SIST EN 60444-5:2002

SLOVENSKI STANDARD
SIST EN 60444-5:2002
01-september-2002
Measurement of quartz crystal unit parameters - Part 5: Methods for the
determination of equivalent analyser techniques and error correction (IEC 60444-
5:1995)
Measurement of quartz crystal unit parameters -- Part 5: Methods for the determination
of equivalent electrical parameters using automatic network analyzer techniques and
error correction
Messung von Schwingquarz-Kennwerten -- Teil 5: Meßverfahren zur Bestimmung der
elektrischen Ersatzschaltungsparameter von Schwingquarzen mit automatischer
Netzwerkanalysatortechnik und Fehlerkorrektur
Mesure des paramètres des résonateurs à quartz -- Partie 5: Méthodes pour la
détermination des paramètres électriques équivalents utilisant des analyseurs
automatiques de réseaux et correction des erreurs
Ta slovenski standard je istoveten z: EN 60444-5:1997
ICS:
31.140 3LH]RHOHNWULþQHLQ Piezoelectric and dielectric
GLHOHNWULþQHQDSUDYH devices
SIST EN 60444-5:2002 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 60444-5:2002

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SIST EN 60444-5:2002

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SIST EN 60444-5:2002

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SIST EN 60444-5:2002

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SIST EN 60444-5:2002

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SIST EN 60444-5:2002
NORME CEI
IEC
INTERNATIONALE
444-5
INTERNATIONAL
Première édition
STANDARD
First edition
1995-03
Mesure des paramètres des résonateurs
à quartz
Partie 5:
Méthodes pour la détermination des paramètres
électriques équivalents utilisant des analyseurs
automatiques de réseaux et correction des erreurs
Measurement of quartz crystal unit parameters —
Part 5:
Methods for the determination of equivalent
electrical parameters using automatic network
analyzer techniques and error correction
© CEI 1995 Droits de reproduction réservés — Copyright — all rights reserved
Aucune partie de cette publication ne peut être reproduite ni No part of this publication may be reproduced or util ized in
utilisée sous quelque forme que ce soit et par aucun pro- any form or by any means, electronic or mechanical,
cédé, électronique ou mécanique, y compris la photocopie et including photocopying and microfilm, without permission
les microfilms. sans l'accord écrit de l'éditeur. in writing from the publisher.
Suisse
Bureau Central de la Commission Electrotechnique Internationale 3, rue de Varembé Genève,
Commission Electrotechnique Internationale
CODE PRIX
International Electrotechnical Commission
PRICE CODE
IEC Me*nyHapoaslaa 3neKrporexHH4ecKaa IioMHCCHa
• Pour prix, voir catalogue en vigueur
•
For price, see current catalogue

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 3 –
CONTENTS
Page
FOREWORD 5
Clause
1 Scope 7
2 Introduction 7
2.1 General 7
2.2 Methods of admittance measurement 9
2.3 Admittance analysis and estimation of equivalent circuit parameters 13
2.4 Normative references 13
3 Measurement procedures 15
3.1 General 15
3.2 Environmental control 15
3.3 Calibration 15
3.4 Level of drive 15
3.5 Co measurements 15
3.6 Choice of measurement frequencies 17
3.7 Data collection 17
3.8 Data correction 19
3.9 Admittance calculation 19
3.10 Admittance analysis an
d estimation of the equivalent circuit parameters 19
4 Choice of admittance measurement method 19
4.1 General 19
4.2 Advantages and disadvantages of the one-port S-parameter reflection method 19
4.3 Advantages and disadvantages of the two-port S-parameter tr ansmission method 21
4.4 Advantages and disadvantages of the direct tr ansmission method 21
5 Calibration techniques 23
5.1 S-parameter method 23
5.2 Direct transmission method 23
Verification of calibration 5.3 23
6 Low-frequency measurements 25
7 Admittance analysis and estimation of the equivalent circuit parameters 25
7.1 General least-squares fitting method 25
7.2 Linear least-squares fitting procedure 27
7.3 Circle-fitting method 33
7.4 Two-point iterative method 37
8 Measurement errors, instrumentation and test fixtures 41
8.1 General comments 41
8.2 Measurement conditions 41
8.3 Reproducibility 43
d
8.4 Measurement an test fixtures 43
Figures 49
Annexes
A Calibration 71
B Low-frequency measurement 93
C Bibliography 100

