FR2745667A1 - Selective excitation piezoelectric resonator for electronic oscillator - Google Patents

Abstract

The resonator includes the piezoelectric crystal (10) with rectangular shape and rectangular electrodes (21,31) placed on two opposite surfaces (11,12) of the crystal. The electrodes are positioned over vibrating areas (41,43) present on the crystal surface. A second pair of electrodes (22,32) are placed over other two vibrating areas (42,44) of the crystal. Conductors (21a,31a,22a,32a) connect the electrodes to the terminals (71,72) of a voltage source (70). The electric field generated by the electrodes is orientated along the normal direction to the crystal surface.

Description

 The subject of the present invention is a piezoelectric resonator with selective excitation, comprising a piezoelectric crystal in the form of a plate with first and second main faces on which or in the vicinity of which are placed metal electrodes connected to a source of electric voltage and creating a field. electric mainly oriented along the thickness of the plate in a direction A perpendicular to a mean plane of the plate.

 Various types of piezoelectric resonators are already known, comprising a plate-shaped piezoelectric crystal with main faces of bi-plane, plan-convex or biconvex type. With this type of resonator, both mechanically and electrically, we can observe many resonances in thickness mode. These modes are preferably excited by facing metal electrodes arranged on the large faces of the plate or of the armatures close to these.

 In many known embodiments, the resonant mode is excited using a single pair of electrodes, each face carrying only one unitary electrode. Such a type of embodiment is generally suitable for the maintenance of modes which can be described as metrological, the mechanical displacement phase of which does not involve any change in sign in the plane of the plate.

 It has also been proposed, for example by document US Pat. No. 5,041,754, to use, on the same crystal plate, two pairs of electrodes in order to reduce the sensitivity of the resonator to acceleration.

 In this case, the two pairs of electrodes are supplied electrically in parallel from the same voltage source, and external components producing a phase shift, such as capacitors or inductors, are interposed between at least one electrode and one connection terminal to the voltage source. Such an arrangement makes it possible to introduce a phase shift and a variation in amplitude in the excitation current applied by one of the pairs of electrodes in order to compensate for parasitic disturbances due to asymmetries in the arrangement and to allow obtaining of a metrological thickness mode whose sensitivity to accelerations is reduced so as to maintain a stable frequency. Such an assembly, which uses external components such as capacitors or inductors, does not in practice make it possible to obtain excellent performances in terms of stability and signal / noise ratio and, moreover, does not provide a means of selective excitation of non-metrological modes, called anharmonic modes, which are thickness modes with a mechanical displacement whose distribution in the plane of the plate comprises at least one change of sign following at least one direction of the plate of the crystal.

 The present invention aims to remedy the drawbacks of the resonators of the prior art, and to allow the production of a piezoelectric resonator vibrating in thickness mode for which the motional impedance of a family of undesirable modes is significantly increased without significantly affecting the motional impedance of the main mode on which the resonator is intended to operate.

 A more particular object of the invention is to produce a piezoelectric resonator with selective excitation of anharmonic thickness modes, which can be manufactured both in the form of a resonator with adherent electrodes and in the form of a resonator with electrodes not adhering to the crystal.

 These objects are achieved by means of a piezoelectric resonator with selective excitation, comprising a piezoelectric crystal in the form of a plate with first and second main faces on which or in the vicinity of which are placed metal electrodes connected to a source of electric voltage and creating a field. electric mainly oriented along the thickness of the plate in a direction A perpendicular to a mean plane of the plate, characterized in that it comprises at least first and second electrodes disposed opposite each other on first and second zones of the first and second main faces and electrically connected respectively to first and second terminals of a voltage source and of the third and fourth electrodes disposed opposite each other respectively on third and fourth zones of the first and second main faces and electrically connected from antisymmetrically respectively to the second and first terminals of said voltage source, so as to ensure in the crystal the excitation and the maintenance of an anharmonic preferred thickness mode corresponding to a mechanical displacement whose distribution of mechanical amplitude comprises in the mean plane of the plate at least one change of sign in at least one direction of the plate located both between said first and third zones and between said second and fourth zones.

 Preferably, the first, second, third and fourth electrodes each have an axis of symmetry corresponding to the axis of symmetry of the preferred anharmonic thickness mode.

