Quartz resonator vibrating in a fundamental torsion mode

A thin quartz plate having opposite major surfaces, each of the opposite major surfaces having a geometrical shape symmetrical or antisymmetrical with respect to an axis of reference; and X, Y and Z crystallographic directions corresponding to electrical, mechanical and optical axes, respectively, of the quartz plate, wherein the axis of reference forms an angle .psi. with said X axis, and the major surfaces form an angle .theta. with a plane defined by said X and Y axes, the angles .theta. and .psi. being chosen such that the first order frequency-temperature coefficient (.alpha.) of the quartz resonator is substantially 0, and the second order frequency-temperature coefficient (.beta.) of said quartz resonator is substantially 0. The shape of the resonator may be rectangular, square, polygonal, circular or elliptical. The resonator is fixed on a supporting base by means of at least one pair of connecting arms located on the extension of a nodal line. The resonator of the invention finds application in the field of relatively low frequency miniature resonators suitable for encapsulation.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to quartz resonators and more particularly to 
resonators having good thermal properties, having a relatively low 
resonance frequency, vibrating in a fundamental torsion mode and being 
adapted to be mass-produced by chemical etching techniques. 
2. Description of the Related Art 
Resonators are known which meet the conditions of having small variation in 
frequency as a function of temperature, having a low resonance frequency 
and being chemically machined. Examples can be found in the following 
references: 
(1) "New quartz tuning fork with very low temperature coefficient" B. 
Momosaki et al., appearing in the 33rd Annual Symposium on Frequency 
Control (A.S.F.C.), 1979, pp. 247-254. 
(2) "Vibration analysis of coupled flexural mode tuning fork type quartz 
crystal resonator" by H. Kawashimi, appearing in the 42nd A.S.F.C. 1988, 
pp. 45-52. 
(3) "A new low frequency thermally compensated contour mode resonator" by 
C. Bourgeois, appearing in the 44th A.S.F.C., 1990, pp. 367-371. 
The three references above relate to resonators using coupling between two 
modes of vibration in order to improve the thermal properties. The first 
two references concern a tuning fork resonator vibrating in a flexural 
mode coupled to a torsion mode, while the third reference concerns a 
resonator vibrating in an elongation mode coupled to a flexural mode. The 
device of the three references described above are characterized by the 
use of relatively close coupling between the modes of vibration. By close 
coupling there is understood a relatively small frequency difference (&lt;2%) 
between the non-coupled modes. A result of this close coupling is that the 
resulting thermal properties depend critically on certain geometrical 
dimensions; this considerably reduces the yield in the manufacture of such 
resonators and restricts practical interest. 
SUMMARY OF THE INVENTION 
Accordingly, one object of the invention is a quartz resonator having good 
thermal properties, being adapted to be mass-produced and not having the 
disadvantages of the examples of the prior art described above. 
Another object of the invention is a quartz resonator whose thermal 
properties do not depend critically on its geometrical dimensions. 
Another object of the invention is a quartz resonator suitable for 
encapsulation. 
The type of vibration selected according to the present invention does not 
rely on mode coupling so that the variation in the frequency of the 
resonator as a function of temperature depends neither on the ratio of 
dimensions of the base rectangle, nor on its thickness. The use of 
vibration out of the plane of the resonator results in a relatively low 
frequency of vibration, for example of the order of 0.5 MHz for a 
miniature resonator capable of being fitted in a cylindrical encapsulation 
of 2 mm external diameter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In a preferred embodiment of the invention, the resonator is a thin plate 1 
of square or rectangular shape. FIG. 1 shows the nodal lines 10a and 10b 
(loci of points with no movement), having one or more fixing arms 11 
extending therefrom. It would be equally possible to fix the resonator by 
means of a support wire soldered to the point of intersection of the nodal 
lines. However, the method of fixing of greatest interest is illustrated 
in FIG. 2, showing the resonator 1 of FIG. 1 fixed to a frame 2 by four 
arms 11 located in the extensions of the nodal lines. Another possible 
solution would consist of only providing two fixing arms, located at the 
opposite ends of the same modal line. Since frame 2 is preferably also 
made of quartz, it is possible to make the resonator, the arms and the 
frame simultaneously. 
FIG. 3 shows the lines of cut of a first embodiment of a resonator in 
accordance with the invention. The axes X, Y and Z of the coordinate 
system correspond respectively to the electrical, mechanical and optical 
axes of the quartz crystal. The resonator 1 is obtained by cutting one 
edge thereof (parallel to the longitudinal axis of symmetry) at an angle 
.theta. with respect to the X axis, followed by the major faces thereof 
being cut at an angle .psi. with respect to the normal. The graph of FIG. 
4 represents the loci of the zero values of the frequency-temperature 
coefficient of the first order, or the coefficient .alpha., which define 
the possible values of the angles of cut .theta. and .psi. for which the 
resonator exhibits good thermal properties, namely a zero 
frequency-temperature coefficient of first order .alpha. and a 
frequency-temperature coefficient of second order, or coefficient .beta., 
which si zero or has a very small value. The loci .alpha.=0 are shown in 
full lines in the regions where the coefficient of second order .beta. is 
very small, that is to say less than a value of 10.10.sup.-9 
/.degree.C.sup.2, and in dotted lines in the other regions. 
FIG. 5 shows the angles of cut of a second embodiment of a resonator in 
accordance with the invention. The resonator is obtained by cutting one 
edge thereof (parallel the longitudinal axis of symmetry) at an angle 
.theta. with respect to the Y axis, followed by the major surfaces thereof 
being cut an angle .psi. with respect to the normal. The graph of FIG. 6 
shows the possible values of the angles of cut .theta. and .psi. for which 
the coefficient of first order .alpha. is zero, in the same way as in FIG. 
