
V
Xr
P = (19)
Z
L
22 2
X 11+ X ++R R + R R + R −
( ) ( )
CL ( CL L T ) L ( L T )
V = PR⋅⋅
(18)
gL 1
RX+
L CL
P R ++R X
( )
( L T CL )
(20)
V =
gL
R
L
In order to get the same level of drive at the load frequency f as at the series resonance
L
frequency f , it is necessary to increase the output power of the generator by the ratio:
s

V RR++ X
( )
R
gL L T CL
r
(21)
ABS =

V R RR+

gr L r T

NOTE 2 If the required power cannot be reached by the generator, a second measurement at resonance frequency
V 
gL
f is performed with a by factor by the ratio lower level and the difference of both series resonance
r ABS  
 
V
gr
 
measurements is added to the load resonance frequency f .
L
5.3 Evaluation of errors
5.3.1 General comments
According to the application of quartz crystal units in oscillators, the measurement accuracy of
the load resonance frequency f is presented here. The accuracy of the load capacitance C
L Leff
can be calculated then from the frequency accuracy and the equivalent parameters of the crystal
C and C from the relation
0 1
ff− C
LS 1
=
(22)
f 2 CC+
( )
S 0L
5.3.2 Accuracy of measurement
The accuracy of the measurement is given by the calibration resistors and the measured
voltages. In order to achieve an accuracy of the voltages of 1 %, it may can be necessary to
calibrate the test equipment in the whole power range.
NOTE Example for a quartz crystal 11 MHz in HC-49/U package.
Figure 4 – Error of the load resonance frequency due to the inaccuracy of the measured
voltages (dashed line) and the calibration resistances (soft line)

Figure 5 – C -error resulting from f error (due to inaccuracy of the measured voltages
L L
and the calibration resistances) Error of the load resonance frequency due to the
change of the setting C for the same crystal as in Figure 4
L
5.3.3 Reproducibility
Since the determination of the load frequency is based on a voltage measurement, the
reproducibility of the f measurement is influenced by noise. Figure 6 shows the error of the
L
load resonance frequency due to noise of V as the measured voltages. And Figure 7 shows
C
the error of load resonance frequency F at different C for typical equivalent parameters of
L L
quartz crystal units for better reproducibility.
Depending on the level of the expected voltage the measured noise is directly proportional to
the evaluated frequency.
To increase the accuracy it is recommended to use smaller bandwidths of intermediate
frequency (IF) filters of the used measurement equipment and to use an averaged signal.
Figure 6 – Frequency error Error of the load resonance frequency due to noise of V
C
as the measured voltages
1,00
0,80
Fund.
0,60
0,40
0,20
2 rd
3 overtone
0,00
1 10 100
Frequency  (MHz)
C tolerance at f {30 pF} ± (pF)
df error at 30 pF ± (ppm)
L nom
IEC  2359/10
load resonance frequency f at 30 pF and 10 pF
Figure 7 – Error of
L
for typical equivalent parameters of quartz crystal units