 However, when it is desired to favor certain anharmonic modes, it may be advantageous for the first, second, third and fourth electrodes each to have an axis of symmetry which is slightly offset in rotation relative to the axis of symmetry of the mode of privileged anharmonic thickness. In this case, it is preferable that the slight rotational offset is less than + 15g.

 The electrodes have a shape and a surface adapted to the mode or modes to be selectively excited. By way of example, the electrodes may have the shape of rectangles, half-discs or even ellipses.

 It will be noted that the resonators according to the invention do not use the so-called parallel field technique which consists in exciting metrological modes by means of electrodes applying to the resonator an electric field oblique to the normal to the plate. On the contrary, according to the present invention, the applied electric field remains mainly oriented along the thickness of the plate, but its direction can locally reverse from one region to another depending on the configuration of the interconnections of the electrodes.

Other characteristics and advantages of the invention will emerge from the following description of particular embodiments, made with reference to the appended drawings, in which:
- Figure 1 is a top view of a first example of a piezoelectric resonator according to the invention comprising multiple electrodes ensuring optimal excitation of an anharmonic vibration mode;
- Figure 2 is a schematic sectional view along the line II-II of Figure 1;
- Figure 3 is a top view of the resonator of Figure 1 showing a metrological vibration mode not excited by the electrodes;
- Figure 4 is a schematic sectional view along line IV
IV of Figure 3 ;;
- Figure 5 is a top view of the resonator of Figure 1 showing an an harmonic vibration mode with degraded excitation;
- Figure 6 is a schematic sectional view along the line Vl-Vl of Figure 5;
- Figure 7 is a top view of another embodiment of a piezoelectric resonator according to the invention provided with multiple electrodes ensuring optimum excitation of an anharmonic vibration mode; and
- Figure 8 is a sectional view along line VIII-VIII of the
Figure 7.

 FIGS. 1 and 2 show the schematic representation of a piezoelectric resonator comprising a piezoelectric crystal in the form of a plate 10 having two large main faces 11, 12 that are plane and parallel. The plate 10 has a median plane 13 and a normal A to this median plane 13.

 Rectangular electrodes 21 and 31 are placed opposite each other on vibrating zones 41, 43 of the main faces 11, 12 of the plate 10.

Other rectangular electrodes 22 and 32 are arranged on other vibrating zones 42, 44 of the main faces 11, 12 of the plate 10.

 The electrodes 21 and 31 are connected by the links 21a and 31a to the terminals 71 and 72 of an electric voltage source 70 delivering a voltage V. At the instant considered in Figures 1 and 2, the potential of the electrode 21 is positive while the potential of the electrode 31 is negative.

The electrodes 22 and 32 are connected by the links 22a and 32a to the terminals 72 and 71 of the voltage source 70. At the instant considered on the
Figures 1 and 2, the potential of electrode 22 is negative while the potential of electrode 32 is positive.

 In general, taking into account the interconnections of the two pairs of electrodes 21, 31 and 22, 32, the adjacent electrodes 21 and 22 of the face 11 are at potentials in phase opposition, as are the adjacent electrodes 31 and 32 of the face 12. The potentials of the electrodes 21, 31, resp. 22, 32, of the same pair of electrodes enclosing the plate 10 are themselves in phase opposition. The interconnection of the electrodes is such that the resonator is seen as an electrical dipole.

The electrodes 21, 22 and 31, 32 have been shown to be adherent to the crystal 10, but they could also be non
adherent to crystal 10 and located in the immediate vicinity thereof
look at faces 11 and 12.

The electric field applied by the electrodes 21, 31 and 22, 32
remains mainly oriented along the thickness of the plate 10, that is to say in the direction A perpendicular to the mean plane 13 of the plate 10.

However, taking into account the cross-connections which are made, the direction of the electric field can locally reverse between regions 41, 43 and regions 42, 44.

 The piezoelectric resonator being inserted like an electric dipole in an electronic oscillator, the electrodes are used simultaneously to maintain the vibration of the crystal by the effect of the electric field which they allow to apply and to collect a current which results from the sum of the electric charges which appear as a result of the piezoelectric effect. In a resonator vibrating in essentially thickness mode, these charges are linked to the distribution of the mechanical displacement in the plane of the plate.

