Abstract:
A quartz crystal tuning fork resonator has quartz crystal tuning fork tines for undergoing vibration in an inverse phase. Each of the quartz crystal tuning fork tines has a first main surface and a second main surface opposite the first main surface, each of the first and second main surfaces having a central linear portion. The quartz crystal tuning fork tines extend from a quartz crystal tuning fork base. At least one groove is formed in the central linear portion of each of the first and second main surfaces of each of the quartz crystal tuning fork tines. A width of the groove in the central linear portion of one of the first and second main surfaces of each of the quartz crystal tuning fork tines is greater than or equal to a distance in the width direction of the groove measured from an outer edge of the groove to an outer edge of the tuning fork tine.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a quartz crystal tuning fork resonator, capable of operating in a flexural mode. 
     2. Background Information 
     Quartz crystal tuning fork resonators, which are capable of vibrating in a flexural mode, are widely used as a time standard in consumer products, wearable time-keeping equipment and communication equipment (such as wristwatches, cellular phones, and pagers). Recently, because of miniaturization and the light weight nature of these products, the need for a smaller quartz crystal tuning fork resonator capable of operating in a flexural mode and having a small series resistance and a high quality factor has arisen. 
     Heretofore, however, it has been impossible to obtain a conventional miniaturized, quartz crystal tuning fork resonator, capable of operating in a flexural mode, and having a small series resistance and a high quality factor. When miniaturized, the conventional quartz crystal tuning fork resonator capable of operating in a flexural mode, as shown in  FIG. 22  (which has electrodes on the obverse faces  203 ,  207 , reverse faces  204 ,  208  and the four sides  205 ,  206 ,  209 ,  210  of each tuning fork tine, and as also shown in  FIG. 23 , which is a cross-sectional view of the tuning fork tines of FIG.  22 ), has a smaller electromechanical transformation efficiency, which provides a small electric field (i.e. Ex becomes small), a large series resistance, and a reduced quality factor. In  FIG. 22 , a conventional tuning fork resonator  200  is shown with tuning fork tines  201 ,  202  and tuning fork base  211 . 
     In addition, it has heretofore been impossible to obtain a quartz crystal tuning fork resonator, capable of operating in a flexural mode, and having a small frequency change over a wide temperature range of between −10° C. to +50° C., because the resonator typically has a temperature coefficient with a parabolic curve, and a second order temperature coefficient of approximately −3.5×10 −8 /° C. 2 . This value is comparatively large as compared with AT cut quartz crystal resonators vibrating in thickness shear mode. 
     Accordingly, it is, therefore, a general object of the present invention to provide embodiments of a quartz crystal tuning fork resonator, capable of operating in a flexural mode, which overcome or at least mitigate one or more of the above problems. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention relate to the shape and electrode construction of a quartz crystal tuning fork resonator, capable of operating in a flexural mode, and in particular, to a novel shape and electrode construction for quartz crystal tuning fork resonator capable of operating in a flexural mode, for consumer products and communication equipment requiring miniaturized, high accuracy, shock proof and low priced quartz crystal resonators. 
     It is a specific object of the present invention to provide embodiments of a quartz crystal tuning fork resonator capable of operating in a flexural mode that are miniaturized and have a small series resistance RI and a high quality factor Q. 
     It is yet another specific object of the present invention to provide embodiments of a quartz crystal resonator tuning fork resonator capable of operating in a flexural mode, and having an excellent frequency temperature behaviour over a wide temperature range, of from about −10° C. to about +50° C.). 
     According to one aspect of the present invention, there is provided a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, which comprises; a pair of tuning fork tines, attached to a tuning fork base, with at least one groove being provided in a central linear portion of each tuning fork tine, at least one first electrode being provided inside each groove, and at least one second electrode being provided on sides of the tuning fork tines, such that for each tuning fork tine the at least one second electrode has an opposite polarity to the at least one first electrode. 
     According to a second aspect of the present invention there is provided a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, which comprises a pair of tuning fork tines, attached to a tuning fork base, with a plurality of grooves being provided on the tuning fork base where the tuning fork tines are attached thereto, and with a plurality of electrodes being provided in the grooves. 
     According to a third aspect of the present invention there is provided a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, which comprises a pair of tuning fork tines, attached to a tuning fork base, with the tuning fork tines having step difference portions, and with there being at least one first electrode on the step difference portions, and at least one second electrode on the sides of the tuning fork tines, such that the at least one first and at least one second electrodes are of opposite polarity. 
     According to a fourth aspect of the present invention there is provided a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, which comprises a plurality of any of the foregoing individual quartz crystal tuning fork resonators capable of vibrating in a flexural mode, with each individual resonator having a pair of tuning fork tines attached to a tuning fork base, and with each individual resonator being connected and formed integrally at each tuning fork base wherein the individual quartz crystal resonators are coupled to each other at the respective tuning fork bases and have an angle of separation of from 0° to about 30°, and such that the resulting coupled resonator has an even numbered plurality of tuning fork tines. 
     Embodiments of the quartz crystal tuning fork resonators capable of vibrating in a flexural mode, according to the present invention, provide a high electromechanical transformation efficiency. 
     Embodiments of the quartz crystal tuning fork resonators capable of vibrating in a flexural mode, according to the present invention, use grooves or step differences and an electrode construction arranged on the tuning fork tines and/or tuning fork base. 
     According to one preferred embodiment, a resonator according to the present invention has grooves provided in a central linear portion of each tuning fork tine and electrodes disposed inside the grooves and on the sides of each tuning fork tine. According to other embodiments, alternatively or additionally, the grooves may be arranged on the tuning fork base with the electrodes also being disposed inside the grooves. 
     According to another preferred embodiment, the resonator has a step difference constructed at the tuning fork tines and/or the tuning fork base, and has electrodes disposed on the step difference portions. 