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 5
INTERNATIONAL ELECTROTECHNICAL COMMISSION
MEASUREMENT OF QUARTZ CRYSTAL UNIT PARAMETERS —
Part 5: Methods for the determination of equivalent electrical parameters
using automatic network analyzer techniques and error correction
FOREWORD
1)
The MC (Internati
onal Electrotechnical Commission) is a world-wide organization for standardization comprising all na tional
electrotechnical committees (IEC National Committees). The object of
the EEC is to promote international cooperation on all ques
tions
concerning standardization in the electrical and
electronic fields. To this end and in addition to other activities, the IEC publishes
International Stan
dards. Their preparation is entrusted to technical committees; any IEC Na tional Committee interested in the
subject
dealt with may participate in this preparatory work. Inte
rnational, governmental and non-governmental organizations liaising with
the
IEC also participate in this preparation. The IEC collaborates closely with the Internati
onal Organization for Standardization (ISO) in
accordance with conditions determined by agreement between the
two organizations.
2) The formal decisions or agreements of the
IEC on technical matters, prepared by technical committees on which all the ti
Na onal
Committees having a special interest therein are
represented, express, as nearly as possible, an international consensus of opinion on
the subjects dealt with.
3) They have the
form of recommendations for inte rnational use published in the form of standards, technical
reports or guides and they
are accepted by
the National Committees in that sense.
4)
In order to promote international unification, IEC National Committees undertake to apply IEC Inte
rnational Standards transparently
to the maximum extent possible in their na tional an
d regional standards. Any divergence between the IEC Standard and the
corresponding national or regional stan
dard shall be clearly indicated in the latter.
International Standard IEC 444-5 has been prepared by IEC technical committee 49: Piezoelectric and dielectric
devices for frequency control and selection.
It forms Part
5 of a series of publications dealing with the measurements of piezoelectric quartz crystal unit
parameters.
Part 1: Basic method for the measurement of resonance frequency and resonance resistance of quartz crystal
units by zero phase technique in a tc network, is issued as IEC 444-1.
Part
2: Phase offset method for measurement of motional capacitance of quartz crystal units,
is issued as
IEC 444-2.
Part 3: Basic method for the measurement of two-terminal parameters of quartz crystal units up to 200 MHz by
phase technique in a iv-network with compensation of parallel capacitance Co, is issued as IEC 444-3.
Part 4: Method for the measurement of the load resonance frequency fv load resonance resistance, R L and the
calculation of other derived values of quartz crystal units, up to 30 MHz,
is issued as IEC 444-4.
Part 6: Measurement of drive level dependence (DLD),
is issued as IEC 444-6.
The text of this standard is based on the following documents:
DIS Report on voting
49(CO)248 49(CO)268
Full information on the voting for the approval of this standard can be found in the repo
rt on voting indicated in
the above table.
Annex A forms an integral part of this standard.
Annexes B and C are for information only.

