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NBSIR 77-855 doNOTJEMOVB^^

QUARTZ CRYSTAL OSCILLATORS WITH

LOW ACCELERATION SENSITIVITY HEGOVEO

DATE...¥Z/^.z. - OTP.-

^

J. J. Gagnepain

F. L. Walls

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

March 1977

NBSIR 77-855

I QUARTZ CRYSTAL OSCILLATORS WITH

LOW ACCELERATION SENSITIVITY

J. J. Gagnepain

F. L. Walls

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

March 1977

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Betsy Ancker-Johnson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

QUARTZ CRYST7xI. OSCILLATORS WITH LOW ACCELERATION SENSITIVITY

J. J. Gagnepaiii* and F. L. Walls**

The acceleration sensitivity of quartz crystal resonators

imposes severe limitation on their use in non-laboratory environments. This work shows that by using two resonators connected

in series and properly orientated with respect to one another,

it is possible to substantially reduce the net acceleration

sensitivity of the composite or compound crystal resonator. First

qualitative experimental results on acceleration, also some ex- perimental theories of studies related to the introduction of the

two resonators comprising the compound resonator, are presented.

From these studies it appears feasible to fabricate compound

crystal resonators exhibiting acceleration sensitivities at least

10 times STialler than the resonators used individually.

Key words: Acceleration field: acceleration sensitivity:

compound crystal resonator: crystalographic axis; non-linear

elastic effect: resonance frequency.

When a quartz crystal resonator is in an acceleration field, the

induced body forces and the reaction forces give a static or quasistatic deformation. Because of the non-linear elastic effects, an interaction occurs between the elastic wave and this static deformation,

changing the wave velocity, and by a small amount, the crystal sizes.

The result is a variation of the resonance frequency, related to the

applied acceleration field direction, as shown in Fig. 1 [1].

FIGURE 1 Frequency variation of a quartz resonator for

several different directions of applied force.

* Laboratoire de Physique et Metrologie des Oscillateurs

** National Bureau of Standards
For a practical application, the acceleration field T can be represented by the two vector components: parallel to the y' axis (therefore perpendicular to the plane of the crystal), and in the crystal

plane /

FIGURE 2 Decomposition of the generalized vector,

r, into two components, F3 and Fi, which are referenced to the x and y' crystalographic

axis

.

where cx is the azimuth angle betweenF^ and the X crystalographic axis.

See Fig, 2.

Rotating the crystal plate around the y' aixis, it is possible to

find some particular values of ot for which the sensitivity due to F is approximately zero.

^

For a given crystal technology, the effect of T ^ cannot be reduced

with only one crystal. However, using two crystal resonators oriented

as mirror images with respect to the y' axis connected in series can lead to first-order cancellation of the acceleration effect.

Fig. 3 shows the equivalent circuit for two crystal resonators

connected in series.

h Ri

FIGURE 3 The equivalent circuit for two crystal resonators connected in series.

2
Solving the equation for j^-j^ yields:

i,2

e| IR^V+R2U-2L^U)^R2Yq'^2 -2L2'^2Vo'^1^^ IR3_R2 (C^a33_+ToW2 ^ ^2L^W^Xv+2L2a)2y'^]

with u = 1 -2L C^^^^

V = 1 - ^^£<0^2 ^

X = 4f y = Af - £ = F - F,

F is the driving frequency.

F^ is the series resonance frequency of the 1st resonator, F^ is the

series resonance frequency of the 2nd resonator and

e is the difference between the frequencies F^ and F^

.

Calculated variations of |^| as a function of the driving frequency

and various parameters are represented in Fig. 4,5,6, and 7:

Fig. 4) Parameter: parallel capacitor C^; F^ = 10 MHz,

Fig. 5) Parameter: '^^r F^ = 10 MHz,

Fig. 6) Parameter: F^ = 10 MHz,

Fig. 7) Parameter: e; F^ = 10 MHz.

