JPS6322085B2 - - Google Patents

Description

[Detailed Description of the Invention] The present invention relates to an AT-cut crystal resonator having a substantially rectangular planar shape, in particular, in which the frequency of parasitic vibration is sufficiently far from the frequency of thickness-shear vibration, which is the main vibration,
This invention relates to a small rectangular AT-cut crystal resonator with excellent resonance sharpness of the main vibration and frequency-temperature characteristics of the resonance frequency.

Conventionally, AT-cut crystal resonators have excellent frequency-temperature characteristics and are widely used as resonators for communication devices, but their shape has an extremely large profile-to-thickness ratio, making them difficult to fit into small volumes such as those used in wristwatches. It was unsuitable when required. Therefore, a rectangular AT-cut crystal resonator has been proposed, but the current length-to-thickness ratio is largely inadequate, and reducing the ratio also strengthens the coupling with parasitic vibrations, resulting in poor frequency-temperature characteristics. At present, the resonance sharpness is significantly deteriorated, and a truly small rectangular AT-cut crystal resonator cannot be obtained. And even more
The inflection point temperature of the frequency-temperature characteristic shown by the cubic curve unique to AT cuts is preferably around room temperature in order to be used as a vibrator for a portable watch, for example, and in this respect too, miniaturization is disadvantageous. It had been.

The present invention eliminates the above drawbacks and is small enough to be used in wristwatches, is not affected by parasitic vibrations, has high resonance sharpness, and has an inflection point temperature of the frequency-temperature characteristic curve near room temperature. The purpose is to provide a rectangular AT cut crystal resonator.

The details of the present invention will be explained below with reference to the illustrated embodiments. In addition, in the following examples,
The right-hand crystal will be explained using the right-hand thread coordinate axis, but in the case of the left-hand crystal, the same thing can be said if the interpretation is changed to the left-hand thread coordinate.

FIG. 1 is a diagram showing the axial orientation of a rectangular AT-cut crystal resonator. The crystal blank 1 is shown in the form of a simple rectangle. With the positive direction (also called + direction) of the crystal's X-axis in front, cut angle θ to the left around the X-axis.
At the new coordinates X, Y', and Z' rotated by approximately 35 degrees, the length l of the crystal 1 is approximately in the X-axis direction, the thickness t is approximately in the Y'-axis direction, and the width w is approximately in the Z'-axis direction. Choose each.

FIG. 2 is a perspective view of a rectangular AT-cut crystal resonator showing one embodiment of the present invention. 2 is a crystal piece,
The length dimension is indicated by l, the width dimension by w, and the thickness dimension by t. Reference numeral 3 denotes a bevel portion, the thickness of which decreases toward both ends of the length, and it is preferable in terms of resonance sharpness and equivalent resistance that the thickness t ₀ of both ends be thinner than the crystal blank thickness t. The X-Z' plane, that is, the planar shape is approximately rectangular, and a rectangular AT-cut crystal resonator is constructed by providing electrodes of gold, silver, etc. on the upper and lower surfaces of the X-Z' plane.

Note that the thickness t is expressed as a representative value of the thickness of a portion of the crystal piece where an electrode for exciting thickness-shear vibration is provided (this portion is referred to as the main vibrating portion). The reason for the bevel shape is that it weakens the coupling between parasitic vibration and the main vibration, thickness shear vibration, and also concentrates the energy of thickness shear vibration in the center of the plate surface, thereby preventing a decrease in resonance sharpness when supported. It's for a reason. Furthermore, a beveled shape as shown in FIG. 3 is also included in the bevel shape of the present invention.

Further, instead of the bevel shape, a convex shape as shown in FIG. 4, a plano bevel or plano convex shape on only one side of the plate surface as shown in FIGS. 5a and 5b may be used. It goes without saying that a simple rectangle as shown in FIG. 1 may also be used.

The main vibration of the AT cut crystal resonator is thickness shear vibration, but there are also many parasitic vibrations such as contour vibration. This parasitic vibration must be avoided in order to improve the resonance sharpness of the main vibration and the frequency-temperature characteristics. Therefore, it is necessary to carefully examine the parasitic vibrations near the main vibration and find a size ratio that allows parasitic vibrations with a large frequency response to be sufficiently far away from the main vibration, and parasitic vibrations with a small frequency response to be separated from the main vibration by the necessary frequency interval. .

