JP2003037462A - Method for designing piezoelectric oscillator, method for preparing mode chart, method for preparing frequency/temperature characteristics curve, simulation method of the piezoelectric oscillator, designing device of the piezoelectric oscillator and simulation program of the piezoelectric oscillator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To solve the problem, with the high-frequencies of a crystal oscillator, an optimum design range which averts spurious oscillations becoming narrowed, so that design becomes very difficult. SOLUTION: An area of points, representing main oscillation and spurious oscillations of a conventional mode chart is plotted by a value, in proportion to the total charge volume included in each oscillation, and a region which averts the spurious oscillation of a large area is selected as optimum design region.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a piezoelectric vibrator designing method, a mode chart creating method, a frequency temperature characteristic curve creating method, a piezoelectric vibrator designing apparatus, and a piezoelectric vibrator simulation program.

[0002]

2. Description of the Related Art The main vibration frequency of an AT-cut crystal oscillator is the crystal axes x1, x2 of the oscillator having the shape of a rectangular plate.
x3 is defined as in Fig. 1 and each dimension is length 2
In the case of a, thickness 2b, and width 2c, it is determined by the equation (1).

[0003]

[Equation 1]

As shown in FIG. 2, this is called thickness shear vibration in which the crystal blank is displaced in the x1 direction while sliding in the direction x2 of the thickness 2b, and the frequency is
As shown in the equation (1), it is almost inversely proportional to the thickness 2b. This thickness shear vibration is shown in FIG.
As shown in (a), since it has a temperature characteristic of a cubic curve and shows only a frequency deviation of about ± 10 ppm in the use range of the equipment of −50 ° C. to 100 ° C.,
Widely used as a highly stable frequency source.

However, in a crystal blank having a shape as shown in FIG. 1, various mechanical vibrations simultaneously exist in addition to the main vibration, and it is generally called spurious vibration (unnecessary vibration). FIG. 4 shows typical spurious vibration modes, and the formulas for calculating the frequencies derived from the equations of motion corresponding to these modes are shown below. Here, the equation (2) corresponds to the case of FIG. 4A, the equation (3) corresponds to the case of FIG. 4B, and the equation (4) corresponds to the case of FIG. 4C. .

[0006]

[Equation 2]

[0007]

[Equation 3]

[0008]

[Equation 4]

From the equations (2) to (4), it is understood that the frequency is greatly influenced by the blank length 2a and the blank 2c in the mode in which the standing wave stands in the length 2a and the width 2c directions. When this spurious vibration exists near the main vibration, energy coupling with the main vibration occurs, and as a result, the energy of the main vibration is taken and the impedance rises or the frequency shifts. .

Particularly, since spurious vibration has a temperature coefficient much larger than that of the main vibration, the temperature dependence of the main vibration (hereinafter referred to as the temperature characteristic) is shown in FIG. 3B. While measuring, it rapidly approaches the main vibration. Especially, at the temperature where the main vibration and the spurious vibration intersect, the main vibration jumps, and if it is incorporated in the oscillator, a non-firing phenomenon occurs, so avoid spurious vibration when designing the oscillator blank. Thus, the length 2a and the width 2c are determined. Therefore, accurate spurious vibration prediction is an important issue for oscillator design.

Generally, for designing a vibrator, what is called a mode chart, in which the frequency positions of the main vibration and the spurious vibration are plotted with respect to the blank shape, is used. FIG. 5 shows an example of a conventional low frequency mode chart, in which the vertical axis represents frequency and the horizontal axis represents the width 2c of the vibrator. In this figure, the other blank lengths 2a and the dimensions of the electrodes are constant. It should be noted that the vertical axis may be a standardized frequency whose frequency is standardized with the frequency of a crystal blank without electrodes, and the horizontal axis may be a value standardized with a width 2c or a length 2a being a thickness 2b. is there.

In the figure, points on the line are main vibrations, and other points are spurious vibrations. In the area surrounded by a circle in the figure, there is no spurious vibration that intersects with the main vibration. By designing the 2c dimension corresponding to this region as the blank width, it is possible to obtain a vibrator with a stable frequency. In an actual oscillator, an electrode is added or the oscillator is supported, so that the frequency is not observed as calculated by the equations (1) to (4).

In the past, such a mode chart was often created by experiment for each shape, but in recent years, the finite element method (hereinafter FEM (Finite Element) is used.
Method). ) Has established a highly accurate AT-cut transducer analysis (Japanese Patent Laid-Open No. 2000-183415).
It has also become possible to create mode charts using a computer. FIG. 5 also shows the result calculated by FEM.

