JPS60160214A - Rotation y-cut strip crystal resonator and its frequency temperature characteristic adjusting method - Google Patents

Abstract

PURPOSE:To bring a primary temperature coefficient at an inflection point to zero or any other desired value by combining properly a cut azimuth and said ratio near the AT-cut to provide the inflection point of the frequency temperature characteristic curve near room temperature without providing a slope to a strip side face. CONSTITUTION:A slope is given to the side face of a substrate by utilizing positively the coupling between the thickness-shear vibration being the main vibration and the width-shear vibration being the sub-vibration and selecting properly the side ratio gamma=w/h (where; w is the width of a strip in Z' direction and h is the thickness in Y' direction) of the said substrate and the cut azimuth angle theta to the Z axis based on an inflection point temperature moving curve where the primary temperature coefficient at the inflection point of the frequency temperature characteristic curve of the substrate decided definitely from the relation of both is zero or any desired value except zero. The inflection point temperature is decided definitely by the cut azimuth angle theta and the adjustable characteristic is only the primary temperature coefficient at the inflection point changed by the side ratio (gamma).

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a strip type quartz crystal resonator, and particularly to a rotary Y-cut strip quartz crystal sensor that does not require special machining steps such as providing an inclined surface on the side surface of the strip.

AT with excellent frequency-temperature characteristics despite strong demand for ultra-miniaturization
It has been difficult to miniaturize a thickness-shear resonator such as a plate because the dimensions of the element are restricted by its contour when all desired characteristics are to be achieved.

In order to deal with this problem, it has been proposed to reduce one side of the contour and make it into a strip. has a long side in the X-axis direction, and the side ratio γ=w/h (w is the width, h
investigated an AT cut strip crystal resonator with a thickness of about 3, and reported that the coupling between the main vibration (thickness shear vibration) and the secondary vibration (width shear vibration) has a significant impact on its frequency-temperature characteristics. ing.

In addition, Mindlin (R1, D, Mindlin) has already been proposed in the 24th FC8 to alleviate the coupling between the main vibration and the sub-vibration as described above. It is stated that in a vibrator with an integral multiple of 3, characteristics equivalent to y are preserved as in an infinite AT plate.

Furthermore, Onoue et al.
Even if it is 0.5 to 6, an appropriate slope (2
It has been revealed that a small camera element with good frequency-temperature characteristics can be obtained by applying a temperature of 16 degrees to 16 degrees.

However, as mentioned above, in order to alleviate the coupling between the main vibration and the sub-vibration, the process of attaching a specific slope to the side surface of the IJ knob not only requires a considerable number of man-hours but also poses a problem in processing accuracy. If the value deviates from an integer multiple of 3, the influence of bonding increases, resulting in a defect that good temperature characteristics cannot be obtained.

The present invention was made in order to eliminate the above-mentioned defects of the conventional strip type crystal resonator, and even if the side surface of the strip is sloped, when the temperature changes, the main vibration is the thickness shear vibration, and the secondary vibration is the thickness shear vibration. Focusing on the fact that the coupling of width shear vibrations occurs, on the contrary, by actively utilizing the coupling of the main and subside vibrations and appropriately combining the cutting direction θ near the AT cut and the side ratio γ, the strip side surface It is an object of the present invention to provide an inflection-tube crystal resonator that provides an inflection point of a frequency-temperature characteristic curve near room temperature without imparting a slope to the frequency-temperature characteristic curve.

Hereinafter, the present invention will be explained in detail based on theoretical analysis and experimental results.

FIG. 1 is an external view of a strip-type vibrator using a rotating Y-cut crystal substrate according to the present invention, which has a long side in the X-axis direction and is cut by rotating an angle θ from two axes around the X-axis. The strip has corners and excitation electrodes E are attached to the main surface of the strip.

In such a vibrator, energy trapping due to piezoelectric reaction of the base plate, electrode addition effect, bevel processing, etc. is a problem, but the main characteristic of the vibrator is that the displacement distribution is in the long side (X axis) direction. All theoretical analyzes were carried out assuming that it was uniform.

First, if the element dimensions are taken as shown in Fig. 2 and piezoelectricity is ignored, the displacement U of the thickness torsional vibration that does not propagate in the
-(Given in 11.