0,25
0,20
Fund.
0,15
0,10
0,05
rd
3 overtone
0,00
1 10 100
Frequency  (MHz)
df error at 10 pF ± (ppm) C tolerance at f {10 pF} ± (pF)
L nom
IEC  2360/10
Figure 8 – Error of C for typical equivalent parameters of quartz crystal units
Leff
df error ± (ppm)
df error ± (ppm)
dC at f ± (pF)
L
dC at f ± (pF)
L
d)
a) Error of load resonance frequency f at 30 pF for typical equivalent parameters
L
of quartz crystal units
b) Error of load resonance frequency f at 10 pF for typical equivalent parameters
L
of quartz crystal units
Figure 7 – Error of load resonance frequency f at different C for typical equivalent
L L
parameters of quartz crystal units
5.3.4 Comparison with the manual method of IEC 60444-4
The standard for manual measuring method using physical load capacitance has been
developed first as IEC TR 60444-4 [8].
This document has been withdrawn because the content became technically outdated and not
useful. But the main content remains in Annex A, because a few users and manufacturers use
this manual method still now.
The inaccuracy of the measurement of the load resonance frequency f according to IEC 60444-
L
4 the manual method is mainly given by the inaccuracy of the physical load capacitors which
often show a large dependence on frequency.
Comparison measurements ([1], [2], [5]) with quartz crystal units between 4 MHz and 155 MHz
showed an inaccuracy of 1 % of C .
Leff
The corresponding frequency inaccuracy can be calculated with Formula (21).
The inaccuracy for fundamental quartz crystal units with high C is less than 5 ppm with the
standard method presented here and up to 20 ppm with the manual method of IEC 60444-4.
Several series of comparative measurements ([1], [2]) have proven that the reproducibility
between different test systems using the standard method is considerably better than with the
IEC 60444-4 manual method.
5.3.5 Limitations
This method shall not be used for measurements of ageing and for the measurement of load
resonance in the temperature range due to the still remaining measurement uncertainty.
In the presence of activity dips, the described method may can yield unacceptable results and,
therefore, care should be taken.
If narrow frequency tolerances of f are required in an application, it is recommended to
L
determine the effective C of the application circuit by a correlation measurement.
L
Generally, the error of f becomes large when C is smaller than 10 pF or 2 × C .
L L 0
Annex A
(informative)
Manual measuring method of the load resonance frequency fL and load
resonance resistance RL using physical load capacitance
A.1 General
Since the standard for manual measuring method specified by IEC TR 60444-4 [8] has been
withdrawn, Annex A was copied from the main contents of IEC TR 60444-4 for the convenience
of a few users and manufacturers. In case of dispute, the standard method as described in this
document shall be used as reference.
These measurements allow calculation of load resonance frequency offset ∆f , frequency
L
pulling range ∆f and pulling sensitivity S as described in IEC 60122-1.
L1, L2
The method uses the change in resonance frequency from f to f (i.e. ∆f ) which occurs when
r L L
a load capacitance C is inserted in series with the crystal unit. The accuracy is determined
L
mainly by the precision of the frequency measurement and the calibration of the load capacitor.
Measurement of load resonance frequency f with different load capacitances may be used for
L
the determination of C and L as defined in IEC 60122-1.
1 1
It should be noted that when making measurements of the load resonance frequency of a quartz
crystal unit, the accuracy obtainable is a function of the crystal unit design and the value of the
load capacitance, as well as the method of measurement.
Useful information of general interest can be found in IEC 60122-2 [6].
A.2 Measuring circuit
A.2.1 The measuring circuit of a zero phase π-network system
The measuring circuit consists of a zero phase π-network system as described in IEC 60444-1,
in which a calibrated load capacitor can be inserted between the crystal unit terminals and the
contact plates of the π-network, to obtain a specific load capacitance.
The load capacitors are removable and interchangeable, so that the measurements at
resonance or at load resonance with one or more values of load capacitance can be made in
the same network, without disturbing the measurement system.
A.2.2 An outline description
An outline description of a typical design for the load capacitor and the method of insertion into
the π-network together with measurement errors is given in Clause A.4.
A.2.3 Load capacitor specification
-9
a) The residual inductance of the load capacitors shall be less than 1 × 10 H.
b) The tolerance on the specified nominal value should be equal to or better than ± 0,1 pF at
a frequency up to 1 MHz.
c) The cross-talk capacitance of the load capacitors shall be less than 0,05 pF. This can be
measured as described in Clause A.4.
-5
d) The temperature coefficient at 25 °C is recommended to be less than 3 × 10 /°C.
A.3 Method of measurement
A.3.1 Initial adjustment
The calibration and initial adjustment of the zero phase π-network system is performed in
accordance with IEC 60444-1.
a) The reference resistor used in the system is removed from the network, and the crystal unit,
together with the appropriate load capacitor, substituted. The load resonance frequency f
L
is measured at zero phase, and the load resonance resistance R is calculated from the
L
values of V and V as described in IEC 60444-1. The load capacitors used for these
Bs As
measurements shall have the specified value within the tolerances in A.2.3. (Standard
values are given in IEC 60122-1).
b) From these measurements it is possible to calculate the values of ∆f , ∆f and S as
L L1,L2
defined in IEC 60122-1.
c) The motional capacitance C and motional inductance L can also be calculated using the
1 1
formulae given in IEC 60444-5.
A.3.2 The method for the measurement of load resonance frequency and resistance
The method for the measurement of load resonance frequency and resistance is as described
in IEC 60444-1 for the resonance condition.
A.4 Load capacitor design
A.4.1 Mechanical features
Any design that meets the requirements of A.2.3 is suitable. Load capacitors designed as set
out below conform to these requirements.
The capacitors are made by using two capacitive elements secured around their edges by
soldering to the track of the fibre glass substrate as shown in Figure A.1.
The capacitive elements consist of a ceramic substrate with a thin layer of base plating using a
chrome-nickel-gold alloy.
This assembly is then electroplated with a copper layer 0,3 mm thick on each side. The final
coating is of gold plating 5 µm thick.
The construction is illustrated in Figure A.1.
Dimensions in millimetres
Figure A.1 – Typical load capacitor with carrier
The two sections of the load capacitor are approximately equal, each having the value 2C ,
L
where C is the desired load capacitance.
L
The capacitance value may be adjusted by erosion of the edges to meet the specified limits of
the load capacitor specification given in A.2.3.
A.4.2 Insertion into π-network
Figure A.2 illustrates how the load capacitor is inserted into the π-network so as to interpose a
capacitor between each of the network contacts and the terminals of the crystal unit. The
electrical circuit arrangement when the crystal and load capacitor are in position, is shown in
Figure A.3.
Provision should be made so that the load capacitor is held in a vertical position in the π-network.
Dimensions in millimetres
a) Without load capacitor
b) With load capacitor
c) Position of the load capacitor with respect to the network contacting plates