     According to yet another preferred embodiment, at least two individual quartz crystal tuning fork resonators are connected and formed integrally at their respective tuning fork base in order to improve the frequency-temperature behaviour of the device. The quartz crystal resonators, whose peak temperature points are different, may be electrically connected in parallel. As a result, the integrally formed quartz crystal resonator has excellent frequency-temperature behaviour over a wide temperature range, extending from about −10° C. to about +50° C. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention and the manner in which it is implemented may be more fully understood with reference to the following detailed description, examples, and accompanying drawings, in which: 
         FIG. 1  is a general view of a quartz crystal tuning fork resonator of the present invention, capable of vibrating in a flexural mode, and having grooves at each tuning fork tine; 
         FIG. 2  is a cross-sectional view through A-A′ and B-B′ of the tuning fork tines of  FIG. 1 , showing the electrode construction; 
         FIG. 3  is a plan view of the quartz crystal tuning fork resonator of  FIG. 1 ; 
         FIG. 4  is a bottom view of  FIG. 3 ; 
         FIG. 5  is a general view of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention, and having a plurality of grooves at a base of the tuning fork; 
         FIG. 6  is a cross-sectional view through D-D′ of the tuning fork base of  FIG. 5 , showing the electrode construction; 
         FIG. 7  is a plan view of the quartz crystal tuning fork resonator of  FIG. 5 ; 
         FIG. 8  is a plan view of two quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, according to the present invention, connected at their tuning fork bases at an angle φ; 
         FIG. 9  is an electrical connection diagram for the quartz crystal tuning fork resonator of  FIG. 8 ; 
         FIG. 10  is a diagram showing the frequency-temperature behaviour of embodiments of a resonator according to the present invention; 
         FIG. 11  is a plan view of an embodiment of a resonator according to the present invention, which has two quartz crystal resonators, capable of vibrating in a flexural mode, connected at the base of each tuning fork, with the tuning fork of each resonator having different-tuning fork tine dimensional ratios; 
         FIG. 12  is a plan view of one embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention; 
         FIG. 13  is a plan view of another embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention; 
         FIG. 14  is a cross-sectional view through F—F′ of the tuning fork base of  FIG. 13 , showing the electrode construction; 
         FIG. 15  is a general view of an embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention, showing a reference coordinate system for the resonator; 
         FIG. 16  is a plan view of the quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, of  FIG. 15 ; 
         FIG. 17  is a cross-sectional view through I-I′ of the tuning fork tines of the resonator of  FIG. 16 , showing the electrode construction; 
         FIG. 18  is a general view of an embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention, showing a reference coordinate system for the resonator; 
         FIG. 19  is a plan view of the quartz crystal tuning fork resonator of  FIG. 18 ; 
         FIG. 20  is a cross-sectional view through J—J′ of the tuning fork tines of the resonator of  FIG. 19 , showing the electrode construction; 
         FIG. 21  is a plan view of an embodiment of a quartz crystal tuning fork resonator, capable of operating in a flexural mode, according to the present invention, having three resonators; 
         FIG. 22  is a general view of the conventional flexural mode, tuning fork, quartz crystal resonator; and 
         FIG. 23  is a cross-sectional view of the tuning fork tines of FIG.  22  and illustrating electrode construction. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the drawings, the embodiments of the present invention will be described in full detail. 
     Embodiment 1 
       FIG. 1  shows a general view of one embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention, together with a reference coordinate system. The reference coordinate system consists of an origin O, an electrical axis x, a mechanical axis y, and an optical axis z of quartz, namely, O-xyz. A quartz crystal tuning fork resonator  1 , capable of vibrating in a flexural mode, according to the present invention generally comprises a first tuning fork tine  2 , a second tuning fork tine  3 , a tuning fork base  4 , to which the first tuning fork tine  2  and the second tuning fork tine  3  are attached. Additionally, grooves  5  and  11  are formed on an obverse face of tuning fork tines  2  and  3 , in a portion of a central liner portion of each tine, respectively, as shown in FIG.  2 . Corresponding identical grooves are formed on a reverse face of the tines  2  and  3 . A cut angle θ, which has a typical value of from 0° to about 10°, is formed by rotating the resonator about the x-axis through a plane perpendicular to the z-axis. 
       FIG. 2  shows cross-sectional views through A-A′ and B-B′ of the tuning fork tines of the resonator of  FIG. 1 , and details of the electrode construction within the grooves. The A—A′ cross-sectional view of tuning fork tine  2  is shown on the right side and the B—B′ cross-sectional view of tuning fork tine  3  is shown on the left side. Tuning fork tine  2  has grooves  5  and  6  cut into it, in an area covering a portion of central liner region of the tine  2 . The grooves  5  and  6  have a first set of electrodes  7  and  8  of the same electrical polarity, while sides of the tine  2  have a second set of electrodes  9  and  10  having an opposite electrical polarity to the first set of electrodes  7  and  8 . The tuning fork tine  3  has grooves  11  and  12  constructed in a similar manner as tuning fork tine  2 . The grooves  11  and  12  have a third set of electrodes  13  and  14  of the same electrical polarity, and the sides of the tine  3  have a fourth set of electrodes  15  and  16 , with an opposite electrical polarity to the third electrodes  13  and  14 . The electrodes disposed on the tuning fork tines  2  and  3  are electrically connected as shown in  FIG. 2 , forming two electrode terminals C-C′, of opposite electrical polarity. 
     In detail, the first set of electrodes  7  and  8  disposed on the grooves  5  and  6  of tuning fork tine  2  have the same electrical polarity as the fourth set of electrodes  15  and  16  disposed on both sides of tuning fork tine  3 , while the second set of electrodes  9  and  10  disposed on both sides of tuning fork tine  2  have the same electrical polarity as the third set of electrodes  13  and  14  disposed on the grooves  11  and  12  of tine  3 . When a direct voltage is applied between the electrode terminals C-C′, an electric field Ex occurs along the arrow direction inside the tuning fork tines  2  and  3 . As the electric field Ex occurs perpendicular to the electrodes disposed on the tuning fork tines, as shown by the arrow symbols. The electric field Ex has a very large value and a large distortion occurs at the tuning fork tines. As a result, a quartz crystal tuning fork resonator vibrating in a flexural mode, and having a small series resistance R 1  and a high quality factor Q is obtained, with there being a large electro-mechanical transformation efficiency for the resonator, even though miniaturized. 