Here, ζ and ξ are wave numbers in the y-axis and two-axis directions, respectively, and ω is the angular frequency.

Also, the strain S is 5s=aU/9z, 8a=3U/ay-...(
21 Stress T is the elastic constant of crystal t = cij, and the equation of motion is given by the density of crystal: Ts/z+ 7'6/y=-#ω2U --(41
is given by

Therefore, by substituting the above +11, (21 and equation (3) into equation (4), we get Cssξ2+2Cs6ζξ0Cssζ2−#ω2=Q
... = (51 From equation (5), two wave numbers in the thick y-axis direction, ζ1 and ζ2, can be found for any combination of the angular frequency ω and the wave number ξ in the two-axis directions.

± Here, the boundary condition at main surface y-↓h is T6=0 to 5 inches (
ζ1-ζ2) h=o, m' (i7 set 1'& 0, 1
, 2 , −−−−−−, then (ζ1−ζ2)h=mπ ・・・・・・・・・・・・
(6) From the above equations (5) and (6), the dispersion equation for waves propagating in two axial directions (% formula %) where normalized frequency Ω=ωh / J Cs s/-j
)+ ・River...(7) is obtained.

Now, in the case of m=o, from equation (6) above, ζl=ζ
2=-(Css/C611)ξ.

At this time, 71gm=Cs68s+Ca5Sa=-j(
Cseξ+Caaζ)U=−j(Cssξ−Cseξ)U=0.

In other words, the non-dispersive wave of the following zero is T6 everywhere in the photographic area.
= 0”k is satisfied, and the wavefront is not perpendicular to the Z direction but at an angle α
= (an' (C56/Css)).

Also, in the case of m=1, when the wave angle in the two-axis direction ξ=O, ζ=±
ω/s/Ca61a, and this ω corresponds to the resonant frequency of thickness shear vibration in an infinite plate.

Now, regarding the element cross section shown in FIG. 2, the side ratio r will be considered assuming that the surface along the X-axis direction is the main surface. In other words, if the boundary conditions are satisfied as rA7 ===w/h +D'r plate system rD7 ``'' h/W for the AT plate system, then torsional vibration will occur considering the waves propagating in the positive and negative directions of the two axes. displacement (the above formula (1) representing Jy is +jωt) where n = 2 m + 2 and is a number.・・・・・・・・・・・・(8) Then, the boundary condition on the side surface when the slope α is given, Ts' = 7'5 cos α−7'6 sin α (however, z' = ), the Lagrangian L is /d z '=c l=172 (7's'IJJ, dy/d+Z''
-C (9) The minimum condition of the Lagrangian is /B, = 0 (however, p = i to n), and the number ω can be written as jin. If ω is determined, the constant B,
It will be understood that wo can be calculated.

As a result of the above calculation, the side ratio r-1. Side inclination angle α=0
In this case, the difference between the resonance frequency calculated as AT cut and that calculated as DT cut was about 10 ppm, and the validity of the above theoretical analysis was confirmed. The constants of Shimizu et al. were used for the elastic constants, etc. in this calculation.

Now, if we draw the frequency spectrum when using an AT-cut board based on the results of the above analysis, it will be as shown in Figure 3.
If you enlarge the coupling part between this and the secondary vibration (width shear vibration ItlI), it will look like (al, (bl) in Fig. 4).

This figure (at is the figure calculated as all parameters of the relationship between the main motion and the auxiliary vibration of the mountain side angle α, and the same a (b) is i
It is a figure which shows the relationship with the next sub-vibration.

In other words, if the slope α is given to the side surface of the IJ tube, the coupling between the main vibration and the secondary vibration becomes weaker, and α=jan'(C6g
/C6g) when 5°'ft is applied, the bond is completely stopped and degenerates.

On the other hand, when the inclination α of the side surface of the horn is zero, as shown in FIG. As shown in the figure, it changes significantly depending on the change rK. This curve has the dispersion equation (7) and the remaining boundary conditions as elastic constant C1J.
Furthermore, since this elastic constant is a function of the cutting azimuth θ and the temperature t, it can be easily calculated, so the details will be omitted to simplify the explanation. Although not shown, it has been found that when the cutting azimuth angle 0 is changed, the - curve in this figure moves parallel to Y in the vertical axis direction.