 The electrodes 21, 22, 31, 32 have shapes, surfaces and interconnections such that they ensure in the crystal 10 the excitation and the maintenance of a preferred anharmonic thickness mode corresponding to a mechanical displacement whose distribution of mechanical amplitude 1 (FIG. 2) comprises, in the mean plane 13 of the plate 10, a change of sign in a direction 14 of the plate 10 situated in a transition part between the vibration zones 41, 43 and the vibration zones 42, 44 of the plate 10 of the piezoelectric crystal.

 As can be seen in Figure 2, the zones 41 and 42 of the plate 10 carrying the electrodes 21 and 22 vibrate in phase opposition.

The electric charges 51 collected by the electrode 21 are of the same sign as the electric charges 62 collected by the electrode 32 (positive at the instant considered in Figure 2). Likewise, the electrical charges 52 collected by the electrode 22 are of the same sign as the electrical charges 61 collected by the electrode 31 (negative at the instant considered in FIG. 2).

 The electrodes 21, 22, 31, 32 are therefore adapted to a preferential excitation of the anharmonic mode resulting in the distribution of the amplitude of the mechanical displacement with a nodal line in the plane of the plate, implying a change of sign, and vibrations in phase opposition of zones 41, 43 and 42, 44 of the plate 10.

If we consider Figures 3 and 4, we see that the electrodes 21, 22, 31, 32 and their interconnection are unsuitable for excitation or detection of so-called metrological modes, for which the distribution 2 of
the amplitude of the mechanical displacement (Figure 4) does not include a change of sign in the plane of the plate and, consequently, does not include any nodal line in this plane.

 FIG. 3 shows approximately circular or elliptical zones 45, 46 of the faces 11, 12 of the plate 10 corresponding to the natural vibration zones of the metrological mode whose distribution 2 of the amplitude of the mechanical displacement is shown in FIG. 4.

In this case, the electrical charges 53 and 54 collected under this mode of vibration of metrological thickness at the electrodes 21 and 22 located on the same face 11 of the crystal 10 are of the same sign (positive at the instant considered on Figure 4) while the electrical charges 63 and 64 collected at the same time at the electrodes 31 and 32 located on the opposite face 12 are of the same sign (i.e. negative at the instant considered on Figure 4), but of opposite sign to that of charges 53 and 54. In this way, the metrological movement is not maintained by the electrodes 21, 22, 31, 32, and the motional impedance of this metrological mode is much higher than that corresponding to the anharmonic mode chosen and preferably excited represented in Figures 1 and 2.

It is possible to classify the thickness modes as a function of the acoustic propagation speed in the direction b normal to the plate, which defines three families, called A, B, C, in decreasing order of the speeds, and according to the rank of partial, defined indifferently as the approximate number of half wavelengths according to the thickness of the plate or the number of nodal planes of mechanical displacement between the large faces of the plate. For more details concerning this classification, one can refer to the following publication: "lEEE Standard on
Piezoelectricity ", The Institute of Electrical and Electronics Engineers, Inc.,
New York, Standard No. 1761978.

In the case of energy trapping resonators in essentially thickness mode, the orientation of the modal figure in the plane of the piezoelectric plate 10 (represented in FIG. 1 by the angle a between the crystallographic axis 41 and a plane of symmetry AB) depends mainly on the modal family (A, B, C), the rank of partial and
the crystal orientation of the plate. It follows that, with a set of electrodes 21, 22, 31, 32 arranged to optimally excite a
given anharmonic mode, the anharmonic belonging to other modal families or corresponding to other partial ranks will give
significantly increased motional impedances, if the angle a which characterizes them differs from that of the mode which one wishes to favor.

 It is thus possible to improve the selectivity of the operation of a double-rotation sectional resonator.