       FIG. 3  shows a plan view of the quartz crystal tuning fork resonator  1  of FIG.  1 . In  FIG. 3 , the construction and the dimension of grooves  5  and  11  are shown in detail. Groove  5  is formed to include a portion of the central linear region  17  of tuning fork tine  2 ; groove  11  is similarly formed to include a portion of the central linear region  18  of tuning fork tine  3 . Grooves  5  and  11  have a width W 2 , which includes a portion of the central linear regions  17  and  18  respectively, is preferable because the tuning fork tines  2  and  3  can vibrate in flexural mode very easily. A quartz crystal tuning fork resonator, capable of vibrating in a flexural mode with a small series resistance R 1  and a high quality factor Q is possible according to the present invention. The total width W of the tuning fork tines  2  and  3  has a relationship of W=W 1 +W 2 +W 3 , and in general the grooves are constructed so that W 1 =W 3 . In addition, the width W 2  of the grooves is constructed so that W 2 ≧W 1 , W 3 . The length l 1  of the grooves  5  and  11  of tuning fork tines  2  and  3  extends into the tuning fork base  4  (which has a length dimension l 2 ) Furthermore, the total length l is determined by the frequency requirement and the size of the housing case. In this embodiment the grooves  5  and  11  of tuning fork tines  2  and  3  extend into the tuning fork base  4  in series, however, in other embodiments of the present invention a plurality of grooves divided in the length direction of the tuning fork tines are provided. 
       FIG. 4  shows a bottom view of the quartz crystal tuning fork resonator  1  of  FIG. 3 , which has a thickness dimension t. In the embodiments shown in  FIG. 1  to  FIG. 3 , the tuning fork tines have a total of four grooves within the obverse and the reverse faces thereof, with one groove in each of the two faces of each of the two tines, and electrodes provided inside the grooves, as well as electrodes disposed on two sides of the tuning fork tines. Other embodiments of the present invention, however, may have only one groove within a single surface of the tuning fork tines and an electrode inside each of those grooves, as well as electrodes disposed on both sides of each of the tuning fork tines. Furthermore, each of the first electrodes inside the grooves and each of the second electrodes on the sides of the tines, adjacent to the first electrodes, are of opposite electrical polarity. 
     Embodiment 2 
       FIG. 5  shows a general view of another embodiment of a quartz crystal tuning fork resonator  19  of the present invention, capable of vibrating in a flexural mode, and its coordinate system O-xyz. A cut angle θ, which has a typical value of from 0° to about 10°, is formed by rotating the resonator about the x-axis through a plane perpendicular to the z-axis. 
     The quartz crystal tuning fork resonator  19 , capable of vibrating in a flexural mode, comprises two tuning fork tines  20  and  26 , attached to tuning fork base  40 . The tuning fork tines  20  and  26  have grooves  21  and  27 , respectively, with the grooves  21  and  27  extending into the tuning fork base  40 . In addition, the tuning fork base  40  has additional grooves  32  and  36 . 
       FIG. 6  shows a cross-sectional view through D-D′ of the tuning fork base  40  for the quartz crystal tuning fork resonator  19 , capable of vibrating in a flexural mode, of FIG.  5 . In  FIG. 6 , the shape of the electrode construction within the tuning fork base  40  for the quartz crystal tuning fork resonator of  FIG. 5  is shown in detail. The section of the tuning fork base  40 , to which the tuning fork tine  20  is attached, has grooves  21  and  22  cut into the obverse and the reverse faces, respectively, of the base  40 . The section of the tuning fork base  40 , to which tuning fork tine  26  is attached has grooves  27  and  28  cut into the obverse and reverse faces, respectively, of the base  40 . In addition to these grooves, the tuning fork base  40  has grooves  32  and  36  cut between grooves  21  and  27 , and the base  40  further has grooves  33  and  37  cut between grooves  22  and  28 . 
     Additionally, grooves  21  and  22  have first electrodes  23  and  24 , both of the same electrical polarity; grooves  32  and  33  have second electrodes  34  and  35 , both of the same electrical polarity; grooves  36  and  37  have third electrodes  38  and  39 , both of the same electrical polarity, and grooves  27  and  28  have fourth electrodes  29  and  30 , also both of the same electrical polarity. The sides of the base  40  have fifth and sixth electrodes  25  and  31 , respectively, each of opposite electrical polarity. The fifth, fourth, and second electrodes  25 ,  29 ,  30 ,  34  and  35  have the same electrical polarity, while the first, sixth and third electrodes  23 ,  24 ,  31 ,  38  and  39  also have the same electrical polarity, which is opposite to the electrical polarity of the other electrodes, mentioned above. The individual electrodes are electrically connected and two electrode terminals E-E′ are constructed. The electrodes disposed inside the grooves opposite each to each other in the thickness (z-axis) direction of the tuning fork tines have the same electrical polarity. Also, the electrodes disposed opposite to each other across adjoining grooves have an opposite electrical polarity to one another. 
     When a direct voltage is applied between the electrode terminals E-E′ (e.g., with the E terminal being the positive (+) terminal, having a positive electrical polarity; and the E′ terminal being the negative (−) terminal, having a negative electrical polarity), an electric field Ex occurs, having an orientation as shown by the arrows in FIG.  6 . Because the electric field Ex occurs perpendicular to the electrodes disposed on the tuning fork base, the electric field Ex has a very large value and a large distortion occurs at the tuning fork base, so that the quartz crystal tuning fork resonator operates in a flexural mode, and has a small series resistance R 1  and a high quality factor Q, even though the resonator is miniaturized. 