Figure A.2 – Method of insertion of load capacitor into π-network
Figure A.3 – Circuit diagram of π-network including load capacitor C
L
A.4.3 Calibration and measurement of load capacitors
Calibration of the load capacitor shall be carried out at a frequency of 1 kHz using an
appropriate capacitance meter allowing the measurement of one-port capacitors (with one lead
of which is earthed). The procedure is as follows:
a) Measure the capacitance of the test fixture C of the capacitance meter without the load
capacitor inserted.
b) Insert the load capacitor and measure the two sections of it. The resulting capacitance
values are C and C
RA RB.
c) The actual value of the load capacitance C is calculated from the relation:
L
CC+− 2C
RA RB i
C = (A.1)
L
The cross-talk attenuation of the capacitor can be measured in a similar way to that described
in IEC 60444-1:1986, 5.1, using the following formula:
V
Bs
A = 20log
C (A.2)
c
VV−
( )
Bo-total Bo-network
where
V is the B channel voltage measured with the load capacitor inserted;
Bo-total
is that measured with the network only;
V
Bo-network
V is the voltage measured with the shorting blank inserted in place of the load
Bs
capacitor.
Cross-talk capacitance measurement:
The cross-talk capacitance C can be calculated from the measurement of the cross-talk
c
attenuation of the load capacitor. The relation between the cross-talk attenuation and the
cross-talk capacitance is given by the formula:
A
C
c
−
10 (A.3)
C =
c
25ω
A.5 Measurement errors
A.5.1 General
The standard method for measurement of the motional capacitance C and motional inductance
L is given in IEC 60444-2 [7]. However, the π-network in conjunction with the load capacitor
described above can also be used to measure the motional capacitance C and inductance L .
1 1
A.5.2 Main sources of measurement errors
The main sources of measuring errors are:
– crystal holder capacitances C and C ;
AH BH
– residual stray capacitances;
– residual contact resistances;
– accuracy of load capacitance value calibration;
– accuracy of frequency and resistance measurement in the π-network using the zero-phase
method.
The load capacitance inaccuracy due to calibration uncertainty and frequency dependence is
shown in Figure A.4. The main reason is the residual inductance L of the load capacitor which
r
results in a slight increase of C with frequency. The fractional value of this increase can be
L
calculated from the approximate formula:
Cf − Cf
( ) ( )
L L0
≈ 4π f LC
(A.4)
rL
Cf
( )
L0
where
f = 1 kHz.
For L = 1 nH, f = 30 MHz and C = 30 pF this increase is less than 0,2 %.
r L
When making measurements in a temperature range, the influence of temperature can be
important. This influence is determined mainly by the temperature coefficient of the ceramic
material used as a dielectric in the load capacitor.
Figure A.4 – Load capacitance inaccuracy as a function of frequency, for a load
capacitance of 30 pF inclusive of calibration inaccuracy and residual inductance effects
(worst case situation)
A.5.3 Effects of the frequency/temperature characteristics of the crystal unit
The effects of the frequency/temperature characteristics of the crystal unit can be minimised by
ensuring that the temperature of the crystal unit is the same for all frequency measurements
required for the determination of the series arm equivalent circuit components.
A.5.4 Accuracy of the frequency measurements
The accuracy of the frequency measurements should be as high as possible when an accurate
determination of C and L is required since the results involve the difference between two or
1 1
more very similar frequencies.
A.6 Analysis of errors
A.6.1 Measurement error of load resonance frequency f
L
The relative measurement error of f due to load capacitance inaccuracy is given by the formula:
L
df
L
= SC d
(A.5)
L
f
r
where
S is the pulling sensitivity.
The relative measurement error of f as a function of the pulling sensitivity S for various
L
frequencies is shown in Figure A.5.
Figure A.5 – Relative measurement error of f versus crystal pulling sensitivity for
L
various frequencies at a load capacitance of 30 pF
A.6.2 Measurement error of load resonance resistance R
L
The relative measurement error of R due to load capacitance inaccuracy is given by the formula:
L
dR 2dC
LL
=
(A.6)
R CC+
L 0L
and shown in Figure A.6.
Figure A.6 – Relative measurement error of R versus frequency, for
L
various values of C
L
A.6.3 Measurement errors of C
A.6.3.1 Load capacitance inaccuracy
The relative measurement error of C due to load capacitance inaccuracy is given by the formula:
d CC−
dC ( )
L2 L1
= (A.7)
C CC−
1 L2 L1
The relative measurement error of C as a function of frequency is represented by Figure A.7.
Figure A.7 – Relative measurement error of C as a function of frequency
A.6.3.2 The relative measurement error of C
The relative measurement error of C caused by t he inaccuracy of measured frequencies
f , f and f is due, for example, to changes in ambient temperature, drive level, including
L1 L2 s
zero phase indication errors.
The fractional error of C can be calculated by the formula:
dC
= −0,5dff+−2d 1,5df
( )
(A.8)
L1 L2 r
...