4. 
It should be noted that the rotation of the substrate about its normal, 
likewise the angular orientation of the resonator, are much more difficult 
to control than the rotation of the substrate itself, (rotation about the 
X axis in FIG. 3 or the Y axis in FIG. 5). It follows that, to be of 
practical use, a cut should satisfy the two following conditions: 
1) it should be located in a region where the coefficient of second order 
.beta. is small; 
2) the tangent to the locus .alpha.=0 should be close to vertical (infinite 
value). 
The three following cuts allow conditions 1 and 2 to be met. They are: 
For resonators of the first embodiment, 
1) .theta.=-33.degree.; .psi.=0 
2) .theta.=+34.degree.; .psi.=+45.degree. 
For resonators of the first embodiment, 
1) .theta.=33.degree. to 35.degree.; .psi.=65.degree. to 75.degree. 
Furthermore, if the resonators are made by means of a chemical etching 
method, for example by using hydrofluoric acid or ammonium bifluoride, the 
following approximate limits have been to be taken into account, beyond 
which the quality of the cut provided chemically is no longer acceptable; 
-30.degree.&lt;.theta.&lt;+65.degree. for a rotation about the X axis and 
.vertline..theta..vertline.&lt;55.degree.. This means that, in the case of 
manufacture by chemical etching, only the cuts 2) and 3) are suitable. It 
should also be noted that the frequency-temperature coefficients depend, 
albeit weakly, on the following factors: 
ratio of dimensions and relative thickness of the resonator; 
dimensions of the fixing arm and of the frame; 
geometry, thickness and material of the metallized regions needed to effect 
piezoelectric coupling and adjustment of the frequency of the resonator; 
secondary elastic constants which depend themselves on the selected 
crystallographic orientation and can slightly alter the overall movement 
of the resonator. 
The angles of cut to enable the coefficients .alpha. and .beta. to be 
zeroed and in particular the angles of cut 1), 2) and 
3) above might as a result depart in some degree from the values given in 
FIGS. 4 and 6. 
FIG. 7 shows a preferred embodiment of the invention. The resonator 1 (FIG. 
7a) is fixed to a frame 2 by four arms 11; this ensures the best 
resistance to possible shocks. The frame can be fixed by soldering or 
bonding on a cylindrical base (not shown) provided with insulated 
electrical connections. The assembly of the resonator and cylindrical base 
is then sealed under vacuum by a cylindrical metal cap fitted in a sealed 
manner to the base. Two distinct systems of metallization are shown in 
FIG. 7a. 
The first system comprises metallized zones 12a which are located on the 
two faces of the resonator and in each of the corners of the rectangular 
plate, and are not connected to the outside. The purpose of this first 
system of metallization is to allow adjustment of the frequency of the 
resonator after manufacture, through selective vaporization of metal with 
the aid of a laser beam. This operation which is necessary because of 
manufacturing tolerances, allows the design frequency to be achieved. A 
coarse adjustment can be effected directly on the substrate and the final 
adjustment when the resonator is mounted on its base. The second system of 
metallization comprises a set of two-pole electrodes 12b on each face, 
which enable piezoelectric coupling which is necessary for excitation of 
the torsional mode of vibration. The electrodes 12b are formed in the 
central part of the resonator and are aligned on a straight line whose 
inclination depends on the selected crystallographic cut. The section of 
FIG. 7b shows the reversal of polarity of the electrodes 12b on the two 
faces of the resonator. The electrodes 12b are connected to electric 
conductors on the supporting base through metallic tracks 12c on the 
external frame and the region of bonding/soldering. 
In one particular embodiment, the characteristics of a resonator such as is 
represented in FIG. 7 are as follows: 
______________________________________ 
frequency 524 KHZ 
cut .THETA. = +34.degree.; = +45.degree. 
inclination of electrodes 
45.degree. 
thickness 80 .mu.m 
square plate 0.75 mm .times. 0.75 mm 
overall dimensions 1.2 mm .times. 2.3 mm. 
______________________________________ 
Various modifications, corresponding to changes of greater or lesser 
significance in the described examples can be envisaged. The simple square 
or rectangular geometry, such as that shown, is not the only geometry 
which allows implementation of the torsional mode characteristic of the 
invention. In particular modified square or rectangular shapes, such as 
are shown in FIGS. 8 and 9, can be considered, or parallelograms, circles 
or ellipses (not shown). Such modifications can significantly alter the 
thermal properties, especially the frequency-temperature coefficient of 
second order. These modifications can likewise, depending on the 
particular case, imply an alteration in the angles of crystallographic cut 
of some degrees. In a similar manner the coupling electrodes can be 
changed and can, for example, incorporate non-straight parts. The shape of 
the electrodes depends on the shape chosen for the resonator. The various 
embodiments of the resonator shown each have two pairs of opposed arms 
connecting resonator and frame. However, as mentioned above, it is 
possible to dispense with one of the two pairs to reduce the perturbing 
effect of the external frame on the central resonator. In this case a 
smaller resistance to shocks results. Moreover, notches can be provided 
between the frame and the actual mounting region in order to increase the 
Q factor and to reduce the influence of the mounting on the base of the 
resonator. 
Although the invention has been described with reference to specific 
embodiments, it is obvious that it can be subject to modification and 
variants without departing from its scope.