Therefore, first, in order to determine the width w, it is necessary to sufficiently separate the width shear vibration, which has a particularly large frequency response with respect to the width dimension, from the main vibration. The width shear vibration is is given by However, n is the overtone order, ρ
is the density, and C' ₅₅ is the elastic constant in the X, Y', and Z' coordinate axes. Therefore, the resonant frequency f of width shear vibration
However, when w/t is calculated to be equal to the resonant frequency f of the thickness shear vibration, w/t=1.5n in the case of a rectangular AT-cut crystal resonator. Here, it was conventionally thought that this width-shear vibration appeared only when n was an odd number, but according to our experiments, it also appears when n = 2, that is, w/t = 3, which is an even number. We found that it is coupled with thickness shear vibration. In other words, even width shear vibrations have a large adverse effect on the frequency-temperature characteristics and resonance sharpness of thickness shear vibrations, even when the number is even. Therefore, it is desirable that the width of the small rectangular AT-cut crystal resonator be set to an appropriate size with w/t between 3 and 1.5 to avoid width shear vibration.

Next, in order to determine the length l, regarding the length dimension, it is necessary to sufficiently separate the bending vibration, which has a particularly large frequency response and is strongly coupled to the main vibration, the thickness shear vibration, from the main vibration. The resonance frequency f of bending vibration is is given by However, n is the overtone order (even number), and ρ is the density. Generally, as the length l becomes smaller, the resonance sharpness becomes smaller. As a watch vibrator, it is necessary to make it more compact, so n = 10 and n
If the l dimension is selected between =12, sufficient resonance sharpness can be obtained with a small size. So when n=10 and n=12,
When l/t is about 7.8 and about 9.6, the frequencies of the main vibration and the bending vibration become equal and they are combined. That is, if l/t is a dimensional ratio between about 7.8 and about 9.6, it is considered that there is a dimensional range in which the adverse effects of bending vibration can be avoided.

However, even within the above dimension ratio range that avoids width-shear vibration and bending vibration, which are parasitic vibrations with a particularly large frequency response, there are many other parasitic vibrations with a small frequency response that adversely affect the main vibration. give. Therefore, in order to improve resonance sharpness, frequency temperature characteristics, etc., the frequency of this parasitic vibration with a small frequency response must be kept away from the main vibration frequency to some extent.

Therefore, in order to investigate parasitic vibration with a small frequency response and resonance sharpness, the dimension ratio w/t that avoids width-shear vibration is constant at ≒ 2.5, and the dimension ratio l/t that avoids bending vibration is between approximately 7.8 and approximately 9.4. change it little by little,
The frequency response and equivalent resistance R ₁ of each were investigated. FIG. 6 is a mode chart showing changes in frequency response at that time. In the figure, M indicates thickness shear vibration, and the straight line group indicates parasitic vibration. The experiment is
Since the main vibration was aimed at approximately 4.2 MHz, the thickness t differs somewhat depending on each l dimension. From Figure 6, when the main vibration is about 4.2MHz, the l dimension is about 3.23 to 3.42 mm, that is, the l/t dimension ratio is about 7.9 to about 8.4, which is a good dimension with no parasitic vibration near the main vibration. It is an area. FIG. 7 is a diagram showing the equivalent resistance R ₁ of a rectangular AT-cut crystal resonator with respect to the length-to-thickness ratio l/t when w/t≈2.5. The vertical axis is l/t
The equivalent resistance when is 8.1 is assumed to be 1 and is shown as a magnification. The ● mark indicates the average value of six samples for each size ratio. From Fig. 7, the equivalent resistance is small when l/t is between about 7.9 and about 8.4, and even a slight change in l/t dimensional ratio causes a smaller change compared to other l/t dimensional ratios, resulting in resonance. High sharpness can be maintained.