As explained with reference to Figures 3 and 4,
The antisymmetric interconnection of the electrodes allows elimination of the excitation of the metrological modes whose amplitude distribution is symmetrical relative to the center of the resonator, and only allows the excitation of anharmonic modes with antisymmetric distribution, by favoring the modes of which the axes of symmetry 14 are aligned with the axes of symmetry of the electrodes (Figure 1). In comparison, a mode such as that illustrated in FIGS. 5 and 6, having vibration zones 47, 49 and 48, 50 whose axes of symmetry CD are oblique with respect to the axes of symmetry AB of the electrodes 21, 22, 31 , 32, is excited in a degraded way. Thus, if the electric charges 55, 56, 65, 66 collected by the electrodes 21, 22, 31, 32 under the mode having axes of symmetry
Oblique CDs (Flgure 6) are distributed with the same signs as the electric charges 51, 52, 61, 62 collected by the electrodes 21, 22, 31, 32 under the mode having axes of symmetry AB corresponding to those of the electrodes ( Figure 2), the distribution 3 of the amplitude of the mechanical displacement along the axis AB, in the section of Figure 6, shows a strong attenuation compared to the distribution 4 of the amplitude of the mechanical displacement (shown in dotted lines) which would be present in a section comprising the axis of symmetry CD of the parasitic mode considered.

 It should be noted that the orientation of the electrodes can be chosen to operate a compromise between an optimal excitation of a single mode or of a set of given modes, and the elimination of sets of modes belonging to other families. thick (A, B, C) and deemed undesirable.

 In this case, there is an offset between the axis of symmetry of each of the electrodes 21, 31, 22, 32 and the axis of symmetry corresponding to the axis of symmetry of the preferred anharmonic thickness mode. This offset corresponds to a slight rotation which must remain less than + 15-.

Subject to a minimal degradation of the anharmonic mode that one wishes to favor, it is thus possible, in certain cases, to attenuate in a more marked way other an harmonic modes considered as parasitic.

 We have considered above the case of a resonator comprising two pairs of electrodes, of given surface, interconnected to select an anharmonic mode whose distribution of mechanical amplitude comprises only one nodal line in the plane of the plate , and therefore only one sign change.

 It is however possible to use a greater number of pairs of electrodes, interconnected in an asymmetric manner, that is to say with adjacent electrodes of opposite polarities, to favor anharmonic modes whose distribution of mechanical amplitude comprises several nodal lines in the plane of the plate, that is to say several changes of sign.

avec k =(e26 A1 +e22 A2 + e24 A3)2/e22c (2) où û représente la distribution, dans le plan du résonateur, de l'amplitude de la vibration du mode considéré, A1, A2, A3 les composantes du déplacement mécanique pour ce mode, alors que c' désigne le coefficient élastique effectif associé à sa propagation suivant la direction normale à la plaque et O désigne le coefficient de qualité du mode. Dans la formule, e22, e24, e26 et E22 sont les coefficients piézoélectriques et diélectriques pour l'orientation cristalline de la plaque constituant le résonateur dont l'épaisseur est ho. L est un facteur de normalisation qui dépend du mode de vibration pris en compte. In general, if we consider a resonator comprising several pairs of electrodes, denoted q, of surface Sq, on which are applied potential differences Vq = + V at the resonance frequency s of a natural mode of the resonator, the current I, due to the vibration of the resonator and flowing through all of the electrodes, is given by the following formula:

with k = (e26 A1 + e22 A2 + e24 A3) 2 / e22c (2) where û represents the distribution, in the plane of the resonator, of the amplitude of the vibration of the mode considered, A1, A2, A3 the components of the mechanical displacement for this mode, while c 'denotes the effective elastic coefficient associated with its propagation in the direction normal to the plate and O denotes the quality coefficient of the mode. In the formula, e22, e24, e26 and E22 are the piezoelectric and dielectric coefficients for the crystal orientation of the plate constituting the resonator whose thickness is ho. L is a normalization factor which depends on the vibration mode taken into account.

 For any anharmonic mode of vibration considered, it is thus possible to choose combinations of voltage Vq associated with surfaces of electrodes Sq leading to a zero or on the contrary maximum current in the resonator, which makes it possible to produce a resonator with high selectivity .

 The electrodes can have various shapes, for example rectangular, elliptical, semicircular and the piezoelectric crystal can itself be bi-plane, plan-convex or even biconvex.