IEC 60444-11 ®
Edition 2.0 2026-04
NORME
INTERNATIONALE
Mesure des paramètres des résonateurs à quartz -
Partie 11: Méthode normalisée pour la détermination de la fréquence de
résonance avec capacité de charge f et de la capacité de charge effective C à
L Leff
l'aide de techniques d'analyseur de réseau automatiques et de correction
d'erreur
ICS 31.140  ISBN 978-2-8327-1199-6

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SOMMAIRE
AVANT-PROPOS . 3
INTRODUCTION . 5
1 Domaine d'application . 6
2 Références normatives . 6
3 Termes et définitions . 6
4 Concepts généraux . 6
4.1 Fréquences de résonance avec capacité de charge f et f . 6
Lr La
4.2 Capacité de charge efficace C . 7
Leff
5 Plan de référence et conditions d'essai . 8
5.1 Généralités . 8
5.2 Principe de mesure . 8
5.3 Évaluation des erreurs . 12
5.3.1 Observations générales . 12
5.3.2 Précision de la mesure . 12
5.3.3 Reproductibilité . 13
5.3.4 Comparaison avec la méthode manuelle . 15
5.3.5 Limites . 15
Annexe A (informative) Méthode de mesure manuelle de la fréquence de résonance
avec capacité de charge f et de la résistance de résonance de charge R en utilisant
L L
la capacité de charge physique . 16
A.1 Généralités . 16
A.2 Circuit de mesure . 16
A.2.1 Le circuit de mesure d'un système à réseau en π de phase zéro . 16
A.2.2 Une description sommaire . 16
A.2.3 Spécification du condensateur de charge . 17
A.3 Méthode de mesure . 17
A.3.1 Ajustement initial . 17
A.3.2 Méthode de mesure de la fréquence et de la résistance de résonance
de charge . 17
A.4 Conception du condensateur de charge . 17
A.4.1 Caractéristiques mécaniques . 17
A.4.2 Insertion dans le réseau en π . 18
A.4.3 Étalonnage et mesure des condensateurs de charge . 20
A.5 Erreurs de mesure . 21
A.5.1 Généralités . 21
A.5.2 Principales sources d'erreurs de mesure . 21
A.5.3 Effets des caractéristiques fréquence/température de l'unité de cristal . 22
A.5.4 Précision des mesures de fréquence . 22
A.6 Analyse des erreurs . 22
A.6.1 Erreur de mesure de la fréquence de résonance f . 22
L
A.6.2 Erreur de mesure de la résistance de résonance de charge R . 23
L
A.6.3 Erreurs de mesure de C . 24
Bibliographie . 27