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SIST EN 60444-5:2002
444-5 ©IEC:1995 –
7
MEASUREMENT OF QUARTZ CRYSTAL UNIT PARAMETERS —
Part 5: Methods for the determination of equivalent electrical parameters
using automatic network analyzer techniques and error correction
1 Scope
The objective of this Inte rn
ational Standard is to give methods for determining the best representations of
modes in quartz crystal resonators by linear equivalent circuits. Circuit representations are based on electrical
parameters measured with vector network analyzer equipment using automatic error correction. Determination
of the equivalent parameters by the method of this st dard is based on the measurement of device immittance
an
in the vicinity of series resonance. The further problem of characterizing the device for operation with a series
load capacitance has not been directly addressed, although it is recognized that some applications require such
characterization. The same measuring equipment, an rt of measurement, provides
d fundamentally the same so
the means to characterize completely the test load capacity fixture as well as the series combination of load
capacity fixture and crystal unit.
2 Introduction
2.1 General
2.1.1 This st
andard describes methods for determining the values of the electrical parameters of piezoelectric
quartz crystal units using automated vector network analyzer equipment. The recommended procedures for S-
parameter systems use shielded open-circuit, short-circuit, an resistive terminations, and (in the case of
d
transmission methods) thru-line connections. Coaxial open-circuit, short-circuit and resistive terminations
designed for 50 SI systems are readily available, and can be calibrated in terms of national st andards of
impedance over very wide frequency r anges. At the present time thru-line connections suitable for calibrating
the test fixtures must be calibrated by the user or supplier; however, the techniques for doing this are quite
well known. Non-coaxial standard resistors for use in the direct tr ansmission (n-network) method are
commercially available as well, but are not as easily traceable to National Standards. Further guidance on the
application of this standard may be found in IEC 1080.
2.1.2 The procedure involves the measurement of crystal resonator admittance at prescribed frequency points
by one of a number of methods followed by data interpretation and evaluation of the equivalent circuit
parameters (figure 1).
2.1.3 The measurement methods described are intended to provide reference values for the electrical
equivalent circuit parameters. Manufacturers and users may employ other methods of measurement, but the
values thus obtained shall be correlated with those obtained by the reference method.
2.1.4 This standard is only concerned with the representation of quartz crystal resonators by linear equivalent
circuits which are valid over a narrow frequency b and covering at most a small percentage of the resonance
frequency.
2.1.5 In general, some degree of non-linearity will be present and the circuit parameters may have a
noticeable dependence on d rive level. If non-linear effects are very large then the accepted circuit
representations may be unusable.

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SIST EN 60444-5:2002
444-5 © IEC:1995 – 9
2.1.6 Normally, the
equivalent circuit will be used to represent an
isolated mode of vibration, but occasionally
additional modes may occur extremely close to
the main response; a more complex circuit representation may
then be used, and consideration of this problem is included in this standard. See reference [1]*.
2.2
Methods of admittance measurement
2.2.1 The following terminology will be used to describe the circuit elements. See figures 3 and 4:
Co is the static capacitance (for the one-port model)
C01
is the electrode to can capacit ance
CO2 is the static capacitance (for the simplified two-po
rt model)
CO3 is the electrode to can capacitance
G0 is the conductance associated with C0
G01 is the conductance associated with
C01
G02
is the conductance associated with
CO2
G03 is the conductance associated with
CO3
R 1 is the motional resistance
L 1 is the motional inductance
C1
is the motional capacitance
1
(.0 = series resonance frequency (rads/s)
1/2
1 C1)
(L
The transfer admittance function, th
Y,12 for e equivalent circuits shown in figures 3 and 4, describes a circular
locus in the complex admittance plane, as
depicted in figure 5a. The transform of this locus to the impedance (Z
= 1/Y) plane is also a circle as
in figure 5b. There are six characteristic frequencies associated with such a circuit:
fs is the series resonance frequency
fm is the frequency of maximum admittance (minimum impedance)
fr is the resonance frequency (zero ph ase)
fa is the anti-resonance frequency (zero ph ase)
4 is the parallel resonance frequency (lossless)
fn is the frequency of minimum admittance (maximum impedance)
Of these, the series resonance frequency alone is essentially independent of the
value of static capacitance, and is
therefore the parameter of choice for purposes of specification as
it will be little influenced by strays. The
relationships of the characteristic frequencies to fs may be found in IEC 302, or in EIA St
andard 512 (1985).
2.2.2 Three basic methods of measurement are described (see figure 2a):
a) Single-port
reflection method; the crystal resonator is characterized as a one-po rt device with one
electrode driven and all other electrodes and
the crystal enclosure earthed.
In a reflection measurement the admittance Y can be calculated from the measured value of S11.
1-S11
(2.1)
ROY 1 +S 11
NOTE - R o is the value of the standard termination used in calibration of the system.
* The figures in square brackets refer to the bibliography in annex C.