       FIG. 7  shows a plan view of the quartz crystal tuning fork resonator  19  of FIG.  5 . In  FIG. 7 , the disposition of the grooves  21  and  27  is shown in detail. The tuning fork tine  20  has groove  21  cut thereinto, such that the groove includes a portion of the central liner region  41  of the tuning fork tine, and the tuning fork tine  26  also has groove  27  cut thereinto, such that the groove includes a portion of the central linear region  42  of the tuning fork tine. A quartz crystal tuning fork resonator according to this embodiment of the present invention additionally has grooves  32  and  36  formed between the grooves  21  and  27  at the tuning fork base  40  where the tuning fork tines  20  and  26  are attached to the tuning fork base. 
     Thus, a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, and having a shape and an electrode construction according to the embodiments of the present invention has excellent electrical characteristics, even though it is miniaturized. Such a quartz crystal resonator has a small series resistance R 1  and a high quality factor Q. The width dimension W=W 1 +W 2 +W 3 , and length dimensions l 1  and l 2 , of such a resonator are as described above with respect to the embodiment of FIG.  3 . 
     Embodiment 3 
       FIG. 8  shows a plan view of another embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention, having a plurality of resonators. Two quartz crystal tuning fork resonators  101 ,  102 , capable of vibrating in a flexural mode, with each resonator having first and second tines, are connected and are integrally formed, with an angle φ of from 0° to about 30° between each tuning fork base  103 . In addition, the tuning fork tines  104  and  106  of quartz crystal tuning fork resonator  101  have grooves  105  and  107 , and the tuning fork tines  108  and  110  of the quartz crystal tuning fork resonator  102  have grooves  109  and  111 . 
     Because each quartz crystal tuning fork resonator capable of vibrating in a flexural mode has a different frequency temperature behaviour, dependent on the angle φ, an improvement of the frequency-temperature behaviour for the quartz crystal tuning fork resonator is obtainable by electrically connecting the two quartz crystal tuning fork resonators in parallel. The objects of embodiments of the present invention are achievable even if the same-designed resonators have an angle φ=0° because quartz crystal tuning fork resonators capable of vibrating in a flexural mode, which are mass produced, exhibit a distribution of frequency-temperature behaviour due to manufacturing tolerances. In other words there will be small differences between the two resonators. An electrical connection diagram for both quartz crystal tuning fork resonators  101 ,  102  is shown in FIG.  9 . The resonators are electrically connected in parallel. 
     Embodiment 4 
       FIG. 10  shows an example of frequency temperature behaviour for an integrally formed flexural mode, tuning fork, quartz crystal resonator embodying the present invention. The quartz crystal resonator  101 , shown in  FIG. 8 , exhibits a frequency-temperature behaviour  120 , with a peak temperature point of about 30° C., while the resonator  102  shown in  FIG. 8  has frequency temperature behaviour  121  with a peak temperature point of about 10° C. The compensated frequency-temperature behaviour for both quartz crystal resonators connected in parallel electrically is shown by the curve  122 . The integrally formed embodiment of the quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention, has the advantages of being capable of being fabricated in miniature and of demonstrating excellent frequency-temperature behaviour. 
     Embodiment 5 
       FIG. 11  shows a plan view of a further embodiment of a quartz crystal, tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention. As shown in  FIG. 8 , two quartz crystal tuning fork resonators are generally constructed having an angle φ between them in order to change the peak temperature point of the resonators. In the embodiment of the present invention shown in  FIG. 11 , however, it is possible to change the peak temperature point of the quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, by changing at least one dimension of the tuning fork tines, including the width x 1 , and length y 1  of the first tuning fork tine, and the width x 2  and length y 2  of the second tuning fork tine. A peak temperature point of the frequency-temperature behaviour for a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, depends upon the width-to-length ratio (x/y) of either the first tuning fork tine (x 1 /y 1 ) or the second tuning fork tine (x 2 /y 2 ), or both. 
     Accordingly, complex quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, that are fabricated from a plurality of individual quartz crystal tuning fork resonators, each resonator individually being capable of vibrating in a flexural mode, and with each individual resonator having a different peak temperature point, are obtained by changing the width- to- length ratio of at least one tuning fork tine of at least one of the individual quartz crystal tuning fork resonators. As a result, the frequency temperature-behaviour as shown in  FIG. 10  is obtained. More particularly, a resonator having a shape as shown in  FIG. 11 , is provided by quartz crystal tuning fork resonators  130  and  131 , capable of vibrating in a flexural mode, which are connected and formed integrally at their tuning fork base  132 . The resonators are arranged in parallel in a length-wise direction. The tuning fork tines  133 ,  135  and the tuning fork base of quartz crystal tuning fork resonator  130  have grooves  134 ,  136  and grooves  137 ,  138 , respectively. The grooves  134  and  136  are constructed within the tuning fork tines  133  and  135 , and extend to the tuning fork base of the resonator  130 . 
     Similarly, the tuning fork tines  139 ,  141  and the tuning fork base of quartz crystal tuning fork resonator  131  have grooves  140 ,  142  and grooves  143 ,  144 , respectively. Grooves  140  and  142  extend to the tuning fork base of resonator  131 . Because both quartz crystal tuning fork resonators  130 ,  131 , capable of vibrating in a flexural mode, are connected and formed integrally at each tuning fork base  132 , the miniaturization of the resonator is possible, and two quartz crystal tuning fork resonators with different frequency-temperature behaviour are obtained. In addition, an integrally formed multiple quartz crystal tuning fork resonator with excellent frequency-temperature characteristics is realized by electrically connecting the two individual resonator components in parallel. 
     Embodiment 6 
       FIG. 12  shows a plan view of still another embodiment of a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to the present invention. The quartz crystal tuning fork resonator  145 , capable of vibrating in a flexural mode, includes first and second tuning fork tines  146 ,  147 , and tuning fork base  148 . The tuning fork base has an obverse face and a reverse face. One end of each of the tuning fork tines  146  and  147  is connected to the tuning fork base  148 . In this embodiment, a plurality of grooves  149 ,  150 ,  151  and  152  are constructed on the obverse face of the tuning fork base  148 , and not on the tuning fork tines themselves. Additionally, a plurality of grooves is similarly constructed on the reverse face of tuning fork base  148 . 