Q: This figure agrees extremely well with Royer's experimental results mentioned above, making it even clearer that the above theoretical analysis is correct.

Now, from the above analysis results, the slope of the strip side is α=
In the case of jan' (Css /Ces), c is the main vibration m
The first-order temperature coefficient of y becomes zero regardless of the side ratio r, and becomes infinite A
Although it seems that characteristics close to those of the T plate can be obtained, the above ta
a''(Cas/Cs+i)=α has an extremely large dependence on temperature as shown in Figure 6, so even if the side inclination angle α is set to match that at 20°C (approximately 5°), the temperature will not change. It was found that when deviates from 20°C, the coupling of both the main and sub-oscillations occurs, and its frequency-temperature characteristics vary greatly depending on the side ratio r, as shown in Figure 7.Incidentally, the analysis results in Figure 7 are based on the aforementioned Onoue Rotation Y with a small side ratio, which corresponds well with the experimental results of et al. and was previously thought to be incomprehensible.
It can be said that the reason why the temperature characteristics of cut crystal substrates vary depending on the side ratio r has been completely theoretically elucidated.

By the way, from the above analysis results, even if the side surface of the IJ tube is tilted, if the temperature changes, the combination of the two sides will occur, and it is virtually impossible to obtain temperature characteristics similar to an infinite AT plate with any side ratio. It turned out to be impossible. On the other hand, from the above analysis results, the side ratio r at which the first-order temperature coefficient becomes zero, for example, depends on the cutting azimuth θ, as explained with reference to FIG. 5 above.

Furthermore, in the case of an infinite AT plate, as is well known, the first-order temperature coefficient at the point of inflection changes depending on the cutting azimuth θ, but the point of inflection hardly changes.

On the other hand, in the case of a strip-shaped substrate, when the side inclination angle α is fixed, the temperature at the inflection point is almost unchanged depending on the side ratio r, but the first-order temperature coefficient at the inflection point is shown in Figure 7. As a result of the experiment, it was confirmed that there was a large fluctuation as shown in the figure.

This phenomenon similarly occurs when the side surface inclination angle α is zero.

Therefore, even if the inclination angle α of the strip side surface is selected to be 0 degrees, which is the easiest to process, it is likely that a combination of θ and r can be obtained that sets the first-order temperature coefficient at the inflection point to a desired value. Note that Royer has already disclosed some experimental results regarding controlling the inflection point by appropriately selecting the combinations of θ and r, but the present invention is based on a systematic theoretical analysis. In order to apply this to products of The first-order temperature coefficient of the rotating Y-cut infinite plate shown in Figure 8 is the cutting angle of A'r cut, θ = 35
Using the well-known knowledge that the polarity reverses at the 15' degree boundary, the first-order temperature coefficient at the inflection point is zero and ±ippm.
FIG. 9 shows the results of calculations using the inflection point temperature as a parameter for the combination of the cutting azimuth θ and the side ratio r in the case of /'C.

This figure shows calculation results for the case where the main vibration and the first-order and third-order sub-vibrations are combined, and as the side ratio r increases, the specific gravity of the high-order sub-vibrations increases.

Next, in order to confirm the accuracy of this theoretical analysis, the results of an experiment performed on a rectangular cross-sectional strip in the case of the following temperature coefficient of zero and a board obtained by further convex processing of this strip are shown in Figure 10, respectively. Shown in

Similarly, in this experiment, we prepared a test side with an appropriate cutting azimuth θ, and adjusted the side ratio r based on the results shown in Fig. 7 to make the first-order temperature coefficient substantially close to zero. The above data was obtained by polishing the gold substrate, which has a slightly larger diameter than the ratio, little by little. The same applies to convex processing.

As is clear from FIG. 9, the theoretical curve and the experimental data match extremely well, so it can be said that the validity of the above-mentioned theoretical analysis, which is the basis of the present invention, has been completely verified.

By the way, in the case of manufacturing the strip type vibrating steel according to the present invention, the inflection point temperature is uniquely determined by the cutting azimuth θ, and the adjustable characteristics are only the first-order temperature coefficient at the inflection point that changes depending on the side ratio r. be. As is clear from the experimental results shown in Figure 10, this side ratio r is somewhat influenced by various factors, such as the way the edges of the strip are chamfered, the slight slope of the sides, the method of mounting, etc. It will be understood that there is no. Therefore, considering the experimental results shown in Figure 10, the side ratio r is about ±10% of the theoretical value when the first-order temperature coefficient is zero, if the 3σ of the variation is taken into account, including the case of bevel convex processing. There will be a range.