As described above, the mode chart is indispensable for efficiently performing the spurious vibration prediction of the crystal unit and searching for the optimum design value.

[0015]

Recently, there has been an increasing demand for higher frequencies for crystal oscillators. As shown in Expression (1), at high frequencies, the contour vibration depending on the length 2a and the width 2c shown in Expressions (2) to (4) becomes a higher-order wave. If higher-order waves exist in the length 2a direction and the width 2c direction, many spurious vibrations that combine them are generated, and the number of spurious vibrations further increases.

FIG. 6 shows a conventional mode chart in the high frequency region. As is clear from comparison with FIG. 5, at high frequencies, the intervals of spurious vibrations become close, and the region suitable for design becomes very narrow. Moreover, in mass production,
Since there is a processing error and the frequency shift due to the temperature of spurious vibration must be taken into consideration, it is almost impossible to find the optimum region.

However, it has been empirically known that not all spurious vibrations calculated in the temperature characteristics cause frequency jumps, but some of them splice with the main vibrations to deteriorate the temperature characteristics. . In order to evaluate the degree to which the spurious vibration is applied to the main vibration, it has been proposed to use the electric charge generated on the surface.
45 (1997-09)). Since crystal has piezoelectricity, strain in the crystal generated by vibration is converted into electric charge.
The charge amount is represented by the equation (5).

[0018]

[Equation 5]

Since the displacement amount of each spurious vibration is calculated in the FEM calculation, the total amount of electric charge generated on the surface can also be calculated by integrating the displacement amount of each spurious vibration. However, the surface charge of spurious vibration is
By interaction with other spurious vibrations or the main vibration,
While it changes moment by moment, the conventional evaluation method is not one that captures continuous movement.

Therefore, an object of the present invention is to design a piezoelectric vibrator capable of evaluating the influence of spurious vibration on the main vibration while considering the interaction between the spurious vibration and the main vibration. A method for creating a frequency-temperature characteristic curve, a device for designing a piezoelectric vibrator, and a simulation program for a piezoelectric vibrator are provided.

[0021]

In the present invention, the total surface charge amount under each dimensional condition of each spurious vibration calculated by using the equation (5) is used as an index for judging the strength of the spurious vibration. Since quartz is a piezoelectric crystal, generating a large amount of charge means vibrating due to a large displacement, and of course, when it exists near the main vibration, it becomes a factor that hinders thickness shear vibration. Because I thought. Specifically, the area of the points representing the main vibration and the spurious vibration of the conventional mode chart is plotted with a value proportional to the total amount of electric charge when each vibration is coupled.

[0022]

BEST MODE FOR CARRYING OUT THE INVENTION A method of designing a piezoelectric vibrator according to an embodiment of the present invention will be described below with reference to the drawings. (Embodiment 1) Instead of the mode charts shown in FIGS. 5 and 6, displacements of the main vibration and spurious vibrations of the piezoelectric vibrator are obtained by the finite element method, and the amount of charge generated on the electrode surface by this displacement is calculated. 7 and 8 show mode charts plotted by a method in which this charge amount is used for weighting. 7 shows a low frequency mode chart, and FIG.
Shows a high frequency mode chart. The white circles in FIGS. 7 and 8 are the main vibrations, and since the total charge amount is much larger than other spurious vibrations, it is 1/2 of the charge amount.
It is displayed as 0. Other circles represent spurious vibrations.

What has been clarified from FIG. 8 is that, as in the case of the x3 axis width sliding contour vibration, that which is likely to cause a frequency jump in the temperature characteristic in combination with the main vibration is indicated by an arrow in the figure. , The spurious vibration itself has a large amount of electric charge, which greatly affects the main vibration. Also, for other spurious vibrations, as shown by the circles, the charge amount is not large in the region greatly apart from the main vibration, but when it approaches the main vibration, the charge amount is combined with the main vibration and the charge amount becomes large. There is something to increase.

The increase in the charge amount of the spurious vibration means that charge leakage from the main vibration to the spurious vibration occurs, and the charge amount of the main vibration decreases. That is, the main vibration is hindered, causing an impedance increase and a frequency jump. On the other hand, there are spurious vibrations that show almost no change in the amount of electric charge even when they approach the main vibration, and that they move away from each other. Several experiments were conducted to confirm these phenomena.

