IEC 60444-11:2010

IEC 60444-11 ®
Edition 1.0 2010-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
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

Mesure des paramètres des résonateurs à quartz –
Partie 11: Méthode normalisée pour la détermination de la fréquence de
résonance à la charge f et de la capacité de charge efficace C utilisant des
L Leff
analyseurs automatiques de réseaux et correction des erreurs

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IEC 60444-11 ®
Edition 1.0 2010-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
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

Mesure des paramètres des résonateurs à quartz –
Partie 11: Méthode normalisée pour la détermination de la fréquence de
résonance à la charge f et de la capacité de charge efficace C utilisant des
L Leff
analyseurs automatiques de réseaux et correction des erreurs

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
N
CODE PRIX
ICS 31.140 ISBN 978-2-88912-210-3
– 2 – 60444-11 © IEC:2010
CONTENTS
FOREWORD.3
1 Scope.5
2 Normative references .5
3 General concepts .6
3.1 Load resonance frequencies f and f .6
Lr La
3.2 Effective load capacitance C .6
Leff
4 Reference plane and test conditions.7
4.1 General .7
4.2 Principle of measurement .7
4.3 Evaluation of errors .10
Bibliography.14

Figure 1 – Admittance of a quartz crystal unit .6
Figure 2 – X as a function of frequency (solid line) in the vicinity of f .9
C L
Figure 3 – Level of drive of a crystal in a π-network vs. frequency .9
Figure 4 – Error of the load resonance frequency due to the inaccuracy of the
measured voltages (dashed line) and the calibration resistances (soft line) .11
Figure 5 – C -error resulting from f error (due to inaccuracy of the measured voltages
L L
and the calibration resistances) for the same crystal as in Figure 4.11
Figure 6 – Frequency error due to noise of the measured voltages .12
Figure 7 – Error of load resonance frequency f at 30 pF and 10 pF for typical
L
equivalent parameters of quartz crystal units .12
Figure 8 – Error of C for typical equivalent parameters of quartz crystal units .13
Leff
60444-11 © IEC:2010 – 3 –
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
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60444-11 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 standard is based on the following documents:
CDV Report on voting
49/852/CDV 49/883/RVC
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.

– 4 – 60444-11 © IEC:2010
A list of all parts of the IEC 60444 series 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 amendment and the base publication will
remain unchanged until the stability date indicated on the IEC web site under
"http://webstore.iec.ch" in the data related to the specific publication. At this date, the
publication 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.
60444-11 © IEC:2010 – 5 –
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

1 Scope
This part of IEC 60444 defines the standard method of measuring load resonance frequency
f at the nominal value of C , and the determination of the effective load capacitance C at
L L Leff
the nominal frequency for crystals with the figure of merit M > 4.
M, according to Table 1 of IEC 60122-1:2002, is expressed in the following equation:
Q 1
M = = (1)
r ωC0R1
This gives good results in a frequency range up to 200 MHz. This method allows the
calculation of load resonance frequency offset Δf , frequency pulling range Δf and pulling
L L1,L2
sensitivity S as described in 2.2.31 of IEC 60122-1:2002. 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 30MHz by the method of IEC 60444-4 to 200MHz approximately.
This method is based on the error-corrected measurement technique of IEC 60444-5:1995,
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.
XC = −XCL = (2)
ωLCL
Furthermore this method allows to determine the effective load capacitance C at the
Leff
nominal frequency f .
nom
2 Normative references
The following referenced documents are indispensable for the application 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/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

– 6 – 60444-11 © IEC:2010
3 General concepts
3.1 Load resonance frequencies f and f
Lr La
As can be seen in Figure 1, there are two intersection frequencies where XX=− , f with
CCL
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
L
with 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
L
the lower of the two frequencies.
f can be calculated by:
In a first approximation
L
LCC()+C
11 0 L
≈π2 (3)
fC++CC
L10L
f
f
m
f
s
ω ⋅ C
Conductance
f
γ
f
a
ω ⋅ C
L
f f
La
Lγ
R
2R R
γ
IEC  2353/10
Figure 1 – Admittance of a quartz crystal unit
3.2 Effective load capacitance C
Leff
C is defined by the reactance of the crystal at the nominal frequency

Leff
Susceptance
60444-11 © IEC:2010 – 7 –
C Leff = (4)
ω nom XC(ω nom)
4 Reference plane and test conditions
4.1 General
Reference plane: as in 8.4 of IEC 60444-5:1995.
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 4.2.
4.2 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.
Similar to IEC 60444-5:1995, 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;
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
V is the error-corrected “short” voltage
s
V is the error-corrected “open” voltage
o
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);
Z1Z 2(V1− V 2) + Z 2Z3(V 2 − V 3) + Z 3Z1(V 3 − V1)
RT = (5)
Z1(V 2 −V 3) + Z 2(V 3 − V1) + Z 3(V 2 − V 2)