Next, the relationship between the slope of the frequency temperature characteristic and the length-to-thickness ratio l/t will be explained. FIG. 8 is a diagram showing the slope of the frequency-temperature characteristic curve with respect to the length-to-thickness ratio l/t. It is a bevel-shaped one, and the slope of the frequency-temperature characteristic curve is ∂(△f/f)/
∂T is the slope at temperature T=20°C. The sample used in Figure 8 is the same as the sample used in Figure 7,
The cutting angle θ is 34°48′. From FIG. 8, it can be seen that the slope of the frequency-temperature characteristic curve changes depending on l/t, and when the slope with respect to the change in l/t dimension is large, the processing accuracy of l/t becomes stricter.
This is disadvantageous in terms of mass production. In other words, in a region that is relatively flat against changes in the l/t dimension ratio, l/t is approximately 7.9
It can be seen that the machining accuracy is better in comparison to other l/t values between ~8.4 and 8.4. Furthermore, in order to obtain a flat frequency-temperature characteristic curve near room temperature, the cutting angle θ may be corrected so as to have a zero temperature coefficient according to the value of l/t.

From the above, regarding l/t, a region between about 7.9 and about 8.4 avoids parasitic vibration, has high resonance sharpness, and has a good dimensional ratio in terms of processing accuracy. However, it is not possible to freely select w/t within this l/t region due to parasitic vibration reasons.

Below, we will describe the w/t and l/t dimensional range of the present invention, which avoids the adverse effects of parasitic vibrations with a small frequency response in terms of w/t when l/t is around about 7.9 to about 8.4.

In order to investigate in detail the parasitic vibrations with small frequency responses around w/t≒2.5 and l/t≒8.2,
In the crystal blank 2 of the present invention shown in the figure, w/t≒
2.5, the center value of l/t≈8.2 was selected, and the width w and length l of the crystal resonator were changed little by little, and the frequency response in each case was measured. Figure 9a is the width w
Figure 9b is a mode chart showing the change in frequency response when the length l is changed, and the straight line group connects the measured values, and the vertical axis is the frequency constant f・t. shows.

Straight line E shown in Figures 9a and 9b represents the main thickness shear vibration, and the frequency constant is approximately 1716 KHz·mm.
Straight lines F, G, H, and I are parasitic vibrations. The slopes of these straight lines are approximately straight lines in minute regions. Here, the parasitic vibrations to be noted when determining w/t and l/t are straight lines F, G, H, and I. The frequency constants of these four parasitic vibrations w/t
And when expressed as a function of l/t, it is as follows. Here, the unit is KHz·mm.

Straight line F f _F・t=-457.5w/t-72.7l/t+
3430.2 Straight line G f _G・t=−52.5w/t−216.3l/t+
355.10 Straight line H f _H・t=-267.0w/t-130.0l/t+
3492.6 Straight line I f _I・t=−86.0w/t−204.2l/t+
3647.2 In order for the thickness shear vibration E to be unaffected by these four parasitic vibrations, the following equation must be satisfied, assuming that the frequency constant of the thickness shear (assumed to be constant at 1716 KHz) is f _E・t .

f _E・t≧f _F・t, f _E・t≧f _G・t f _E・t≦f _H・t, f _E・t≦f _I・t By the way, the frequency of thickness shear vibration E depends on the thickness of the electrode. It can be adjusted by At that time, the changes in the frequency constants of the four parasitic vibrations shown above are much smaller than the changes in the frequency constants of the thickness shear vibrations. Experimentally, it is possible to change the frequency constant of thickness shear vibration by electrodes by about ±10KHz・mm.

Therefore, the condition of the above equation becomes as shown in the following equation.

f _E・t+10≧f _F・t, f _E・t+10≧f _G・t f _E・t−10≦f _H・t, f _E・t−10≦f _I・t Furthermore, substitute the numerical values into the above equation Then, the following formula is obtained.

1726≧-457.5w/t-72.7l/t+3430.2 1726≧-52.5w/t-216.3l/t+3551.0 1706≦-267.0w/t-130.0l/t+3492.6 1706≦-86.0w/t- 204.2l/t+3647.2 A rectangular AT cut crystal resonator with w/t and l/t that satisfies the above four equations avoids the effects of width shear vibration and bending vibration, which are parasitic vibrations with particularly large frequency responses. together with Figures 9a and b.
This is a resonator that avoids the effects of parasitic vibrations with a relatively small frequency response as shown in FIG.