Width (2c) dimension of point A that is most likely to be affected by the x3 axis width sliding contour vibration shown in FIG.
FIG. 9 shows the temperature characteristics of the vibrator prototyped at (1296 μm). FIG. 9A shows the temperature dependence of the main vibration frequency deviation, and FIG. 9B shows the deviation amount (curve fit) from the cubic curve of the main vibration frequency deviation depicted in FIG. 9A. Error) is plotted. FIG. 9C shows
The temperature dependence of impedance is shown. As can be inferred from the mode chart of FIG. 8, it can be seen that there are a plurality of large frequency jumps on the high temperature side. From this, it was confirmed on the mode chart that spurious vibrations exist even in the actual device around the spurious vibrations where the charge amount is large.

As described above, paying attention to the total charge amount generated by the coupling of the main vibration and the spurious vibration, the spurious vibration that has a large effect on the decrease in the charge amount of the main vibration is displayed relatively large, and the main vibration The spurious vibration, which has a small effect on the decrease in the amount of electric charge, is displayed relatively small. Accordingly, it is possible to easily determine which spurious vibration deteriorates the temperature characteristic of the main vibration, and it is possible to easily design the piezoelectric vibrator in consideration of the frequency temperature deviation. (Embodiment 2) FIG. 10 shows FE under the same condition at point A.
It shows the temperature characteristics using the total amount of charges calculated by M analysis. That is, not only the frequency position of the spurious vibration but also the coupling displacement of the main vibration and the spurious vibration of the piezoelectric vibrator is obtained by the finite element method, and the method of calculating the charge amount generated on the electrode surface due to this coupling displacement is adopted. The temperature characteristic curve was created by weighting the vibration.

Similar to the mode chart in the first embodiment,
The frequency deviation of spurious vibration due to temperature change and the state of coupling with the main vibration can be clearly confirmed. 9 (a)-
As confirmed by the experimental result of (c), in the high temperature region,
There are three spurious vibrations SP1, SP2, SP3, and in particular, two spurious vibrations SP2, SP on the high temperature side.
No. 3 suggests that the charge amount is large and induces a large jump of the main vibration frequency. As described above, even in the temperature characteristic, more accurate temperature characteristic prediction can be performed by considering the charge amount. (Example 3) Similarly, the phenomenon of spurious vibration having a small amount of charge existing near the main vibration was examined by an experiment. The temperature characteristic measurement results of the oscillator prototyped under the same conditions are
It is shown in FIGS. In addition, FIG.
12B shows the frequency-temperature characteristic at point B, FIG. 12B shows the curve-fit error at point B, and FIG. 12C shows the impedance-temperature characteristic at point B.

From the measurement results, it was not possible to observe particularly noticeable spurious vibrations. In this way, in the evaluation of the charge amount, when it is determined that there is no large coupling with the main vibration, no large spurious vibration is observed even in the actual device, and using the charge amount as an index is an effective means. I was able to confirm that. On the other hand, FIG. 11 shows temperature characteristics in consideration of the calculated charge amount. As shown by the line in the figure, two spurious vibrations SP4 and S
Although P5 intersects, the total charge amount has not increased significantly. (Embodiment 4) As described above, adopting the mode chart in consideration of the amount of electric charge is effective in observing the frequency positional relationship between the main vibration and other spurious vibrations and the degree of charge transfer. However, there is a drawback that the area around the spurious vibration with a large amount of electric charge is hidden, and it is not possible to see even small points.

Therefore, paying particular attention to the main vibration, the change in the charge amount and the frequency may be plotted as shown in FIG. FIG. 13 shows the width (2c) size dependence of the main vibration and the amount of electric charge. This is the result of calculation under the same conditions as in FIG. In FIG. 13, since changes in the charge amount and the frequency are expressed at the same time, it is well observed that the charge of the main vibration leaks to the spurious vibration and the frequency shifts due to the influence of the decrease in the charge amount. be able to. Based on this graph, it is possible to select a region in which both frequency and charge amount are stable, and it is possible to realize optimum design of the vibrator.

FIG. 14 shows an AT according to an embodiment of the present invention.
It is a flow chart which shows operation of an analysis program. In FIG. 14, a model to be analyzed is determined (step S1). Specifically, the blank shape, the presence or absence of electrodes,
The material, temperature, boundary conditions, etc. of the electrodes and piezoelectric body are determined.