Figure 8 shows the experimental results obtained with a pair of 3rd

overtone AT cut 10 MHz crystals whose resonance frequencies are widely

separated. Figure 9 shows the experimental results with a pair of 3rd

overtone AT cut 10 MHz crystals. Figure 10 shows the results for a pair

of 5th overtone AT cut 5 MHz crystals manufactured at the Ecole Nationale

Superieure de Chronometrie et Micromecanique (ENSCM)

.

The experimental curves verify that the series connected resonators

essentially produce a single resonance curve even when the individual

resonance frequencies differ by more than the linewidth. This means that

3
resonators need only be reasonably close in frequency which is easily

satisfied by current manufacturing tolerances. In fact the separation

of curves A and B in Fig. 8 (350 Hz is more than 5 times larger than

standard tolerance for these types of crystals .

Using crystal blanks from Manufacturer A, two resonators have been

mounted using glass tiibes as supports, their individual resonance frequencies were:

Quartz A) = 10 000 155 Hz,

Quartz B) F = 9 998 805 Hz. o

These resonators were connected in series and used in the circuit shown in

Fig. 11. The frequency response has two peaks: a very small one at

F = 10 000 800 Hz and a large one at f = 9.999 049 Hz which was used for

the measurements.

This circuit was mounted on a loudspeaker and subjected to vibrations

at a frequency of 500 Hz.

a) For constant amplitude sinusoidal acceleration in the r3 or y"

direction the phase variation amplitudes which is proportional to the

frequency difference between the compound crystal resonator and the

driving frequency, was:

Quartz A alone: amplitude 0.07 V per arbitrary unit of acceleration

Quartz B alone: amplitude 0.15 V

Quartz A + B: amplitude 0.05 V

b) By proper rotations of the crystals about the y' axis the

acceleration sensitivity could be reduced to the noise level, or less

than .01 div. The noise was primarily due to thermal transient effects

caused by the lack of enclosures around the resonators.

Although the two individual resonators do not have the same acceleration sensitivities, the compound crystal nevertheless, exhibits a substantial reduction in acceleration sensitivity. Also the acceleration sensitivities

of production crystals should be inherently much more closely matched than

these two prototype crystals. It therefore appears that a factor of 10

reduction in acceleration sensitivity can be achieved without elaborate

matching techniques.

4
These first experiments show qualitatively that it is possible

to decrease the total acceleration sensitivity of a quartz crystal

oscillator using two resonators in series. Further work in this area needs to be done to quantitavely demonstrate the amount of

acceleration desensitization that can be achieved .

To obtain quantitative results, improved mounting including

good enclosures and an improved measurement system are necessary.

Reference [1] Influence of environment conditions on a quartz

resonator. M. Valdois, J.J. Gagnepain, J. Besson.

Proc. 28th Annual Freq, Contr. Symp. , Fort Monmouth,

NJ, 1974.

Acknowledgment

We would like to thank S. Jarvis for writing the computer program

used in calculating the effect of various parameters on the resonate

behavior of the resonators.

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NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 77-855

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLI-: AND SUBTITLE

QUARTZ CRYSTAL OSCILLATORS WITH LOW ACCELERATION

SENSITIVITY

5. Publication Date March 1977

6. Performing Organization Code

277.04

7. AUTHOR(S)

J. J. Gagnepain and F. L. Walls

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

1 u» Project/ 1 ask/ Work Unit INo. 2774246

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period Covered

In. sponsoring Agency ^ocle

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The acceleration sensitivity of quartz crystal resonators imposes severe limitation on their use in non- laboratory environments. This work shows that by

using two resonators connected in series and properly orientated with respect to one another, it is possible to substantially reduce the net acceleration sensitivity

of the composite or compound crystal resonator. First qualitative experimental results on acceleration, also some experimental theories of studies related to the introductio:

of the two resonators comprising the compound resonator, are presented. From these

studies it appears feasible to fabricate compound crystal resonators exhibiting

acceleration sensitivities at least 10 times smaller than the resonators used

individually.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Acceleration field; acceleration sensitivity, compoiind crystal resonator;

crystalographic axis; non-linear elastic effect; resonance frequency

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