JP2003229739A - Quartz oscillator and its manufacturing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a quartz oscillator and its manufacturing method, whose output signal has a small equivalent series resistance R<SB>1</SB>at a frequency of a fundamental wavelength mode vibration and which is provided with a flexible quartz vibrator, having a high quality coefficient Q value in a micro tuning-fork shape. <P>SOLUTION: The quartz oscillator is provided with a tuning-fork arm and a tuning-fork substrate, a groove or a through-hole is provided in the tuning-fork arm or in upper and lower faces of the tuning-fork arm and the tuning-fork substrate and the tuning-fork-shaped flexible quartz resonator arranging an electrode at the side face of the groove or the through-hole is provided. The quartz oscillator, whose output signal is the frequency of the fundamental wavelength mode can be realized at high accuracy by making the equivalent resistance R<SB>1</SB>of a fundamental wavelength mode vibration smaller than R<SB>2</SB>of a secondary higher harmonic mode vibration and by a relationship between an amplification factor of an amplification circuit and the feedback ratio of a feedback circuit. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a crystal oscillator having a tuning fork shape consisting of a tuning fork arm vibrating in a bending mode and a tuning fork base, an amplifier, a capacitor and a resistor, and a method for manufacturing the same. In particular, a crystal oscillator best suited as a reference signal source for information and communication equipment that is strongly required to be compact, highly accurate, shock resistant, and inexpensive, and has a new shape, new electrode configuration, and ultra-compact tuning fork shape with optimal dimensions. The present invention relates to a crystal oscillator, which is composed of a bent crystal oscillator, and whose output signal is the frequency of fundamental mode vibration.

[0002]

2. Description of the Related Art As a conventional crystal oscillator, there is well known a crystal oscillator including an amplifier, a capacitor, a resistor, and a tuning fork type bent crystal oscillator in which electrodes are arranged on upper and lower surfaces and side surfaces of a tuning fork arm. FIG. 9 is a schematic view of a tuning fork-shaped bent crystal unit 200 used in this conventional oscillator. Figure 9
In the crystal unit 200, the two tuning fork arms 201, 20
2 and a tuning fork base 230. FIG. 10 shows a sectional view of the tuning fork arm of FIG. As shown in FIG. 10, the excitation electrodes are arranged on the upper and lower surfaces and side surfaces of the tuning fork arm. The cross-sectional shape of the tuning fork arm is generally rectangular. An electrode 203 is arranged on the upper surface and an electrode 204 is arranged on the lower surface of the cross section of one tuning fork arm. Electrodes 205 and 206 are provided on the side surface. The electrode 207 is arranged on the upper surface of the other tuning fork arm, the electrode 208 is arranged on the lower surface, and the electrodes 209 and 210 are arranged on the side surfaces to form a two-electrode terminal H-H 'structure. H-H 'now
When a DC voltage is applied between them, the electric field works in the direction of the arrow. As a result, when one tuning fork arm bends inward, the other tuning fork arm also bends inward. The reason is that the electric field components Ex in the x-axis direction are opposite in direction inside each tuning fork arm. Vibration can be sustained by applying an alternating voltage.
Also, JP-A-56-65517 and JP-A-2000-2239
92 (P2000-223992A) discloses a groove on the tuning fork arm and an electrode configuration.

[0003]

In the tuning fork-shaped bent crystal oscillator, the loss equivalent series resistance R ₁ becomes smaller and the quality factor Q becomes larger as the electric field component Ex becomes larger. However, as shown in FIG. 10, the conventional tuning fork-shaped bent crystal oscillator has electrodes arranged on the upper and lower surfaces and side surfaces of each tuning fork arm. For this reason, the electric field does not act linearly, and when the tuning fork type bent crystal oscillator is downsized, the electric field component Ex becomes small, the loss equivalent series resistance R ₁ becomes large, and the quality factor Q value becomes small. Was left unsolved. Further, as a method for solving the above-mentioned problems, for example, Japanese Patent Application Laid-Open No. 56-65517 discloses a groove in a tuning fork arm and a groove structure and an electrode structure. However, the configuration of the groove, not disclose the relationship and Figa of merit M of the equivalent series resistance R ₂ of the equivalent series resistance R ₁ of the second harmonic mode vibration in the vibration mode and fundamental mode vibration and dimension Absent. At the same time, if the oscillator provided with the groove is connected to a conventional circuit to configure a crystal oscillation circuit, the output signal of the fundamental vibration mode is affected by shock or vibration, and the output signal is the frequency of the second harmonic vibration. There was a problem such as change and detection. For this reason, there is a demand for a crystal oscillator having a tuning fork-shaped bent crystal resonator that vibrates in a fundamental wave mode that suppresses second-harmonic vibration that is not affected by shock or vibration. It was At the same time, if the load capacitance C _L is made small in order to reduce the current consumption of the crystal oscillator, the vibration of the second harmonic mode is likely to occur, and there remains a problem that the output frequency of the fundamental mode vibration cannot be obtained. Was there. Therefore, a tuning fork shape having a groove configuration and an electrode configuration with a very small size that oscillates in the fundamental wave mode, a small equivalent series resistance R _{1, and} a high quality factor Q value and that has a high electromechanical conversion efficiency and an electrode configuration. It was desired to have a crystal oscillator having a bent crystal oscillator, whose output signal is the frequency of fundamental mode vibration. Further, in order to obtain a crystal oscillator with good time accuracy, a crystal oscillator having a tuning fork-shaped bent crystal oscillator having high frequency stability has been desired.