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 11 –
b) Two-port transmission method; the crystal resonator is treated as a two-po rt device with two driven
electrodes, all other electrodes and the crystal enclosure being earthed.
In transmission the transfer admittance of the two-po
rt circuit in figure 4 is:
r
1
+ jc0 Co2 (2.2)
Y12 = 1G02
R 1 + jcoLl +1/ jwC1J
Using the relationships between admittance and scattering parameters we may define, as above, a
quantity Y
^ 1
R Y = R + jwCO2 + I
G02
0 o
Rt
+ j00L1 + 1 /
jwC1J
(2.3)
_ 2S 12
(1
+S11)(1+
l
S22)— S21S12
which is easily calculated from the measured S-parameters.
c) Direct amplitude/phase transmission method. The crystal resonator is treated as a two-terminal
device according to figure 3 in a transmission fixture using nominally resistive elements, as in IEC 444.
The impedance of the device is determined from the amplitude and phase of the signal across the
fixture. Using standard equations, this impedance is converted to an admittance.
1
Y = Go + + (2.4)
jc,)CO
+ +1/ jwCl
R 1 jü)L 1
2.2.3 The S-parameter reflection measurement is potentially the most accurate, only coaxial traceable
as
standard impedances are used for calibration. The S-parameter two-po rt measurement provides most
information about the device, while the direct transmission determines the transimpedance of the device.
2.2.4
Restrictions to the validity of the models
The following approximations are implicit in these equivalent circuits.
a) It is assumed that a lumped circuit representation is valid.
b) It is assumed that the device closely approximates an ideal lossless component, and hence that all
significant resonances have high Q factors.
However, over narrow bandwidths, spanning at most a small percentage of the resonance frequency, the
circuits of figures 6 and 7 provide a very good representation of the resonances in the majority of c ases.
2.2.5 Accuracy and traceability
The accuracy and traceability of the measurements are directly related to the calibration components, and are
largely independent of the particular network analyzer system. However, the system shall conform to the
theoretical models described in annex A, and shall therefore be a linear vector detector system capable of high
accuracy in the ratio mode (AIR etc.); beyond this, no detailed specification need be given. A frequency source
traceable to a national st an
dard of frequency is also required.

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 13 –
2.2.6 Equipment
The use of computer controlled instruments is essential for data collection, error correction, admittance
calculations and for the estimation of the crystal parameters. Error correction a rises from the need to
characterize the measurement circuit. This is achieved by means of a calibration using known st andards of
impedance. Data collection of large numbers of measurement points is required for subsequent admittance
calculations.
2.2.7 Application to other devices
This standard is specifically concerned with single resonator measurements. However, many of the techniques
are directly applicable to more complex devices such as bipoles and monolithic filters; these generalizations
are indicated where appropriate.
2.3 Admittance analysis and estimation of equivalent circuit parameters
There are
four methods (see figure 2b) of admittance analysis leading to the crystal equivalent circuit. If the
crystal being measured is described by the nonnal equivalent circuit and, for instance, the device behaves
linearly, then all these methods are equivalent.
a) General least-squares method
This is the more general non-linear technique which can be applied in all situations. The method is
capable of measuring multiple resonances, such as inharmonics.
b) Linear least-squares method
This method minimizes the sum of the squares of weighted differences between the measured and
theoretical admittan an
ces d is applicable to models with a single resonance.
c) Circle-fitting method
This method fits a circle to an odd number of equally spaced points on the right-hand side of the
admittance circle of the crystal resonator (±45°).
d) Two point iterative method
This is potentially the fastest method and could be used for production. It involves obtaining two
frequencies which lie approximately ±45° on the admittance circle of the resonator. The calculated
crystal parameters are used to re-estimate better values of these two frequencies. Iterations continue
until the estimate is within a given tolerance.
2.4 Normative references
The following normative documents contain provisions which, through reference in this text, constitute
provisions of this part of IEC 444. At the time of publication, the editions indicated were valid. All normative
documents are subject to revision, and parties to agreements based on this part of IEC 444 are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below.
Members of IEC and ISO maintain registers of currently valid Inte rnational Standards.
IEC 302: 1969, Standard definitions and methods of measurement for piezoelect r
ic vibrators operating over
the frequency range up to 30 MHz