     The grooves  149  and  150  are each constructed on the obverse face of the tuning fork base  148  at a portion thereof where the end of one of the tuning fork tines  146  and  147  is connected to the tuning fork base  148 , respectively. The grooves  151  and  152  are constructed on the obverse face of the tuning fork base between grooves  149  and  150 . The electrode disposition and the construction is not shown in  FIG. 12 , but is similar to that already explained in detail with regard to  FIG. 6 , above. By so constructing the grooves and the electrodes, a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, is obtained, having a small series resistance R 1  and a high quality factor Q, because a large distortion occurs at the tuning fork base. 
     Embodiment 7 
       FIG. 13  shows a plan view of yet another embodiment of a quartz crystal tuning fork resonator  153 , capable of vibrating in a flexural mode, according to the present invention. The quartz crystal tuning fork resonator  153  includes first and second tuning fork tines  154 ,  155 , and tuning fork base  156 . The tuning fork tines  154  and  155  have grooves  157  and  158 , which extend to the tuning fork base  156 . In addition, a groove  159  is constructed on the tuning fork base  156  between the grooves  157  and  158 . 
       FIG. 14  shows a cross-sectional view through F-F′ of  FIG. 13 , of the tuning fork base  156 , of the quartz crystal tuning fork resonator  153 , capable of vibrating in a flexural mode, according to FIG.  13 .  FIG. 14  shows details of the shape and the electrode construction, in cross-sectional view, of the tuning fork base  156  for the quartz crystal tuning fork resonator  153  of FIG.  13 . As shown in  FIG. 14 , the quartz crystal tuning fork resonator  153  has grooves  157  and  160 , opposite to one another, constructed within the obverse and the reverse faces of the tuning fork base  156 , respectively, where tuning fork tine  154  is connected to tuning fork base  156 . Similarly, the resonator  153  has grooves  158  and  161 , opposite to one another, constructed within the obverse and the reverse faces of the tuning fork base  156 , respectively, where tuning fork tine  155  is connected to tuning fork base  156 . Additionally, groove  159  is constructed between groove  157  and groove  158 , and groove  162  is constructed opposite groove  159 , and between groove  160  and groove  161 . 
     Grooves  157 ,  160  have electrodes  163 ,  164  of the same electrical polarity; respectively; grooves  159 ,  162  have electrodes  165 ,  166  and electrodes  167 ,  168 ; grooves  158 ,  161  have electrodes  169 ,  170  of the same electrical polarity, and both sides of the tuning fork base  156  have electrodes  171 ,  172  of opposite electrical polarity. The electrodes are connected in such a way that electrodes disposed opposite the sides of the grooves  157 ,  158 ,  159 ,  160 ,  161 ,  162  have different electrical polarities. Thus, the electrodes  165 ,  167 ,  169 ,  170 ,  171  are all the same electrical polarity while electrodes  163 ,  164 ,  166 ,  168 ,  172  are of the opposite electrical polarity. The electrodes are electrically connected so that the resonator has two electrode terminals G-G′. 
     Groove  159  has electrode  165  and electrode  166 , each of opposite electrical polarity; similarly, groove  162  has electrode  167  and electrode  168 , each of opposite electrical polarity. The electrodes opposite the electrodes on the sides of the adjoining grooves in the x-axis direction are of opposite electrical polarity. Therefore, for this embodiment, electrode  173 , which is disposed on the side of groove  157 , and electrode  165 , which is opposite to electrode  173  and is disposed on the side of groove  159 , are of opposite electrical polarities. Similarly, electrodes  175  and  167  are of opposite electrical polarity; electrodes  166  and  174  are also of opposite electrical polarity; and electrodes  168  and  176  are of opposite electrical polarity. Electrode  163  and electrode  164 , disposed inside the grooves  157  and  160 , constructed opposite to one another, in the thickness (z-axis) direction of the tuning fork tines, are of the same electrical polarity. Likewise, electrode  169  and electrode  170 , which are respectively disposed inside the grooves  158  and  161  constructed opposite to one another in the thickness (z-axis) direction of the tuning fork tines, are also of the same electrical polarity. Electrodes  163 ,  164 ,  169 ,  170 , disposed respectively inside grooves  157 ,  160 ,  158 ,  161 , and electrodes  171 ,  172 , disposed on the sides of the tuning fork base  156 , extend from tuning fork base  156  to tuning fork tines  154 ,  155 . 
     When an alternating voltage is applied between the two electrode terminals G-G′, an electric field Ex occurs alternately along the arrow directions shown by the solid and broken lines in FIG.  14 . As a result, vibration of the quartz crystal tuning fork resonator in a flexural mode is generated in the inverse phase. Because the electric field E x  occurs perpendicular to the electrodes, between the electrodes disposed on the sides of the grooves, the electric field E x  becomes large, and because the tuning fork base  156  also has grooves  159 ,  162 , with electrodes  165 ,  166 ,  167 ,  168 , a markedly large distortion occurs at the tuning fork base, so that the quartz crystal tuning fork resonator vibrating in a flexural mode has a small series resistance R 1  and a high quality factor Q. 
     In the above-mentioned embodiments, the grooves are constructed on the tuning fork tines and/or the tuning fork base, however, still other embodiment of the present invention include holes instead of grooves or a combination of grooves and holes. 
     Embodiment 8 
       FIG. 15  shows a general view of another embodiment of a quartz crystal tuning fork resonator  300 , capable of vibrating in a flexural mode, according to the present invention, and its coordinate system.  FIG. 16  is a plan view of the resonator  300  shown in  FIG. 15 , and  FIG. 17  shows a cross-sectional view through I-I′ of the tuning fork tines shown in FIG.  16 . As shown in  FIG. 15 , the resonator  300  is formed from a quartz crystal wafer rotated about its x-axis and with a cut angle θ. In general, cut angle θ has a value of from 0° to about 10°. The y′ and z′ axes are new y and z-axes obtained after rotation about the x-axis. This quartz crystal tuning fork resonator  300 , capable of vibrating in a flexural mode, includes first and second tuning fork tines  301 ,  302 , attached to tuning fork base  303 , and has thickness t. Tuning fork tine  301  has step difference portions, and the step difference portion  304  (at the inner side of upper surface portion  301   a ) is formed between upper surface portion  301   a  and medium surface portion  301   b . The medium surface portion  301   b  and the step difference portion  304  extend to the tuning fork base  303 . 
