IEC 60444-9:2007

IEC 60444-9 ®
Edition 1.0 2007-02
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Measurement of quartz crystal unit parameters –
Part 9: Measurement of spurious resonances of piezoelectric crystal units

Mesure des paramètres des résonateurs à quartz –
Partie 9: Mesure des résonances parasites des résonateurs piézoélectriques

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IEC 60444-9 ®
Edition 1.0 2007-02
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Measurement of quartz crystal unit parameters –

Part 9: Measurement of spurious resonances of piezoelectric crystal units

Mesure des paramètres des résonateurs à quartz –

Partie 9: Mesure des résonances parasites des résonateurs piézoélectriques

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX P
ICS 31.140 ISBN 978-2-8322-0881-6

– 2 – 60444-9  IEC:2007
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT OF QUARTZ
CRYSTAL UNIT PARAMETERS –
Part 9: Measurement of spurious resonances
of piezoelectric crystal units

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60444-9 has been prepared by IEC technical committee 49:
Piezoelectric and dielectric devices for frequency control and selection.
This bilingual version (2013-08) corresponds to the monolingual English version, published in
2007-02.
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.
The French version of this standard has not been voted upon.

60444-9  IEC:2007 – 3 –
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
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• withdrawn,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.
– 4 – 60444-9  IEC:2007
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 – 5 –
L L L
1 2 3
C
G
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)
∑
tot 0 0 i
i
with
−1

Y = G + jB =  (i = 1,2,…n) (2)
R +ωjL +

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
a 20⋅log (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
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 – 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
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
– 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, the peak is considered as a
fake.
Lower limit Q :
min
Q = k ·Q  with k = 0,1 … 0,5 (recommended: k = 0,2) (13)
min min 1 min min
The maximum 3 dB half-bandwidth BW for a spurious resonance peak is therefore
max
f
BW = (14)
max
2Q⋅
min
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 greater than according to Q :
max
Y (f )
res peak
≥ 2 (15)
±
Y (f BW )
res peak max
then the selected peak is accepted as a true spurious resonance peak. Otherwise, the
peak is considered as a fake.
i
Resulting parameters: n–1 spurious resonance frequencies f (i = 2 … n)
m
NOTE If the spurious resonances are very close to strong modes, it is recommended that a 1 dB instead of a 3 dB
bandwidth is used. In the above equations, the term 2 must then be replaced by the factor 1,122, and the values
for BW and BW must be changed accordingly.
max min
60444-9  IEC:2007 – 9 –
Increment j by 1
Re(Y(i)) > Re(Y(j–1))
NO
AND
START j = 2
Re(Y(i)) > Re(Y(j+1))
YES
f f
1 1
BW = , BW =
min max
2 × Q 2 × Q
max min
Y(f )
peak
NO
≤ 2
Y(f ± BW )
peak min
YES
Y(f )
peak
NO
> 2
Y(f ± BW )
peak max
YES
Peak is a resonance peak
IEC  326/07
Figure 3 – Flowchart for spurious resonance search
d) zooming of the identified spurious resonances
For each of the true spurious peaks f (i) identified in step c) a new set of admittance
spur
data is taken by zooming the frequency intervals f (i) ± BW with at least N = 11 data
spur max i
points per sweep interval and a minimum sweep time t of
swp
10⋅⋅Q Q
min max
t ≥ (16)
swp
k ⋅ω
min 1
– 10 – 60444-9  IEC:2007
Resulting parameters:
i
Arrays of admittances for each spurious resonance Yf , expressed by the arrays of
( )
raw
i
i i
amplitude Yj , phasearg(Y j ) , and frequency f (j)  with i = 2 … n and j = 1. 11
( ) ( )
res res
e) removal of the admittances of the main mode (i = 1) and of C
i
From each set of raw admittances Yf the contribution of the main mode and of the
( )
raw
static capacitance C are subtracted.
i i
Yf = Yf – Y (f) – Y (f)  (i = 2 … n) (17)
( ) ( )
res raw 1 0
with
−1

Y (f) = R +ωjL + (18)

1 ii
jCω
i

Y ( f ) = jωC (19)
0 0
ω= 2fπ (20)
Resulting parameters:
i
Arrays of admittances for each spurious resonance Yf , expressed by the arrays of
( )
res
i
i i
amplitude Yj , phasearg(Y j ) , and frequency f (j)  with i = 2 … n and j = 1. 11
( ) ( )
res res
f) Calculation of the series resonance frequency and the equivalent parameters of the
strongest (remaining) mode
th
The strongest (remaining) mode is selected. This is the k mode, in which the maximum
value of the real part given by
i
max Re Y f
( )
( ( res ))
is largest.
k
Calculation for the series resonance frequency f , the motional parameters R , C , and L ,
s k k k
k
and the Q-factor Q from Y (f) are given in IEC 60444-5.
k res
Resulting parameters:
k
Series resonance frequency f , motional parameters R , C , L , and Q of strongest
s k k k k
(remaining) mode.
NOTE If the settling time computed from
Q
k
k
t = (21)
set
k
2fπ
s
t
swp
is larger than (see equation (16)), then the measurement of that spurious mode must be repeated with an
N
i
accordingly corrected sweep time.
g) Removal of the evaluated spurious resonance
i th
From all remaining sets of admittances Yf the contribution of the k spurious mode
( )
res
evaluated in f) is subtracted.

