# IEC 60444-11:2010

(Main)## Measurement of quartz crystal unit parameters - Part 11: Standard method for the determination of the load resonance frequency f_{L} and the effective load capacitance C_{Leff} using automatic network analyzer techniques and error correction

## Measurement of quartz crystal unit parameters - Part 11: Standard method for the determination of the load resonance frequency f<sub>L</sub> and the effective load capacitance C<sub>Leff</sub> using automatic network analyzer techniques and error correction

IEC 60444-11:2010 defines the standard method of measuring load resonance frequency fL at the nominal value of CL, and the determination of the effective load capacitance CLeff at the nominal frequency for crystals with the figure of merit M > 4.

## Mesure des paramètres des résonateurs à quartz - Partie 11: Méthode normalisée pour la détermination de la fréquence de_résonance à la charge f<sub>L</sub> et de la capacité de charge efficace C<sub>Leff</sub> utilisant des analyseurs automatiques de réseaux et correction des erreurs

La CEI 60444-11:2010 définit la méthode normalisée de mesure de la fréquence de résonance à la charge fL à la valeur nominale de CL et la détermination de la capacité de charge efficace CLeff à la fréquence nominale pour des résonateurs de facteur de mérite M > 4.

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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

IEC 60444-11:2010

---------------------- Page: 1 ----------------------

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---------------------- Page: 2 ----------------------

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

CODE PRIX

ICS 31.140 ISBN 978-2-88912-210-3

® Registered trademark of the International Electrotechnical Commission

Marque déposée de la Commission Electrotechnique Internationale

---------------------- Page: 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 La3.2 Effective load capacitance C ...............................................................................6

Leff4 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 LFigure 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 themeasured 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 Land 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 typicalequivalent parameters of quartz crystal units ........................................................................12

Figure 8 – Error of C for typical equivalent parameters of quartz crystal units ..................13

Leff---------------------- Page: 4 ----------------------

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

international co-operation on all questions concerning standardization in the electrical and electronic fields. To

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Publications.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.

---------------------- Page: 5 ----------------------– 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 correctunderstanding of its contents. Users should therefore print this document using a

colour printer.---------------------- Page: 6 ----------------------

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 Leffthe 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 1M = = (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,L2sensitivity 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 Leffequivalent 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 Copposite 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

Leffnominal 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

resonance resistance R and the calculation of other derived values of quartz crystal units, up

to 30 MHzIEC 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---------------------- Page: 7 ----------------------

– 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

CCLhigh admittance (low impedance) and f with low admittance (high impedance).

The load resonant frequency f is one of the two frequencies of a crystal unit in association

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

the lower of the two frequencies.f can be calculated by:

In a first approximation

LCC()+C

11 0 L

≈π2 (3)

fC++CC

L10L

ω ⋅ C

Conductance

ω ⋅ C

f f

2R R

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

---------------------- Page: 8 ----------------------

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-networkV is the error-corrected “short” voltage

V is the error-corrected “open” voltage

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)

---------------------- Page: 9 ----------------------

– 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

From the measured voltage with a quartz crystal unit V , the impedance Z of the quartz

c ccrystal unit is calculated with:

(V S−V C)

ZC = R T (8)

(V C−V 0)

d) Measurement procedure for f

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

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».

functions.e) Evaluation of R

The computation of the load resonance resistance R from the real part of Z at the load

L cresonance frequency f by the formula:

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°.Only for < 10 this method yields reasonable results.

In all other cases, the R should be computed from the equation given in IEC 60122-1:

⎛⎞CRR=+1 (12)

⎝⎠L

f) Measurement procedure for C

Leff

The reactance X ( ω ) is measured at the nominal frequency and the effective load

c nomcapacity C is then calculated with the following equation:

Leff

CLeff = (13)

ω nom XC(ω nom)

---------------------- Page: 10 ----------------------

60444-11 © IEC:2010 – 9 –

Figure 2 shows X as a function of frequency (solid line) in the vicinity of f .