     Similar to tuning fork tine  301 , a medium surface portion  302   b  and a step difference portion  305  are formed on the obverse face of tuning fork tine  302 , as shown in FIG.  16  and FIG.  17 . The upper surface portion  303   a , the medium surface portion  303   b , and the step difference portion  306  are formed on tuning fork base  303 . As shown in  FIG. 16 , tuning fork tine  301  of resonator  300  has a step difference portion  304 , while tuning fork tine  302  has a step difference portion  305 . These step difference portions extend to the tuning fork base  303 , and the step difference portions  304  and  305  are connected at the step difference portion  306  of the tuning fork base  303 . In this embodiment the step difference portions of the tuning fork tines are constructed in series, however, alternative embodiments of the present invention include a plurality of step difference portions spaced along the length direction of the tuning fork tines. 
     As shown in  FIG. 17 , a structure similar to the obverse face of tuning fork tine  301  is also constructed on the reverse face. The step difference portion  307  is formed between the lower surface portion  301   c  and the medium surface portion  301   d , with the step difference portion  307  extending to the tuning fork base  303 . The step difference portion  304  of the obverse face is oriented towards the inside of tuning fork tine  301  and the step difference portion  307  of the reverse face is oriented towards the outside of tuning fork tine  301 . Electrode  308  is disposed on the step difference portion  304  and electrode  309 , which is connected to electrode  308 , is disposed on the medium surface portion  301   b . Electrode  310  is disposed on the step difference portion  307  and electrode  311 , which is connected to electrode  310 , is disposed on the medium surface portion  301   d . Electrode  312  is disposed on the side of tuning fork tine  301 , opposite to electrode  308 , which is disposed on the step difference portion  304 . Electrode  313  is disposed on the side of tuning fork tine  301 , opposite to electrode  310 , which is disposed on the step difference portion  307 . 
     According to this arrangement of electrodes, an electric field Ex occurs perpendicularly between electrodes  308  and  312  and electrodes  310  and  313 . Similarly, tuning fork tine  302  also has the step difference and corresponding electrodes of left and right symmetry to tuning fork tine  301 . The step difference portions  305 ,  314 , the upper surface portion  302   a , the medium surface portion  302   b , and the medium surface portion  302   d , are constructed on both the obverse and the reverse faces of tuning fork tine  302 . Electrode  315  is disposed on the step difference portion  305  and electrode  316 , which is electrically connected to electrode  315 , is disposed on the medium surface portion  302   b . Electrode  317  is disposed on the step difference portion  314  and electrode  318 , which is electrically connected to electrode  317 , is disposed on the medium surface portion  302   d . Electrode  319  is disposed on the side of tuning fork tine  302 , opposite electrode  315 , and electrode  320  is disposed on the side of tuning fork tine  302 , opposite electrode  317 . The first set of electrodes  308 ,  309 ,  310 ,  311 ,  319  and  320  have the same electrical polarity and the second set of electrodes  312 ,  313 ,  315 ,  316 ,  317  and  318  have the same electrical polarity, which is opposite to the polarity of the first set of electrodes. As a result, two electrode terminals K-K′ are constructed. 
     When an alternating current (AC) voltage is applied between the electrode terminals K-K′, an electric field E x  occurs perpendicularly and alternately between the electrodes, as shown by the solid and broken arrow symbols in  FIG. 17. A  flexural mode vibration can be easily excited in the resonator, so that a quartz crystal tuning fork resonator vibrating in a flexural mode, and having a small series resistance R 1  and a high quality factor Q, is obtained because the electromechanical transformation efficiency for the resonator becomes large. 
     Embodiment 9 
       FIG. 18  shows a general view of still another embodiment of a quartz crystal tuning fork resonator  321 , capable of vibrating in a flexural mode, according to the present invention, and its coordinate system.  FIG. 19  is a plan view of the resonator  321  of  FIG. 18 , and  FIG. 20  shows a cross-sectional view through J-J′ of the tuning fork tines of FIG.  19 . The coordinate system of this embodiment is the same as that shown in  FIG. 15. A  quartz crystal tuning fork resonator  321 , capable of vibrating in a flexural mode, according to this embodiment, includes first and second tuning fork tines  322 ,  323 , attached to tuning fork base  324 . The tuning fork tines have a thickness t. Tuning fork tine  322  further has a step difference, as shown in FIG.  18  and FIG.  20 . Upper surface portion  322   a , medium portion  322   b ,  322   d , step difference portion  325 ,  328 , and lower surface portion  322   c  are formed on tuning fork tine  322 . The medium surface portion  322   b ,  322   d , and the step difference portion  325 ,  328  extend to the tuning fork base  324 , which has an obverse face that is shaped to the upper surface portion  324   a , the medium surface portion  324   b  and the step difference portion  327 , and which has a reverse face with the same shape as the obverse face (not shown in FIGS.  18  and  19 ). 
     Similarly, upper surface  323   a , medium portions  323   b ,  323   d , step difference portions  326 ,  329 , and lower surface portion  323   c  are formed on tuning fork tine  323 . The medium surface portions  323   b ,  323   d  and the step difference portions  326 ,  329  extend to the tuning fork base  324  in a manner similar to tuning fork tine  322 . As shown in  FIGS. 19 and 20 , the tuning fork tines  322  and  323  have the step difference portions  325  and  326 , which extend to the tuning fork base  324 , and connect at the step difference portion  327 . The step difference portions  325  and  328  are constructed at the obverse and the reverse faces, respectively, of tuning fork tine  322 , and the step difference portions  326  and  329  are constructed on the obverse and the reverse faces, respectively, of tuning fork tine  323 . In this embodiment, the step difference portions  325 ,  328  and  326 ,  329  face the inside of the tuning fork tines  322  and  323 . The same effect is obtained when the step difference portions  325 ,  328  and  326 ,  329  face the outside of the tuning fork tines  322  and  323 . 