Next, an analysis mesh in the finite element method is created (step S2), and eigenvalue analysis is performed (step S3). Specifically, after creating a matrix having mesh points as elements, eigenvalues and eigenvectors are calculated to obtain the resonance frequency. Next, each resonance frequency is analyzed to calculate the amount of displacement, strain, and surface charge (step S
4).

Next, a mode chart corresponding to the surface charge is created (step S5) and a temperature characteristic curve is displayed (step S6). As described above, according to the above-described embodiment, the total charge amount generated by the combination of the main vibration and the spurious vibrations is not obtained separately from the charge amount generated by the main vibrations and the charge amount generated by the spurious vibrations. Ask for.

As a result, of the various spurious vibrations, the spurious vibrations that are combined with the main vibrations to deteriorate the temperature characteristics are specified, and the spurious vibrations that are not combined with the main vibrations and do not deteriorate the temperature characteristics are specified. It becomes possible to do. Therefore, as shown in the high-frequency mode chart of FIG. 6, spurious vibrations that are buried in spurious vibrations in all regions and where it is difficult to find a region with good temperature characteristics identify spurious vibrations that are not coupled to the main vibration. By doing so, it becomes easy to find a region having a good temperature characteristic, and it becomes possible to design with a margin.

[0034]

According to the present invention, the following effects can be obtained by taking the method as described above. According to the present invention, displacement amounts of various spurious vibrations existing in the frequency characteristic of the crystal unit and the amount of charges of the spurious vibrations calculated from the displacement amounts are calculated by FEM analysis, and the values are simultaneously displayed on the mode chart. By plotting, the influence of the spurious vibration on the main vibration can be predicted more accurately, and the optimum design area can be accurately grasped. As a result, not only the design margin is increased and the mass productivity is improved, but also efficient development can be performed, so that the number of prototypes can be reduced and the development period can be shortened.

[Brief description of drawings]

FIG. 1 shows a coordinate system of a vibrator according to the present invention and definitions of symbols representing respective dimensions.

FIG. 2 shows vibration modes of a main vibration.

FIG. 3A shows a frequency-temperature characteristic of a general AT-cut crystal resonator, and FIG. 3B shows a frequency jump that occurs in the frequency-temperature characteristic due to the presence of spurious vibrations.

FIG. 4 shows a vibration mode of a typical spurious vibration,
(A) shows thickness slip secondary vibration, (b) shows x3 axis width slip contour vibration, (c) shows x1 axis contour vibration.

FIG. 5 is a conventional mode chart in which the horizontal axis represents width (2c) and the vertical axis represents frequency.

FIG. 6 shows a conventional mode chart in a high frequency band.

FIG. 7 shows a low frequency mode chart with charge consideration for each spurious oscillation according to one embodiment of the invention.

FIG. 8 shows a high frequency mode chart in which charge is taken into account for each spurious vibration according to one embodiment of the present invention.

FIG. 9A shows frequency-temperature characteristics at point A,
(B) shows the temperature characteristic of the curve fit error at the point A, and (c) shows the impedance temperature characteristic at the point A.

FIG. 10 shows a temperature characteristic curve considering electric charges.

FIG. 11 shows temperature characteristics (calculated values) at point B.

FIG. 12A shows frequency temperature characteristics at point B, FIG. 12B shows temperature of curve fit error at point B, and FIG. 12C shows impedance temperature characteristics at point B.

FIG. 13 shows the width (2c) size dependence of the main vibration and the charge amount.

FIG. 14 is a flowchart showing an operation of an AT analysis program according to an embodiment of the present invention.

   ─────────────────────────────────────────────────── ─── Continued front page    F-term (reference) 5B046 AA07 BA01 JA02 JA04                 5J108 AA01 AA04 BB02 CC04 DD02                       MM11    (54) [Title of Invention] Piezoelectric vibrator design method, mode chart creation method, frequency temperature characteristic curve creation method, piezoelectric vibration                     Child simulation method, piezoelectric vibrator design device, and piezoelectric vibrator simulation program                     Mu

Claims (19)