C .

790

780 1 -5

X =

770 ω ⋅ C -10

760 -15

750 -20

740 -25

730 -30

720 -35

710 -40

700 -45

-500 -400 -300 -200 -100 100 200

Δ frequency (ppm)

S f

X (Ω)

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

given by the voltage V across the crystal100 %

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

P = (14)

and

Vg Rr

VXr = (15)

Rr + RT

X (Ω)

P {f }/P {f } C

eff L max s

---------------------- Page: 11 ----------------------

– 10 – 60444-11 © IEC:2010

Rr + RT

Vg = PRr (16)

At load resonance frequency f , the impedance Z of a quartz crystal unit is given by the

L Lload resonance resistance R and the modulus of the reactance of the load capacitor X :

L L|Z | = RX+ (17)

and therefore the drive level is

P =

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

frequency f , it is necessary to increase the output power of the generator by the ratio:

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

⎛⎞Vf is performed with a by factor ABS lower level and the difference of both series resonance measurements

is added to the load resonance frequency f .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

capacitance C can be calculated then from the frequency accuracy and the equivalent

Leffparameters 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.---------------------- Page: 12 ----------------------

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

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 Land 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.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)

V (dB)

---------------------- Page: 13 ----------------------

– 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

-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)

Theoretical signal

theoretical signal measured amplitude

Error

V [dB]

Signal noise ±0,05 dB

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

for typical equivalent parameters of quartz crystal units

V (dB)

df error ± (ppm) VDUT[dB]

dC at f ± (pF)

---------------------- Page: 14 ----------------------

60444-11 © IEC:2010 – 13 –

0,25

0,20

Fund.

15 0,15

0,10

0,05

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

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 with the 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 method.e) Limitations

This method shall not be used for measurements of aging and for the measurement of

load resonance in the temperature range due to the still remaining measurementuncertainty.

In the presence of activity dips, the described method may yield unacceptable results and

therefore care should be taken.If narrow frequency tolerances of f are required in an application, it is recommended to

determine the effective C of the application circuit by a correlation measurement.

Generally the error of f becomes large when C is smaller than 10 pF or 2 × C .L L 0

___________

Figures in square brackets refer to the bibliography.

df error ± (ppm)

dC at f ± (pF)

---------------------- Page: 15 ----------------------

– 14 – 60444-11 © IEC:2010

Bibliography

[1] NEUBIG, Bernd: PI-Network Measurement of the Load Resonance Frequency without

Load Capacitor, Proc. 4 European Frequency and Time Forum (EFTF), pp.481-486,1990

[2] ZIMMERMANN, Rolf: Messung der Lastresonanzfrequenz von Schwingquarzen ohne

physikalische Lastkapazität, Report Tele Quarz, 31.3.1995

[3] ROSE, Dwane: Load Resonant Measurements of Quartz Crystals, www.saunders-

assoc.com

[4] LEE, Arthur and CHAN, K.: Direct Impedance Method for Load Resonant Measurement

of Crystals; Proc. 21 Piezoelectric Devices Conference & Exhibition, 1999[5] VAN HERWIJNEN, M.and SOHRE, Frieder K.C.: Load-Resonance Measurement

Accuracy of Ceramic Surface Mount Quartz Crystals, Proc. 14 European Frequency

and Time Forum (EFTF), 2002

___________

---------------------- Page: 16 ----------------------

– 16 – 60444-11 © CEI:2010

SOMMAIRE

AVANT-PROPOS..................................................................................................................17

1 Domaine d’application ....................................................................................................19

2 Références normatives...................................................................................................19

3 Concepts généraux ........................................................................................................20

3.1 Fréquences de résonance à la charge f et f .....................................................20

Lr La3.2 Capacité de charge efficace C ..........................................................................21

Leff4 Plan

**...**

## Questions, Comments and Discussion

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