     Electrode  330  is disposed on step difference portion  325  and electrode  331 , which is connected to electrode  330 , is disposed on medium surface portion  322   b . Electrode  332  is also disposed on step difference portion  328 , and electrode  333 , which is connected to electrode  332 , is disposed on the medium surface portion  322   d . Electrodes  334 ,  335  are disposed on both sides of tuning fork tine  322 . Electrode  335  is disposed opposite electrodes  330  and  332 , which are of opposite electrical polarity to electrode  335 . Similarly, tuning fork tine  323  also has the step difference and electrodes of left and right symmetry to tuning fork tine  322 . 
     Tuning fork tine  323  has difference portions  326 ,  329 , upper surface portion  323   a , medium surface portions  323   b ,  323   d , and lower surface portion  323   c . Step difference portion  326  has electrode  336 , which is connected to electrode  337 , which is disposed on the medium surface portion  323   b . Step difference portion  329  has electrode  338 , which is connected to electrode  339 , which is disposed on the medium surface portion  323   d . Electrodes  340 ,  341  are disposed on both sides of tuning fork tine  323 . Electrode  341  is disposed opposite to electrodes  336  and  338 , which are of opposite electrical polarity to electrode  341 . As shown in detail in  FIG. 20 , the first set of electrodes  330 ,  331 ,  332 ,  333 ,  340  and  341  have the same electrical polarity, while the second set of electrodes  334 ,  335 ,  336 ,  337 ,  338  and  339  have the same electrical polarity, which is opposite to the electrical polarity to the first set of electrodes. The electrodes are connected to form two electrode terminals L-L′. 
     When an alternating current (AC) voltage is applied between the two electrode terminals L-L′, an electric field E x  occurs, oriented perpendicular to and alternately between the electrodes, as shown by the solid and broken arrow symbols in  FIG. 20 , and a flexural mode vibration is easily excited, so that a quartz crystal tuning fork resonator vibrating in a flexural mode is obtained. The resonator has a small series resistance R 1  and a high quality factor Q because the electromechanical transformation efficiency for the resonator becomes large. In this embodiment, tuning fork tines  322  and  323  have medium surface portions  322   b ,  322   d ,  323   b  and  323   d  on the inside of the tines, however, the same effect as that of this shape is obtained when the medium surface portions are constructed on the outside of tuning fork tines  322  and  323 . 
     Embodiment 10 
       FIG. 21  shows a plan view of yet still another embodiment of a quartz crystal tuning fork resonator  342 , capable of vibrating in a flexural mode, according to the present invention. In this embodiment three quartz crystal tuning fork resonators  343 ,  344 ,  345 , each individually capable of vibrating in a flexural mode, are connected at the tuning fork bases and are integrally formed by an etching or mechanical process. As shown in  FIG. 21 , each resonator  343 ,  344  and  345 , uses the step difference embodiment of quartz crystal tuning fork resonators  300  and  321 . The first resonator  343  includes tuning fork tines  346 ,  347 , attached to tuning fork base  348 ; the second resonator  344  includes tuning fork tines  349 ,  350 , attached to tuning fork base  351 ; and the third resonator  345  includes tuning fork tines  352 ,  353 , attached to tuning fork base  354 . The first resonator  343  and the second resonator  344  are integrally formed through base portion  355  of tuning fork bases  348  and  351 . 
     Similarly, the second resonator  344  and the third resonator  345  are integrally formed through base portion  356  of tuning fork bases  351  and  354 . These resonators  343 ,  344  and  345  are designed so as to each have a different ratio of width to length of their tuning fork tines. As a result of this, the three individual quartz crystal tuning fork resonators  343 ,  344  and  345 , capable of vibrating in a flexural mode, are integrally formed and have different frequency-temperature behaviour characteristics, yet constitute a single piece integrated quartz crystal resonator. 
     Furthermore, as described in detail hereinabove with respect to the embodiments shown in  FIGS. 8-11 , an improvement of the frequency-temperature behaviour characteristics of this embodiment may be obtained by electrically connecting these resonators  343 ,  344  and  345  in parallel. Although this embodiment illustrates the formation of an integrated quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, having, three individual component quartz crystal tuning fork resonators, there is nothing that limits the integrated resonator to three individual component resonators, and an integrated resonator having more than three individual component resonators can also readily be fabricated. 
     Furthermore, in such embodiments, although a plurality of individual component quartz crystal tuning fork resonators, each capable of vibrating in a flexural mode, and having the same shape, are used to improve the frequency-temperature behaviour characteristics of the integrated resonator, the frequency-temperature behaviour characteristics of such a resonator can also be improved by forming an integrated resonator utilizing a combination of different individual component resonators, such as, for example, (1) by utilizing a combination of quartz crystal tuning fork resonators with grooves as shown in  FIGS. 1 ,  5 ,  12  and  13  and a quartz crystal tuning fork resonator with step difference as shown in  FIGS. 15 and 18 ; (2) by a combination of resonators as shown in  FIGS. 1 ,  5 ,  12  and  13 ; (3) by a combination of resonators as shown in  FIGS. 15 and 18 ; (4) by a combination of resonators as shown in  FIGS. 1 ,  5 ,  12 ,  13 ,  15  and  18  with a conventional resonator as shown in  FIGS. 22 and 23 . 
     In other words, an improvement of the frequency-temperature behaviour characteristics of an integrated quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, can be accomplished by employing an embodiment of a quartz crystal tuning fork resonator according to the present invention, and electrically connecting it in parallel to another resonator. 