[Claims] 1. A method of designing a piezoelectric vibrator, which comprises obtaining a displacement of a main vibration and a spurious vibration of a piezoelectric vibrator by a finite element method, and calculating an electric charge amount generated on an electrode surface by this displacement. 2. When designing a piezoelectric vibrator, in a method of creating a mode chart showing the dimensional dependence of main vibration and spurious vibration and determining an optimum design value from the mode chart, a finite element method is used. A method of creating a mode chart, characterized in that displacements of main vibration and spurious vibrations of a piezoelectric vibrator are obtained, an amount of electric charges generated on an electrode surface by the displacements is calculated, and the amount of electric charges is used for weighting. 3. When designing a piezoelectric vibrator, in a method of creating a mode chart showing dimensional dependence of main vibration and spurious vibration, and determining an optimum design value from the mode chart, the finite element method is used. Obtain the displacement of the main vibration and spurious vibration of the piezoelectric vibrator, calculate the amount of charge generated on the electrode surface due to this displacement, and determine the optimum design area of the piezoelectric vibrator from the mode chart that uses this amount of charge for weighting. A method for designing a piezoelectric vibrator. 4. A method of creating a frequency-temperature characteristic curve of a piezoelectric vibrator calculated by the finite element method, wherein not only the frequency position of the spurious vibration but also the displacement of the main vibration and the spurious vibration of the piezoelectric vibrator is calculated by the finite element method. A method of creating a frequency-temperature characteristic curve, characterized in that a method of calculating the amount of electric charge generated on the electrode surface by this displacement is employed to weight the spurious vibration. 5. A method for designing a piezoelectric vibrator using a frequency-temperature characteristic curve of the piezoelectric vibrator calculated by the finite element method, wherein not only the frequency position of spurious vibration but also the main vibration of the piezoelectric vibrator by the finite element method is used. And determine the optimum design area by using the temperature characteristic curve created by weighting the spurious vibrations by calculating the displacement of spurious vibrations and calculating the amount of charge generated on the electrode surface by this displacement. A method for designing a piezoelectric vibrator. 6. A charge amount of the main vibration is calculated by a method of calculating displacements of the main vibration and spurious vibrations of the piezoelectric vibrator by the finite element method, and calculating a charge amount generated on the electrode surface by this displacement. A method for designing a piezoelectric vibrator, characterized in that an optimum design shape is determined from shape dependence. 7. The method of designing a piezoelectric vibrator according to claim 6, wherein, in addition to the charge amount, shape dependency of frequency is also taken into consideration, and a region in which both the charge amount and the frequency are stable is set as an optimum design region. A method for designing a piezoelectric vibrator, comprising: 8. The method according to claim 1, 3, 5, 6, or 7,
A method for designing a piezoelectric vibrator, wherein the piezoelectric vibrator is a crystal vibrator. 9. The method for producing a mode chart according to claim 2, wherein the piezoelectric vibrator is a crystal vibrator. 10. The method according to claim 4, wherein the piezoelectric vibrator is a crystal vibrator. 11. A method for designing a piezoelectric vibrator, characterized in that a blank size of the piezoelectric vibrator is determined based on a total amount of charges generated by coupling of main vibration and spurious vibration. 12. The method of designing a piezoelectric vibrator according to claim 11, wherein the blank size is determined so that a decrease in the charge amount of the main vibration due to the spurious vibration is equal to or less than a predetermined value. 13. A method of simulating a piezoelectric vibrator, which comprises calculating a total amount of charges generated by coupling of a main vibration and a spurious vibration. 14. A parameter input means for inputting a blank size of a piezoelectric vibrator as a parameter, and a total charge amount calculating means for calculating a total charge amount generated by coupling of a main vibration and a spurious vibration with respect to the blank size. A device for designing a piezoelectric vibrator, comprising: 15. The design of the piezoelectric vibrator according to claim 14, further comprising a mode chart display means for enlarging and displaying a point indicating the spurious vibration on a mode chart corresponding to the total charge amount. apparatus. 16. The device for designing a piezoelectric vibrator according to claim 15, wherein the mode chart display means displays a point indicating the spurious vibration with a circle having an area corresponding to the total charge amount. . 17. The main vibration display means for displaying changes in the charge amount and frequency of the main vibration with respect to the blank size is further provided.
The piezoelectric vibrator design apparatus described. 18. A computer program for simulating a piezoelectric vibrator, which causes a computer to execute a step of calculating a charge amount generated by coupling of a main vibration and a spurious vibration using a blank size of the piezoelectric vibrator as a parameter. 19. A simulation of a piezoelectric vibrator, comprising causing a computer to execute a step of calculating an amount of electric charge generated by coupling of a main vibration and a spurious vibration with a temperature as a parameter for a specified blank dimension. program.