Figure 1 – Admission d'une unité de cristal de quartz . 7
Figure 2 – X en fonction de la fréquence (trait plein) au voisinage de f . 10
C L
Figure 3 – P comme niveau d'entraînement d'un cristal dans un réseau en π en
eff
fonction de la fréquence df/f . 11
nom
Figure 4 – Erreur de fréquence de résonance avec capacité de charge due à
l'imprécision des tensions mesurées (ligne pointillée) et des résistances d'étalonnage
(ligne souple) . 13
Figure 5 – Erreur de la fréquence de résonance avec capacité de charge résultant de
la variation du réglage C pour le même cristal que sur la Figure 4 . 13
L
Figure 6 – Erreur de la fréquence de résonance avec capacité de charge due au bruit
de V comme tensions mesurées . 14
C
Figure 7 – Erreur de la fréquence de résonance avec capacité de charge f à
L
différentes valeurs de C pour les paramètres équivalents types d'unités de cristal de
L
quartz . 14
Figure A.1 – Condensateur de charge typique avec support. 18
Figure A.2 – Méthode d'insertion du condensateur de charge dans le réseau en π . 19
Figure A.3 – Schéma de circuit du réseau en π avec condensateur de charge C . 20
L
Figure A.4 – Imprécision de la capacité de charge en fonction de la fréquence, pour
une capacité de charge de 30 pF incluant l'imprécision de l'étalonnage et les effets de
l'inductance résiduelle (situation la plus défavorable) . 22
Figure A.5 – Erreur de mesure relative de f par rapport à la sensibilité de traction du
L
cristal pour différentes fréquences à une capacité de charge de 30 pF . 23
Figure A.6 – Erreur de mesure relative de R en fonction de la fréquence, pour
L
différentes valeurs de C . 23
L
Figure A.7 – Erreur de mesure relative de C en fonction de la fréquence . 24
Figure A.8 – Erreur de mesure relative de C en fonction de C pour différentes
1 1
erreurs de mesure de fréquence C = 5 pF; C = 15 pF; C = 30 pF . 25
o L1 L2
Figure A.9 – Erreur de mesure relative de C en fonction de C pour différentes
1 1
valeurs du facteur de qualité Q C = 3 pF; C = 15 pF ; C = 30 pF . 26
o L1 L2
COMMISSION ÉLECTROTECHNIQUE INTERNATIONALE
____________
Mesure des paramètres des résonateurs à quartz -
Partie 11: Méthode normalisée pour la détermination de la fréquence
de résonance avec capacité de charge f et de la capacité de charge
L
effective C à l'aide de techniques d'analyseur de réseau
Leff
automatiques et de correction d'erreur

