IEC 60444-9:2007

INTERNATIONAL IEC
STANDARD 60444-9
First edition
2007-02
Measurement of quartz crystal unit parameters –
Part 9:
Measurement of spurious resonances
of piezoelectric crystal units
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INTERNATIONAL IEC
STANDARD 60444-9
First edition
2007-02
Measurement of quartz crystal unit parameters –
Part 9:
Measurement of spurious resonances
of piezoelectric crystal units
© IEC 2007 ⎯ Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
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– 2 – 60444-9 © IEC:2007(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT OF QUARTZ
CRYSTAL UNIT PARAMETERS –
Part 9: Measurement of spurious resonances
of piezoelectric crystal units

FOREWORD
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International Standard IEC 60444-9 has been prepared by IEC technical committee 49:
Piezoelectric and dielectric devices for frequency control and selection.
The text of this standard is based on the following documents:
FDIS Report on voting
49/764/FDIS 49/774/RVD
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.

60444-9 © IEC:2007(E) – 3 –
A list of all parts of 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 publication will remain unchanged until
the maintenance result 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• withdrawn,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.
A bilingual version of this standard may be issued at a later date.

– 4 – 60444-9 © IEC:2007(E)
MEASUREMENT OF QUARTZ
CRYSTAL UNIT PARAMETERS –
Part 9: Measurement of spurious resonances
of piezoelectric crystal units

1 Scope
This part of IEC 60444 describes two methods for determining the spurious (unwanted) modes
of piezoelectric crystal resonators. It extends the capabilities and improves the reproducibility
and accuracy compared to previous methods.
The previous methods described in IEC 60283 (1968) were based on the use of a measuring
bridge, which applies to non-traceable components such as variable resistors and a hybrid
transformer, which are no longer commercially available.
Method A (Full parameter determination)
Full parameter determination allows the determination of the equivalent parameters of the
spurious resonances and is based on the methods described in IEC 60444-5 using the same
measurement equipment. It is the preferred method, which can be applied to the
measurement of low and medium impedance spurious resonances up to several kΩ.
Method B (Resistance determination)
Resistance determination should be used for the determination of high impedance spurious
resonances as specified, for example for certain filter crystals. It uses the same test
equipment as method A in conjunction with a test fixture, which consists of commercially
available microwave components such as a 180° hybrid coupler and a 10 dB attenuator, which
are well-defined in a 50 Ω environment. This method is an improvement to the “reference
method” of the obsolete IEC 60283.
2 Overview
Piezoelectric crystal units show multiple resonances, which can be electrically represented by
a parallel connection of a number of series resonant circuits. The one-port equivalent circuit
of the complete crystal unit is shown in Figure 1 (taken from IEC 60444-5).

60444-9 © IEC:2007(E) – 5 –
L L L
1 2 3
C
G 0
C C C
1 2 3
R R R
1 2 3
IEC  324/07
Figure 1 – General one-port equivalent circuit for multiple resonances
The total admittance Y of the equivalent circuit for n resonance modes is therefore
tot
Y = G + jωC + Y (1)
∑ i
tot 0 0
i
with
−1
⎛⎞
Y = G + jB = Rj+ωL +  (i = 1,2,…n) (2)
⎜⎟
i i i ii
jCω
⎝⎠i
Index i = 1 represents the main mode, while i = 2 … n represents the spurious resonance
modes.
The spurious modes are regarded as uncoupled modes. Coupled modes can also be found by
the described test methods, however their strong amplitude dependence does not allow for
the precise determination of their parameters.
i
The attenuation a , of a spurious mode i, is defined as the logarithmic ratio (expressed in
spur
dB) of its resistance R , to the resistance R of the main mode:
i 1
⎛⎞R
i i
a2=⋅0log (3)
⎜⎟
spur 10
R
⎝⎠1
Figure 2 shows a typical spectrum for the spurious resonances of an AT-cut quartz crystal unit
as displayed on a spectrum analyzer using a π-network according to IEC 60444-1.