– 8 – 60444-11 © IEC:2010
V 3Z1Z 2(V1− V 2) + V1Z 2Z 3(V 2 − V 3) + V 2Z 3Z1(V 3 − V1)
VS = (6)
Z1Z 2(V1− V 2) + Z 2Z3(V 2 − V 3) + Z 3Z1(V 3 − V1)
Z1V1(V 2 −V 3) + Z 2V 2(V 3 − V1) + Z3V 3(V1− V 2)
V 0 = (7)
Z1(V 2 − V 3) + Z 2(V 3 − V1) + Z 3(V1− V 2)
NOTE If Z is taken as infinite number (ideal open circuit), the above Equations (5), (6) and (7) result is not
allowed divisions of infinite by infinite.
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:
(V S−V C)
ZC = R T (8)
(V C−V 0)
d) Measurement procedure for f
L
At load resonance frequency, the impedance of a quartz crystal unit is
Z =+RjX (9)
CL L c
For the determination of the load resonance frequency, the frequency f the lower
L
frequency is searched for which Equation (2) is fulfilled, i.e.
XX+= 0 (10)
CCL
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==ωωReZ (11)
() ()()
Lc L c L
may 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
In all other cases, the R should be computed from the equation given in IEC 60122-1:
L
⎛⎞C
RR=+1 (12)
⎜⎟
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 equation:
Leff
CLeff = (13)
ω nom XC(ω nom)
60444-11 © IEC:2010 – 9 –
Figure 2 shows X as a function of frequency (solid line) in the vicinity of f .
L
C .
780 1 -5
X =
C
770 ω ⋅ C -10
L
760 -15
750 -20
740 -25
X
CL
730 -30
720 -35
710 -40
700 -45
-500 -400 -300 -200 -100 100 200
Δ frequency (ppm)
f
S f
f
LL
X (Ω)
C
V
c
IEC  2354/10
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
100 %
10 %
1 %
-500 -400 -300 -200 -100 100 200 300
f f
s L
df/f  (ppm)
nom
P {f }/P {f }
eff L max s
IEC  2355/10
Figure 3 – Level of drive of a crystal in a π-network vs. frequency
with
V
xr
P = (14)
R
r
and
Vg Rr
VXr = (15)
Rr + RT
X (Ω)
P {f }/P {f } C
eff L max s
V
C
– 10 – 60444-11 © IEC:2010
Rr + RT
Vg = PRr (16)
Rr
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
|Z | = RX+ (17)
LL
L
and therefore the drive level is
V
xr
P =
Z
L
22 2
XX11++R+R +RR+R −
() ()
CL()CL L T L()L T
V =⋅PR⋅
(18)
gL 1
RX+
LCL
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
2 2
(RL + RT) + XCL
⎡VgL⎤ Rr
ABS = (19)
⎢ ⎥
Vgr RL Rr + RT
⎣ ⎦
NOTE 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 ABS lower level and the difference of both series resonance measurements
⎜⎟
r
⎜⎟
V
gr
⎝⎠
is added to the load resonance frequency f .
L
4.3 Evaluation of errors
a) 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

L
capacitance C can be calculated then from the frequency accuracy and the equivalent
Leff
parameters of the crystal C and C from the relation

0 1
ff− C
Ls 1
= (20)
f 2()CC+
s0L
b) 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 be necessary to
calibrate the test equipment in the whole power range.

60444-11 © IEC:2010 – 11 –
Typ. frequency error: at CL 10 pF (S = -75,45 ppm/pF): ±16,1 ppm (equiv.: ±0,21 pF)
-35,30
-35,40
Impedance error of test head and
-35,50
calibration s tandards : ±0,5 %
-35,60
-35,70
-35,80
Resolution of V : ±0,05 dB
-35,90 c
-36,00
0 5
-20 -15 -10 -5 10 15 20
df/f  (ppm)
nom
V Max. frequency error
c
IEC  2356/10
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)

10,30
10,20
10,10
10,00
9,90
9,80
9,70
-20 -15 -10 -5 10 15 20
df/f  (ppm)
nom
IEC  2357/10
Figure 5 – C -error resulting from f error (due to inaccuracy of the measured voltages
L L
and the calibration resistances) for the same crystal as in Figure 4
c) Reproducibility
Since the determination of the load frequency is based on a voltage measurement, the
reproducibility of the f measurement is influenced by noise.
L
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 the use of an averaged
signal.
C  (pF)
L
V  (dB)
m
– 12 – 60444-11 © IEC:2010
frequency error caused by m easured noise
Frequency error caused by measured noise
-29,00
-29,0
-29,20
-29,0
--29,29,400
-29,0
-29,60
r
-29,0 Frequency error
-29,80
-30,0
-30,00
-20 -15 -10 -5 10 15 20
-20 -15 -10 -5 0 5 10 15 20
df/f (ppm)
df/f [ppm ]
V  (dB)
C
Theoretical signal
theoretical signal measured amplitude
Error
V [dB]
Signal noise ±0,05 dB
c
signal noise ±0,05dB error
IEC  2358/10
Figure 6 – Frequency error due to noise of 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
Figure 7 – Error of load resonance frequency f at 30 pF and 10 pF
L
for typical equivalent parameters of quartz crystal units
V  (dB)
C
df error ± (ppm) VDUT[dB]
dC at f ± (pF)
L
60444-11 © IEC:2010 – 13 –
0,25
0,20
Fund.
15 0,15
0,10
0,05
rd
3 overtone
0 0,00
1 10 100
Frequency  (MHz)
C tolerance at f {10 pF} ± (pF)
df error at 10 pF ± (ppm)
L nom
IEC  2360/10
Figure 8 – Error of C for typical equivalent parameters of quartz crystal units
Leff
d) Comparison with the method of IEC 60444-4
The inaccuracy of the measurement of the load resonance frequency f according to
L
IEC 60444-4 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 the formula (20).
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 wi
...