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 15 –
IBC 1080: 1991,
Guide to the measurement of equivalent electrical parameters of quartz crystal units
EIA 512: 1985,
Standard methods for measurement of equivalent electrical parameters of quartz crystal units,
1 kHz to 1 GHz
3 Measurement procedures
3.1 General
The procedure for determination of the equivalent circuit parameters of a quartz crystal unit is shown in
figure 8. It is recommended that the crystal enclosure is grounded. In the case of a glass enclosure, the unit is
fitted with a grounded shield cover.
3.2 Environmental control
All crystal devices are influenced to at least some degree by temperature, the rate of ch ange of temperature,
and by the level of drive. It is therefore necessary to protect the device from temperature ch ange during the
period of measurement, and to determine as closely as possible its actual temperature at the time of
measurement, so that measured values can be corrected for differences in temperature between two
measurements. Care shall also be taken to ensure that the d rive level applied during measurement is that
specified for the device. Another possible source of error, when measuring low-frequency, high-Q devices
especially, is unavoidable small temperature drift during the course of the measurement, as relatively long wait
and last data are recorded will cause distortion
times are required. Such slow drifts between the time the first
of the admittance locus. By a first approximation, this can be avoided if alternate points are recorded with
increasing frequency d then the remaining values obtained with decreasing frequency. The least squares
an
estimation methods will effectively average the data so obtained, and thus compensate to a degree for the
differences due to temperature drift.
3.3 Calibration
This is described for each method in clause 5.
3.4 Level of drive
The drive level at fs for the ensuing measurement must be specified either in power or current for that crystal
type. This requires that the output level of the generator be set. If a reasonable estimate of the R t
of the crystal
is known, then this can be used to calculate this level. Alternatively, a quick estimate of the R 1 can be
determined from an initial sweep through the resonance.
3.5 C o measurements
3.5.1 For a one-port measurement at low frequencies the impedance of Co may be much greater than 50 S2.
This results in low sensitivity, and hence poor estimation of the static capacit ance. Sensitivity may be
improved by making a separate measurement at some higher frequency well away from resonance; however, it
is possible that the effective static capacit ance at this frequency will differ from that at resonance. For most
crystal unit types in common use. Co will remain essentially const ant over the frequency range below about
100 MHz. At higher frequencies, it is advisable to measure Co and the other static parameters at frequencies
within a small percentage of the resonance frequency. If the unit will influence the behaviour of wide-band
circuits, it may be necessary to determine the static parameters over a wide frequency r ange.

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 17 –
3.5.2 The measurement of the direct pin-to-pin capacitance Co may be made using one of two methods:
a) For crystals up to 30 MHz, the measurement is to be made at five frequencies slightly above
30 MHz (i.e. 30,1, 30,2, 30,3, 30,4 and 30,5 MHz) and the average of the three values nearest the mean
of the five should be used as the best estimate.
b) For crystals above 30 MHz, it is recommended that three pairs of measurements be made, each pair
being equidistant from the series resonance frequency, fs. i.e. (1 ± 0,05), fs (1 ± 0,06) and fs
fs
and higher frequency is
(1 ± 0,07). For each pair, the mean of the Co values determined from the lower
to be calculated, and then the best estimate taken as the mean of the two such values which are closest
together.
Prior to either measurement a) or b) above, it should be confinned that no spurious responses of the crystal
unit exist at the measurement frequency.
3.5.3 The measurement of the two pin-to-c ase capacitances (usually designated C 13 and C23) when required
by the specification, or to aid in modelling of the transmission fixture, should be made by a separate
measurement with a guarded capacitance bridge.
3.6 Choice of measurement frequencies
Two alternative methods for obtaining admittance data on a crystal resonance can be used. The first is a
multifrequency method used both by the least squares fitting procedure described in 7.1 and 7.2 and the
admittance circle fit described in 7.3.
Here, it is recommended that a total of nine frequency points be used, chosen so that the transadmittance
points determined lie within the right-hand half circle of the Y-pl ane locus (see figure 5a), which implies that
several frequencies should lie within the "Q-bandwidth" centred on the series resonance frequency. The
measurement program must therefore perform a preliminary search for the frequency of series resonance, and
then establish the array of frequencies at which measurements are to be made, based either on an estimate of
the Q furnished by the operator, or from examination of the data. The measurement frequencies may be
equispaced for convenience, and all points should be within a r ange of (ff/2Q) of fs. Additional points outside
this r
ange may also be used, but add little infonnation about the motional parameters of the unit. Closer
ange can be useful if the detection of weak
spacing of the measurement frequencies and coverage of a broader r
unwanted modes is desired. For general purpose use, 9 to 15 data points are adequate, and result in rapid
measurements. For highest accuracy. however. 20 to 30 measurement points are preferred, together with a
stable environment.
The second method is the two-point iterative method described in 7.4.
3.7 Data collection
A c.w. mode of measurement is recommended (rather than swept), with adequate settling time calculated from
g
the estimated Q. There are two reasons for this – first, with most si nal sources available, frequency accuracy
in a slow sweep is degraded and, second, the response of the high-Q crystal devices requires a finite time to
reach equilibrium after the excitation frequency is applied. There are three distinct delay times involved in
such a stepped-frequency mode: a finite time is required for the frequency source to stabilize after being