 By way of example, FIGS. 7 and 8 show a particular embodiment of a 10 MHz SC cut quartz resonator (-22e, O = 34.5-), comprising a crystal 110 having the shape of a disk of diameter 11 mm, of plano-convex section with a radius of curvature equal to 200 mm. The electrodes 121, 122 arranged on the convex face 111 have the form of two half-discs with a radius of 6 mm separated by an interval of 0.6 mm oriented in a direction close to the projection of the optical axis of the quartz crystal 110. electrodes 131, 132 arranged on the flat face 112 also have the form of half-discs placed facing each other with respect to the electrodes 121, 122. The electrodes 121 and 132 are connected by connection lines 121 a, 1 32a to the terminal 171 of the voltage source 170 while the electrodes 122 and 131 are connected by the connection lines 1 22a and 131 a to the other terminal 172 of the voltage source 170. FIG. 7 shows the zones 141, 143 and 142, 144 of the crystal 110 vibrating according to the anharmonic mode selected and giving rise to the creation of the electric charges 151, 152, 161, 162 collected by the electrodes 121, 122, 131, 132. As in the case of FIG. 2, the electric charges 151 and 162 collected by the electrodes 121 and 132 are of the same sign and the electric charges 152 and 161 collected by the electrodes 122 and 131 show the opposite sign. The electric field remains in all cases oriented in the thickness direction in the direction A perpendicular to the mean plane 113 of the crystal 110.

 In the example of the embodiment of Figures 7 and 8, the preferentially excited mode (mode C) has a lower electrical resistance than that of any other mode (including mode B) of at least three decibels.

Claims (9)

 1. Piezoelectric resonator with selective excitation, comprising a plate-shaped piezoelectric crystal (10; 110) with first and second main faces (11,12; 111,112) on which or in the vicinity of which are arranged metal electrodes connected to a source electric voltage and creating an electric field mainly oriented along the thickness of the plate in a direction å perpendicular to a mean plane (13; 113) of the plate,  characterized in that it comprises at least first and second electrodes (21, 31; 121, 131) disposed opposite one another respectively on first and second zones (41, 43; 141, 143) of the first and second main faces (11.12; 111, 112) and electrically connected respectively to first and second terminals (71, 72; 171, 172) of a voltage source (70; 170) and of the third and fourth electrodes (22, 32; 122, 132) disposed vis-à-vis respectively on third and fourth zones (42, 44; 142,144) of the first and second main faces (11,12; 111,112) and electrically connected asymmetrically respectively at the second and first terminals (72, 71; 172, 171) of said voltage source (70; 170), so as to ensure in the crystal (10; 110) the excitation and the maintenance of a preferred anharmonic thickness mode corresponding to a mechanical displacement whose distribution of mechanical amplitude includes in the mean plane (13; 113) of the plate (10; 110) at least one change of sign in at least one direction of the plate (10; 110) situated both between said first and third zones (41, 42; 141,142) and between said second and fourth zones (43, 44; 143, 144).  2. Resonator according to claim 1, characterized in that the first, second, third and fourth electrodes (21, 31, 22, 32; 121, 131, 122, 132) each have an axis of symmetry (AB) corresponding to l axis of symmetry of the preferred anharmonic thickness mode.  3. Resonator according to claim 1, characterized in that the first, second, third and fourth electrodes (21, 31, 22, 32; 121, 131, 122, 132) each have an axis of symmetry which is slightly offset in rotation with respect to the axis of symmetry of the preferred anharmonic thickness mode.  4. Resonator according to claim 3, characterized in that the slight rotation offset is less than +1 5.  5. Resonator according to any one of claims 1 to 4, characterized in that the first, second, third and fourth electrodes (21, 31, 22, 32) have a rectangular shape.  6. Resonator according to any one of claims 1 to 4, characterized in that the first, second, third and fourth electrodes (121, 131, 122, 132) each have the shape of a semi-disc or an ellipse .  7. Resonator according to any one of claims 1 to 6, characterized in that the plate (10) of the piezoelectric crystal has first and second main faces (11, 12) planar and parallel.  8. Resonator according to any one of claims 1 to 6, characterized in that the plate (110) of the piezoelectric crystal comprises a first main face (111) convex and a second main face (112) convex.  9. Resonator according to any one of claims 1 to 6, characterized in that the piezoelectric crystal is a quartz crystal in cross section with double rotation.