– 6 – 60444-9 © IEC:2007(E)
20 900 000 21 000 000 21 100 000 21 200 000
Frequency  Hz
IEC  325/07
Figure 2 – Spectrum of spurious responses
NOTE The attenuation values measured on a network analyzer depend on the termination resistance of the test
fixture used (e.g. 25 Ω for a π-network of IEC 60444-1). They are different from the spurious attenuation as
computed from equation (3).
NOTE The frequencies and attenuation values measured on a network analyzer are different if the crystal
resonator is connected to a load capacitor.
See also note under 3.2.1.2.
3 Measurement methods
The following measurement parameters are necessary and should be given in the detail
specification:
• frequency range of the spurious resonances FR to be evaluated;
spur
• level of drive.
Care must be taken in selecting a suitable measurement (sweep) time.
3.1 Method A (Full parameter determination)
The measurement system consists of a π-network or an s-parameter test fixture in
accordance with IEC 60444-1 and IEC 60444–5 in conjunction with a network analyzer or an
equivalent setup.
The admittance of the crystal is measured within the specified frequency range FR . The
spur
spurious resonances are isolated with the method of successive removal of resonances. From
the admittance data, the equivalent circuit parameters of the various resonance modes are
computed using one of the evaluation procedures described in IEC 60444-5.
3.1.1 Measurement procedure
The technique is described in more detail in [1] . The measurement sequence is as follows:
a) measurement of the static capacitance C as in IEC 60444-5;
—————————
Figures in square brackets refer to the bibliography.
Attenuation  dB
60444-9 © IEC:2007(E) – 7 –
b) measurement of the main mode parameters (i = 1) as in IEC 60444-5, the resulting
parameters are:
ω
series resonance frequency f = f =
s 1
2π
equivalent electrical parameters R , C , and L , and
1 1 1
ω L 1
1 1
quality factor Q = Q = = (4)
R ω C R
1 1 1 1
c) measurement of the complex admittance Y (f) in the specified frequency range FR
res spur
Measurement parameters:
Assuming
Q , Q , …Q ≈ Q (5)
2 3 n 1
the minimum settling time t for each frequency is:
set
Q
t =  (6)
set
ω
For at least two data points within the resonance bandwidth, the minimum number of data
points N is
FR
spur
N = 2 ⋅ (7)
Q
The minimum sweep time t is then
swp
t = t · N (8)
swp set
NOTE If necessary the frequency sweep range FR must be divided into several sub-intervals.
spur
Resulting parameters:
The array of complex admittance Y (f), expressed, for example as arrays for magnitude
res
|Y (j)|, phase Φ (j) and frequency f(j) with j = 1,2, … N and f(1) = f1, the frequency of
res res
the main mode.
Search for spurious resonance peaks
The search for spurious resonances requires several steps to distinguish the resonance
peaks from noise peaks and from broadband responses.
See flowchart in Figure 3 for reference.
– Identify local maxima of Re(Y (j)) for neighbouring data points (j –1, j, j +1)
res
For the analysis the real part of the admittance is used.
Re(Y (j)) = |Y (j)|·cos(Φ (j)) (9)
res res res
For j = 2 …N–1 the admittance values are analysed as follows:
If
Re(Y (j)) > Re(Y (j–1)) and Re(Y (j)) > Re(Y (j+1))
res res res res
then
f f(j) is a candidate for a spurious resonance peak.
peak =
– 8 – 60444-9 © IEC:2007(E)
– Distinguish between real peaks and fake peaks
Fake peaks due to noise, etc. can be identified by assuming a realistic Q-value for the
spurious resonances with respect to Q as determined in step b).
Upper limit Q :
max
Q = k ·Q  with k = 2 … 10 (recommended: k = 5) (10)
max max 1 max max
The minimum 3 dB half-bandwidth BW for a spurious resonance peak is therefore
min
f
BW =  (11)
min
2Q⋅
max
For each candidate for a spurious resonance peak, the data points next to |Y (f )|
res peak
are inspected. If the amplitude at each side is less than according to Q :
max
Y(f )
res peak
≤ 2 (12)
Y(f ±BW )
res peak min
then this peak is still accepted as a candidate. Otherwise, th
...