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référencées est obligatoire pour une application correcte de la présente publication.
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pour responsable de ne pas avoir identifié de tels droits de brevet.
L'IEC 60444-11 a été établie par le comité d'études 49 de l'IEC: Dispositifs piézoélectriques,
diélectriques et électrostatique et matériaux associés pour la détection, le choix et la commande
de la fréquence. Il s'agit d'une Norme internationale.
Cette deuxième édition annule et remplace la première édition parue en 2010. Cette édition
constitue une révision technique.
Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition
précédente:
a) l'essentiel du contenu de l'IEC TR 60444-4 qui a été annulé est reproduit dans l'Annexe A;
b) certaines formules de la première édition ont été corrigées.
Le texte de cette Norme internationale est issu des documents suivants:
Projet Rapport de vote
49/1489/CDV 49/1515/RVC
Le rapport de vote indiqué dans le tableau ci-dessus donne toute information sur le vote ayant
abouti à son approbation.
La langue employée pour l'élaboration de cette Norme internationale est l'anglais.
Ce document a été rédigé conformément aux Directives ISO/IEC, Partie 2, et développé
conformément aux Directives ISO/IEC, Partie 1 et aux Directives ISO/IEC, Supplément IEC,
disponible sur www.iec.ch/members_experts/refdocs. Les principaux types de documents
développés par l'IEC sont décrits plus en détail sous www.iec.ch/publications.
Une liste de toutes les parties de la série IEC 60444, publiées sous le titre général Mesure des
paramètres des résonateurs à quartz, se trouve sur le site web de l'IEC.
Le comité a décidé que le contenu de ce document ne sera pas modifié avant la date de stabilité
indiquée sur le site web de l'IEC sous webstore.iec.ch dans les données relatives au document
spécifique. À cette date, le document sera
– reconduit,
– supprimé, ou
– révisé.
INTRODUCTION
La présente partie de l'IEC 60444 définit la méthode de mesure de la fréquence de résonance
avec capacité de charge f utilisant des techniques d'analyseur de réseau automatique.
L
Dans le même temps, bien que l'IEC TR 60444-4 [8] relative à la méthode de mesure manuelle
ait été supprimée, l'essentiel du contenu de la méthode de mesure manuelle reste en tant
qu'Annexe A pour plus de commodité pour l'utilisateur. Toutefois, en cas de litige, il convient
d'utiliser la méthode normalisée décrite ci-dessous comme référence.
Le facteur de mérite M, selon le Tableau 1 de l'IEC 60122-1:2002, est exprimée dans la formule
suivante:
Q 1
M
(1)
r ωC R
Cela donne de bons résultats dans une plage de fréquences pouvant atteindre 200 MHz.
Cette méthode permet de calculer le décalage de fréquence de résonance avec capacité de
charge ∆f , la plage de traction de fréquence ∆f , ∆f et la sensibilité de traction S comme
L L1 L2
décrit au 2.2.31 de l'IEC 60122-1:2002. Cette technique de mesure évite l'utilisation de
condensateurs de charge physique et permet une plus grande précision, une meilleure
reproductibilité et une corrélation à l'application. Elle étend la limite supérieure de fréquence
de 30 MHz par la méthode manuelle à 200 MHz environ. Cette méthode est basée sur la
technique de mesure corrigée par erreur de l'IEC 60444-5 [9] et permet donc la mesure de f
L
et C ainsi que la détermination des paramètres cristallins équivalents dans une séquence
Leff
sans modifier le dispositif d'essai.
Avec cette méthode, on recherche la fréquence f pour laquelle la valeur de la réactance X du
L C
résonateur est opposée à la valeur de la réactance de la capacité de charge.
XX=−=
(2)
C CL
ωC
LL
En outre, cette méthode permet de déterminer la capacité de charge effective C à la
Leff
fréquence nominale f
nom.
___________
Les chiffres entre crochets renvoient à la Bibliographie.
==
1 Domaine d'application
La présente partie de l'IEC 60444 définit la méthode normalisée de mesure de la fréquence de
résonance à la charge f à la valeur nominale de C et la détermination de la capacité de charge
L L
efficace C à la fréquence nominale pour des résonateurs de facteur de mérite M > 4.
Leff
2 Références normatives
Les documents suivants sont cités dans le texte de sorte qu'ils constituent, pour tout ou partie
de leur contenu, des exigences du présent document. Pour les références datées, seule
l’édition citée s’applique. Pour les références non datées, la dernière édition du document de
référence s'applique (y compris les éventuels amendements).
IEC 60122-1:2002, Résonateurs à quartz sous assurance de la qualité - Partie 1: Spécification
générique
IEC 60122-1:2002/AMD1:2017
IEC 60444-1:1986, Mesure des paramètres des quartz piézoélectriques par la technique de
phase nulle dans le circuit en pi - Partie 1: Méthode fondamentale pour la mesure de la
fréquence de résonance et de la résistance de résonance des quartz piézoélectriques par la
technique de phase nulle dans le circuit en pi
IEC 60444-1:1986/AMD1:1999
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions donnés dans l'IEC 60122-1
s'appliquent.
L'ISO et l'IEC tiennent à jour des bases de données terminologiques destinées à être utilisées
en normalisation, consultables aux adresses suivantes :
– IEC Electropedia: disponible à l'adresse https://www.electropedia.org/
– ISO Online browsing platform: disponible à l'adresse https://www.iso.org/obp
4 Concepts généraux
4.1 Fréquences de résonance avec capacité de charge f et f
Lr La
Comme le montre la Figure 1, il y a deux fréquences d'intersection où XX=− , f avec une
C CL Lr
forte admittance (faible impédance) et f avec une faible admittance (forte impédance).
La
La fréquence de résonance à la charge f est une des deux fréquences du résonateur à quartz
L
associé à une capacité de charge série ou parallèle, pour laquelle l'admittance électrique
(respectivement l'impédance) de la combinaison est résistive. La fréquence de résonance à la
charge f est la plus basse des deux fréquences.
L
En première approximation, f peut être calculée par:
L
f =
(3)
S
2π LC
 