60444-9  IEC:2007 – 11 –
i i
Yf := Yf – Y (f) (i = 2 … n, i ≠ k) (22)
( ) ( )
res res
k
with
−1

Y (f) = R +ωjL + (23)

k kk
jCω
k
i
and Y (f) is replaced by the result of the next iteration.
res
h) Continue with step g) for all remaining spurious resonance

i) Evaluation of the validity of the analysis (optional)
From the parameters of all determined spurious resonance modes and the main mode the
total admittance Y can be computed as
tot
−1
n
 
 
Y ( f ) = R + j2πfL + + j2πfC (24)
tot i i 0
∑
 
j2πfC
i
 
i =1
and compared with the admittance Y (f) measured in step c).
res
From the normalized sum of error squares a measure of the quality of data fitting can be
derived.
NOTE As all resonances can influence each other, the sum of error squares can be minimized further by variation
of the parameters C , f(i), R , C and L with i = 1. n.
0 i i i
3.2 Method B (Resistance determination)
The measurement system consists of the same equipment setup as described in IEC 60444-5,
but uses a different test fixture, which consists of a 50 Ω, 180° hybrid coupler, a 10 dB
attenuator and a variable balancing capacitor. All parts are commercially available
components.
Figure 4 shows the electrical circuit diagram of the test fixture. XUT is the crystal under test,
C is a variable capacitor of 1 ~ 10 pF range. The 50 Ω, 10 dB attenuator is a device having
bal
the lowest possible VSWR in the measurement frequency range, which is commercially
available from a number of sources. The 180° hybrid coupler (or “two-way 0°/180° power
splitter/combiner”) is a commercially available device with 50 Ω termination, suitable for the
frequency range to be measured. Example: type PSCJ2-1 (Mini-Circuits Laboratory, Brooklyn,
N.Y.) for 1 MHz up to 200 MHz.
The mechanical layout of the test fixture must take into account the principles of RF
engineering with low stray capacitances and good shielding between input and output.

– 12 – 60444-9  IEC:2007
XUT
0° OUT
180° hybrid
10 dB attenuation
IN OUT
coupler
180° OUT
C
bal
IEC  327/07
Figure 4 – Electrical diagram of the test fixture for method B
NOTE For automatic operation the variable capacitor can be replaced by two varactor diodes of suitable C(V)
characteristics, which are connected in anti-series and biased accordingly.
3.2.1 Measurement procedure
3.2.1.1 Initial calibration
The RF output level of the generator at the input port must be adjusted so that the maximum
drive level specified is not exceeded.
– Short
Insert a short at the XUT ports. Set C to its minimum capacitance value.
bal
Read complex output voltage U
S
– “Open” balancing
Insert a small capacitor C of about 2 pF to 5 pF at the XUT port, set C to minimum
open bal
The output amplitude should be at least 60 dB lower
and read complex output voltage U
0.
than the short-circuit output voltage

U
S
20⋅log  ≥60 (25)

U

– Reference
Add a reference resistor R of 50 Ω or 100 Ω at the XUT port in parallel to C .
ref open
Read complex output voltage U
ref.
From the complex output voltages U and U compute the (complex) fixture impedance
S ref
R
T
R
ref
R = (26)
T
 U 
S
−1
 
U
 ref 
|R | should be in the order of 100 Ω ± 10 %
T
NOTE In the following, evaluations of the phase measurements are disregarded, only the amplitude
measurements are considered.
60444-9  IEC:2007 – 13 –
3.2.1.2 Response measurement
– Initial balancing
With the crystal unit under test inserted, set the sweep frequency range to about ±500 kHz
or wider. Tune the variable capacitor C for an overall symmetric response shape as
bal
depicted in Figure 5.
–10
–20
–30
–40
–50
–60
–70
–80
20 500 000 21 000 000 21 500 000
Frequency  Hz
IEC  328/07
Figure 5 – Balanced setting of C yields a symmetric frequency response
bal
– Measurement with visual aid
Scan the specified frequency range FR . The sweep time should be as derived in
spur
equations (6) to (8). Inspect visually the amplitude spectrum of spurious resonance peaks.
For more accurate evaluation, the frequency range of individual spurious responses may
be zoomed on the display. The sweep time of the sub-intervals should also be according
to equation (8)
a) Strong spurious resonance modes
For spurious resonance peaks which are well-separated from adjacent responses, and
which are at least 20 dB above the bottom line, the (maximum admittance) frequency
i i
f is located at the peak voltage U and the (maximum admittance) resistance
m m
i
R can be evaluated as
m

U
i S
RR=⋅−1 (27)
mT
i

U
m

If the amplitude is given as attenuation in dB relative to the reference calibration with
i i
R , then the (maximum admittance) resistance is determined from as
R a
ref m ref
i
a
ref
i
R 10 ⋅+R R −R (28)
( )
m T ref T
Relative attenuation
=
– 14 – 60444-9  IEC:2007
i
In most cases it is sufficient to use the magnitude values of R , U and U instead of
m
T S
their complex values.
b) Weak spurious resonance modes
...