It would not be a big mistake to think that this is the same when the - next temperature characteristic is set to a value other than zero.

Figure 11 is a diagram showing the calculation results for the combination of the side ratio r and the cutting azimuth θ when the combination of the main vibration and the third and fifth order sub-vibrations is fully utilized.In this case, the side ratio r The width of the variation can be considered to be about the same as in the case described above.

However, considering the crystal substrate processing technology during mass production, it is virtually impossible to make the inclination angle α of the strip side completely zero, so a cutting error of about ±30' of the angle α naturally occurs. . Therefore, if other requirements are satisfied, the presence of this degree of side inclination should not be considered outside the technical scope of the present invention.

The present invention has been made based on the theory as explained above and through experiments to confirm it, so it is impossible to explain conventionally, and the temperature characteristics of the top-rotating Y-cut crystal *
A small resonator with extremely good temperature characteristics, especially a resonator used in the medium wave band, because the inflection point temperature and the primary temperature characteristics at that point can be controlled arbitrarily based on the fully elucidated hk. It is extremely effective in manufacturing ultra-compact products. Visit,
It goes without saying that the vibrator according to the present invention can be applied to the filter e-element, and the word "vibrator" used in this specification means that it should be applied to all of these electro-mechanical conversion elements. Needless to say.

[Brief explanation of drawings]

FIG. 1 is a perspective view showing the configuration of a strip crystal resonator according to the present invention, FIG. 2 is a diagram explaining parameters for analysis that is the basis of the present invention, and FIG. 3 is a diagram showing the results of the above analysis. Frequency spectrum diagrams of various vibrations, Fig. 4 is a partially enlarged view thereof, +a) shows the state of coupling between the main vibration and the primary sub-vibration, and (b) shows the relationship with the tertiary sub-vibration. Figure 5 shows the theoretical analysis results of the relationship between the side ratio of the IJ tube and the first-order temperature coefficient, and Figure 6 shows the strip side inclination angle α.
Figure 7 is a diagram showing the theoretical analysis results of the relationship between frequency temperature characteristics and side ratio. Figure 8 is a diagram showing the cutting azimuth and the first order of the rotating Y-cut crystal infinite plate. A diagram showing temperature characteristics, Figure 9 shows the side ratio where the first-order temperature coefficient at the inflection point temperature is zero and ±ippm/℃ when using the combination of the main vibration and the first-order and third-order sub-vibrations. A theoretical analysis diagram showing the combination of r and cutting azimuth θ, Figure 10 shows the side ratio r and cutting azimuth θ for rectangular and convex oscillators whose primary temperature coefficient at the inflection point temperature is set to zero.
Figure 11 shows the experimental results showing the combination of the main vibration and the third-order and fifth-order sub-vibrations, and the first-order temperature coefficient at the inflection point temperature is zero and ±1 p p m
It is a theoretical analysis diagram showing a combination of a side ratio r and a cutting azimuth angle of 0, which is /'C. Patent applicant Hiroshi Shimizu

Claims (2)

[Claims] (1) In a strip-shaped rotating Y-cut crystal substrate having a long side in the X-axis direction, the combination of the thickness shear vibration as the main vibration and the width shear vibration as the secondary vibration is actively utilized to The frequency-temperature characteristic curve of the substrate that uniquely determines the ratio γ-w/h7' (W is the strip width in one direction, h is the thickness in the Y' direction) and the cutting azimuth θ with respect to the Z-axis from the relationship between these two. By appropriately selecting an inflection point based on an inflection point temperature movement curve in which the first-order temperature coefficient at the inflection point takes a desired value of zero or other than zero, the inflection point can be set without giving an inclination to the side surface of the substrate. Rotating Y-cut, characterized by the ability to set the temperature arbitrarily.
Strip crystal. (2) The variation in the first-order temperature coefficient at a desired temperature due to the error in the cutting azimuth angle θ is calculated using the side ratio γ of the strip.
A method for adjusting temperature characteristics of a rotating Y-cut strip crystal resonator according to claim (1), wherein compensation is performed by adjusting.