C
ff≈+ 1
  (4)
L S
 
2(CC+ )
0L
 
NOTE f est la fréquence de résonance avec capacité de charge couramment exprimée comme f .
Lr L
Figure 1 – Admission d'une unité de cristal de quartz
4.2 Capacité de charge efficace C
Leff
C est définie par la réactance du résonateur à la fréquence nominale:
leff
C =
(5)
Leff
ω Xω
( )
nom C nom
5 Plan de référence et conditions d'essai
5.1 Généralités
Plan de référence: comme au 8.4 de l'IEC 60444-5:1995 [9].
Conditions d'essai: boîtier du résonateur non relié à la terre.
Niveau d'excitation: le niveau de sortie du générateur est réglé de telle sorte qu'à sa fréquence
de résonance (série), le résonateur en essai soit mesuré au niveau d'excitation nominal.
La mesure de la fréquence de résonance à la charge utilisant la méthode décrite ci-dessous
donne un niveau d'excitation considérablement inférieur à la fréquence de résonance (série)
en raison de la valeur de réactance relativement élevée. Par conséquent, une mesure de
correction est effectuée; pour plus de détails, voir 5.2.
5.2 Principe de mesure
Les principes de mesure sont les suivants.
a) Étalonnage
En raison des mesures à haute impédance de cette méthode, le montage d'essai doit être
étalonné avec précaution.
Comme spécifié dans l'IEC 60444-5 [9], on utilise trois éléments d'étalonnage connus:
1) court-circuit (0 Ω) ou résistance de faible valeur;
2) résistance de 25 Ω ou 50 Ω nominal;
3) circuit ouvert (résistance infinie) ou condensateur de 10 pF nominal;
b) Étalonnage avec trois éléments d'étalonnage connus
1) court-circuit d'étalonnage;
2) charge d'étalonnage (25 Ω ou 50 Ω);
3) circuit ouvert d'étalonnage (ou condensateur d'étalonnage de 10 pF);
Z Z V V + ZZ V −+V ZZ V −V
( ) ( ) ( )
1 2 1− 22 3 2 33 1 3 1
R =
(6)
T
Z V −V + ZV −V + ZV −V
( ) ( ) ( )
12 3 2 3 1 3 1 2
VZ Z (V V )+−V Z Z (V V )+−VZ Z (V V)
3 12 1− 2 12 3 2 3 2 3 1 3 1
V =
(7)
s
Z Z V −+V ZZ V −+V ZZ V −V
( ) ( ) ( )
1 2 1 22 3 2 33 1 3 1
Z V V V + ZV V −V + ZV V −V
( ) ( ) ( )
1 1 2− 3 22 3 1 33 1 2
V = (8)
o
Z V −V + ZV −V + ZV −V
( ) ( ) ( )
12 3 2 3 1 3 1 2
où
Z est l'impédance de l'élément d'étalonnage 1;
Z est l'impédance de l'élément d'étalonnage 2;
Z est l'impédance de l'élément d'étalonnage 3;
V est la tension mesurée avec l'élément d'étalonnage 1;
V est la tension mesurée avec l'élément d'étalonnage 2;
V est la tension mesurée avec l'élément d'étalonnage 3.
Les paramètres suivants sont alors ut
...