     Embodiments of the quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, according to the present invention also utilize two methods of electrode disposition, the choice of which determines the vibration mode of the tuning fork tines. According to a first method (1) electrodes are disposed so that each quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, consists of a plurality of individual resonators that are connected and integrally formed at their tuning fork bases, such that the resonators all vibrate in the same vibration mode; and according to a second method (2) electrodes are disposed so that a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, and including a plurality of individual component resonators that are connected and integrally formed at their tuning fork bases, such that the individual component resonators vibrate in different modes. 
     Each quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, according to these embodiments, is connected and is integrally formed side by side as shown in  FIGS. 8 ,  11  and  21 . However, the present invention is not limited to flexural mode, tuning fork, quartz crystal resonator connected and formed integrally side by side, but includes the connection and integrated formation of any shapes at the tuning fork bases. 
     The embodiments of individual quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, according to the present invention, have two tuning fork tines, however, other alternative embodiments can be fabricated having a greater plurality of tuning fork tines. Still other alternative embodiments of the present invention also include quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, having more than three individual resonator components, which are connected and integrally formed at the tuning fork bases. Yet still other alternative embodiments of quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, according to the present invention, include integrated embodiments including a plurality of individual resonators wherein the individual component resonators are connected and integrally formed at each tuning fork base, and wherein each component resonator has a different shape and a different electrode configuration. 
     The present invention includes those embodiments of quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, having two individual component quartz crystal tuning fork resonators, each capable of vibrating in a flexural mode, wherein the tuning fork bases are connected and integrally formed at an angle φ between the tuning fork bases, as has been described and shown in  FIG. 8 , hereinabove, as well still further including other alternative embodiments of quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, wherein the resonators are substantially the same as those resonators according to the present invention having an angle φ between the base portions of the integrally formed individual component resonators, but wherein the plurality of individual component resonators are formed in parallel and at least one of the plurality of component resonators is designed and formed so that at least two tuning fork tines are inwardly oriented towards at an angle φ, or, alternatively, are outwardly oriented at an angle φ. 
     The following lists some of the results and advantages that are obtained using the quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, according to the present invention, having the resonator shapes and electrode configurations as described hereinabove:
     (1) Because the grooves are constructed in such a way so as to include a portion of the central linear region of the tuning fork tines, an electric field occurs perpendicular to the electrodes, so that the quartz crystal tuning fork resonator, when vibrating in a flexural mode, has a small series resistance R 1  and a high quality factor Q because the electromechanical transformation efficiency is large.   (2) Even when miniaturized, the quartz crystal tuning fork resonator, vibrating in a flexural mode, still has a very small series resistance R 1 .   (3) A miniaturized integrated quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, and including two individual quartz crystal tuning fork resonators integrally formed, is realized by fabricating the resonator using an etching process, and has the two resonators being electrically connected in parallel, resulting in an integrated resonator having excellent frequency-temperature behaviour characteristics.   (4) A low price quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, is realizable because the resonator is integrally formed using an etching process, which enables the formation of an integrated resonator including many individual resonators, fabricated on a single piece of quartz wafer.   (5) Because prior art quartz crystal resonators are generally of the tuning fork type, it is easy to mount a quartz crystal tuning fork resonator according to the present invention on two lead wires or a pedestal, thereby resulting in a decrease in energy losses at the mounting, caused by vibration of the tuning fork tines, and thereby also rendering the resonators of the present invention highly mechanically shock resistant.   (6) Because there are a plurality of grooves of opposite electrical polarity on the tuning fork base and the electrodes that are disposed opposite to the sides of adjoining grooves, the distortion at the tuning fork base is large, resulting in a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, and having a small series resistance R 1  and a high quality factor Q, even when miniaturized.   (7) Because grooves are constructed so as to include the central linear region of the tuning fork tines, with electrodes being positioned on the grooves, and with the grooves extending to the tuning fork base, the quantity of distortion at the tuning fork base is large, resulting in a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, and having a small series resistance R 1  and a high quality factor Q, because there is also a high electromechanical transformation efficiency.   (8) Because, in certain embodiments, electrodes are disposed on step difference portions constructed at obverse and reverse faces of the tuning fork tines, in their width direction, and because sides of the tuning fork tines opposite to electrodes have an opposite electrical polarity to those electrodes, the electromechanical transformation efficiency of the resonator is very large, thereby resulting in a quartz crystal tuning fork resonator, capable of vibrating in a flexural mode, and having a small series resistance R 1  and a high quality factor Q.   (9) Narrow width tuning fork tines are possible in certain embodiments of the resonators according to the present invention, while still maintaining a sufficiently large electro-mechanical transformation efficiency, by constructing step differences on the tuning fork tines.   (10) Because a plurality of quartz crystal tuning fork resonators are integrally formed and are electrically connected in parallel according to certain embodiments of the present invention, the compound series resistance R 1  for the compound, integrated resonator is small. For example, when a compound, integrated quartz crystal tuning fork resonator according to the present invention is fabricated from two individual resonators, each having the same series resistance R 1 , the resulting integrated resonator has only half the total series resistance R 1 . Thus, the compound series resistance R 1  of a compound, integrated resonator can be decreased even more by increasing the number of individual resonators which are integrally formed as part of the compound, integrated resonator.   (11) Because the compound, integrated quartz crystal tuning fork resonators according to certain embodiments of the present invention are formed integrally, and are electrically connected in parallel, the resonator can continue to function even if one of the individual resonators that from the integrated resonator should break or become inoperative, such as due to the component receiving a severe mechanical shock.   

     The quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, according to the present invention, and having the novel shapes and novel electrode configurations described hereinabove demonstrate the foregoing results and advantages over conventional quartz crystal tuning fork resonators previously known in the art. In addition, although the present invention has been described and illustrated with reference to those preferred embodiments thereof disclosed herein, it will be understood by those skilled in the art that additional embodiments of quartz crystal tuning fork resonators, capable of vibrating in a flexural mode, and having still other shapes and electrode configurations are possible and can be made without departing from the spirit and scope of the present invention.