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 19 –
programmed to a specific value T ins, a finite time for the receiver to stabilize to that new frequency (Tree).
There is also a finite delay while the previously applied frequency response of the crystal decays and the new
response builds to equilibrium value (Tr). At low frequencies with high-Q crystals, Tr may be several hundred
milliseconds, or even seconds.
transmission fixture shows that the new
Analysis of the equivalent circuit of the crystal installed in a two-po rt
response will have settled within 0,1% of its final value in a time of about 2,5 (Qeffifs) after application of the
drive signal, where is the loaded Q-factor of the crystal test fixture. The phase transient will decay to
Qeff
within about 0,1 degree of its final value in the same period. For most purposes, this degree of precision is
adequate; however, for highest precision, it is recommended that this interval be extended to at least
so that no significant distortion of the data will be caused by transient phenomena. Thus, the
3,5 (Qeff/fs),
Td= Tins + Tr
program should set the frequency source to a specific frequency, then wait for a period before
and the average value
measuring the system response. At this time, several measurements should be made
recorded, so that random deviations caused by electrical noise and digitizer errors will be minimized – the
actual number of readings to be averaged can be made a function of the magnitude of the response, as relative
noise level increases as the signal decreases.
Alternatively, the rate of frequency stepping can be determined from repetitive measurements at each
frequency until the phase response has settled down. Averaging of several readings is also recommended as
this minimizes the effects of random and quantization noise.
3.8 Data correction
In the case of the S-parameter methods, the data needs to be corrected by means of error matrices. This is
discussed in annex A. This procedure is not required for direct transmission methods.
3.9 Admittance calculation
For S-parameter methods, this is given by the st andard S-parameter to Y-parameter conversion equations. For
direct transmission methods this procedure is outlined in annex A.
3.10 Admittance analysis and estimation of the equivalent circuit parameters
For the various methods, refer to clause 7.
4 Choice of admittance measurement method
4.1
General
For the vast majority of resonators either one-po rt or two-port characterization is quite satisfactory. As it
provides a more complete desc ription, the two-port transmission method is to be considered as the prime
reference standard. However, in ce rtain situations, the one-port technique may provide information under
conditions more nearly approximating end-use conditions.
4.2 Advantages and disadvantages of the one port S-parameter reflection method
a) This method gives better accuracy and traceability because only coaxial reference impedances are
needed for calibration.

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SIST EN 60444-5:2002
444-5 ©IEC:1995 – 21 –
b) This method is more sensitive than transmission for low R 1 crystals, and will give greater
measurement speed than two-port S-parameter transmission measurements as the error correction
routines are simpler and
fewer responses are measured.
c) It is not very satisfactory for crystals with very high although values up to 1 kS2 can be
R 1,
accommodated.
d) this may not be adequate in some
It characterizes the device as a two-terminal component, and
applications.
e)
Less accurate at frequencies below 100 kHz.
4.3
Advantages and disadvantages of the two-port S-parameter transmission method
a) The crystal is evaluated as a three-terminal device, and more information is available.
b) High R crystals are easily measured.
1
c) Measurement and calibration are more complex, and some additional uncertainties in the calibration
may exist.
d) The method is less sensitive for low R1.
e) If the measurement frequency r ange includes the anti-resonance frequency then ver
...