FIG. 10 is a diagram showing the dimensional range of w/t and l/t that satisfies the above four formulas and the dimensional range of the present invention, with w/t on the horizontal axis and l/t on the vertical axis. .
If the points in the figure are expressed as (w/t, l/t), the above 4
The points that satisfy the following equations are point 2A (2.37, 8.51), point 2
B (2.59, 8.41), point 2C (2.93, 7.73), point 2D
(2.48, 7.84). These points 2A, 2B,
The rectangular area formed by the four points 2C and 2D is a dimensional area in which the influence of paranormal vibrations with small frequency responses shown in FIG. 9 is avoided. However, as mentioned above, in terms of resonance sharpness and processing accuracy, l/t between about 7.9 and 8.4 is good, so point A (2.39, 8.4) and point B (2.60 ,
8.4), points c (2.84, 7・9), and points D (2.47, 7.9) are preferable, and are not affected by parasitic vibration regardless of the strength of the frequency response, and are free from resonance sharpness and machining. Small rectangular shape, good in terms of accuracy
AT-cut crystal resonators can be obtained.

Figure 11 shows the X-Y' plane, which is the side surface of the crystal piece 4.
Tilt angle α (approx. 5°) to the left with the + direction of the X-axis facing you.
This reduces the influence of parasitic vibrations. Furthermore, by inclining the side angle α by about 6°30', it is effective because the width dimension machining accuracy is relaxed compared to the case where the side angle is 0°.

FIG. 12 is an example showing the temperature characteristics of a small rectangular AT-cut crystal resonator according to the present invention. J indicates the frequency temperature characteristic, and K indicates the temperature characteristic of the equivalent resistance _R1 .

This characteristic is θ≒34゜33′, l/t≒8.2, w/t
≒2.5, for a sample with α=0°. Within the above-mentioned dimension range of the present invention, the frequencies of the width shear vibration and bending vibration, which have a particularly large frequency response, and the harmful parasitic vibration, which has a small frequency response, are sufficiently separated from the frequency of the thickness shear vibration, which is the main vibration, as shown in Fig. 12. Good frequency-temperature characteristics and flat equivalent resistance temperature characteristics are obtained as shown in . The inflection point temperature of the frequency-temperature characteristic curve at this time is approximately 25°C.

Also, when the thickness t is selected to be approximately 0.4 mm and the main resonance frequency is approximately 4 MHz, the width is approximately 1 mm and the length is approximately
An extremely small rectangular AT-cut crystal resonator of approximately 3.3 mm can be realized.

As described above, the present invention is small and unaffected by parasitic vibrations, has high resonance sharpness, has good frequency-temperature characteristics with an inflection point temperature of about 25°C, and has excellent processing accuracy. We can provide a rectangular AT-cut crystal resonator that can be mass-produced, and the intended purpose can be fully achieved, with great effects.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram showing the axis orientation of a rectangular AT cut crystal resonator, and FIGS. Perspective view, Fig. 6 shows the mode chart, Fig. 7 shows the equivalent resistance R ₁ versus l/t, Fig. 8 shows the slope of the frequency-temperature characteristic curve versus l/t, Fig. 9 a, b are mode chart diagrams, Figure 10 is a diagram showing the dimensional range of the present invention, Figure 1
FIG. 1 is a side view showing the Y'-Z' plane of a crystal piece with its side surface tilted, and FIG. 12 is a diagram showing an example of the temperature characteristics of a small rectangular AT-cut crystal resonator according to the present invention. 1, 2, 4...Crystal piece, 3...Bevel part.

Claims (1)

[Claims] 1. An AT-cut crystal resonator whose planar shape is approximately rectangular, obtained by rotating the crystal by a cutting angle θ (approximately 35°) to the left around the X-axis, with the positive direction of the X-axis facing the front. , the length l of the crystal piece is selected approximately in the X-axis direction, the width w is selected approximately in the Z'-axis direction, and the thickness t is approximately selected in the Y'-axis direction, and the horizontal axis is w/t and the vertical axis is l/t. The coordinate points (w/t, l/t) are: Point A (2.39, 8.4) Point B (2.60, 8.4) Point C (2.84, 7.9) Point D (2.47, 7.9) Four points A , B, C, and D. A rectangular AT-cut crystal resonator characterized in that w/t and l/t are selected within a rectangular area consisting of , B, C, and D. 2. A rectangular AT-cut crystal resonator according to claim 1, wherein both lengthwise ends of the crystal piece have a bevel shape or a convex shape.