[0004]

SUMMARY OF THE INVENTION The present invention provides a crystal oscillator having a tuning-fork-shaped crystal oscillator that vibrates in a bending mode and a method of manufacturing the same, which has advantageously solved the conventional problems by the following method. It is intended.

That is, the first aspect of the crystal oscillator of the present invention is a crystal oscillator comprising a crystal oscillator, an amplifier, a capacitor and a resistor, wherein the crystal oscillator is a tuning fork arm that vibrates in a bending mode. It is composed of a tuning fork-shaped crystal unit composed of a tuning fork base, and the amplifier is a CMOS.
An inverter, wherein at least one groove is provided in the length direction on the upper and lower surfaces of the central portion in the width direction sandwiching the neutral line of the tuning fork arm, and electrodes are arranged on both side surfaces of the groove. The electrodes on the side surface of the groove and the electrodes on the side surface of the tuning fork arm that oppose the electrode have different polarities, and each of the at least one groove is formed so that the inertia moment generated in the tuning fork arm becomes large. Of at least one of the groove width W ₂ and the tuning fork arm width W (W ₂ / W) is 0.35 to 0.
95, the ratio of the thickness t _{1 of the} groove to the thickness t of the tuning fork arm (t
₁ / t) is 0.01 to 0.79, and further, the length l _{1 of the} groove provided in the tuning fork arm or the tuning fork arm and the tuning fork base and the total length l of the tuning fork-shaped crystal unit. And the ratio (l ₁ / l) of the tuning fork shape is within the range of 0.2 to 0.78. The equivalent series resistance R ₁ of the fundamental mode vibration of the bent quartz oscillator is smaller than the equivalent series resistance R _{2 of the second} harmonic mode vibration, and
With the full Iga of merit M ₁ is the crystal oscillator comprises a full Iga of merit M ₂ greater flexural crystal oscillator of the second harmonic mode vibration of the fundamental wave mode vibration constructed, immediately the amplification circuit feedback circuit Amplification factors α ₁ and 2 of the fundamental mode vibration of the amplifier circuit of the crystal oscillator configured as described above
The ratio of the _second harmonic mode vibration to the amplification factor α ₂ of the feedback circuit is 2
It is larger than the ratio of the feedback rate β _{2 of the second} harmonic mode vibration to the feedback rate β ₁ of the fundamental mode vibration, and the amplification rate α ₁ of the fundamental mode vibration and the feedback rate β _{1 of the} fundamental mode vibration.
The crystal oscillator is configured such that the product of the two is greater than 1, and the output signal of the crystal oscillator configured to include the tuning fork-shaped bent crystal resonator has an output whose output is the frequency of the fundamental mode vibration. It is an oscillator.

A first aspect of a method for manufacturing a crystal oscillator according to the present invention is a method for manufacturing a crystal oscillator which comprises a crystal resonator, an amplifier, a capacitor and a resistor, wherein the crystal resonator vibrates in a bending mode. A tuning fork-shaped crystal resonator having a tuning fork arm and a tuning fork base, and at least one groove is provided in the longitudinal direction on the upper and lower surfaces of the central portion in the width direction sandwiching the neutral line of the tuning fork arm. The electrodes are arranged on both side surfaces of the groove, and the electrodes on the side surfaces of the groove and the electrodes on the side surfaces of the tuning fork arm opposite to the electrodes are configured to have different polarities, and the inertia moment generated in the tuning fork arm increases. wherein each ratio of the at least one groove width _{W 2} and the tuning fork arm width W of at least one groove _(W 2 / W) is 0.35 to
At 0.95, the ratio (t ₁ / t) between the thickness t _{1 of the} groove and the thickness t of the tuning fork arm is 0.01 to 0.79, and the tuning fork arm or the tuning fork arm and the tuning fork are further provided. The length l _{1 of the} groove provided in the base and the total length l of the tuning fork-shaped crystal unit
A step of forming the groove and the electrode so that the ratio (l ₁ / l) thereof is within the range of 0.2 to 0.78, and fixing the bent crystal oscillator to the unit case with an adhesive or solder. After that, the step of adjusting the frequency of the crystal unit, the step of housing the tuning fork-shaped bent crystal unit in a surface-mounted or cylindrical unit, and the bent crystal unit using a CMOS inverter as the amplifier. Electrically connecting the child, the CMOS inverter, the capacitor, and the resistor,
And the equivalent series resistance R ₁ of the fundamental mode vibration of the tuning fork-shaped bent crystal oscillator is smaller than the equivalent series resistance R _{2 of the second} harmonic mode vibration, and the figurer of the fundamental mode vibration The crystal oscillator is configured so as to have a bending crystal unit whose merit M ₁ is larger than the second-harmonic-mode-vibration-Figger-of-merit M ₂ , and at the same time, the crystal oscillator is configured to include an amplifier circuit and a feedback circuit. The ratio of the amplification factor α ₁ of the fundamental mode vibration of the amplifier circuit to the amplification factor α ₂ of the second harmonic mode vibration is the feedback factor β ₂ of the second harmonic mode vibration of the feedback circuit and the feedback factor of the fundamental mode vibration. greater than the ratio of the beta _1, and the crystal oscillator as the product of the feedback factor beta ₁ is greater than 1 of the fundamental mode oscillation and amplification factor alpha ₁ of the fundamental mode vibration be configured, the tuning fork Shape bending crystal vibration A method of manufacturing a crystal oscillator, wherein an output signal of the crystal oscillator configured to include a child has a frequency of fundamental mode vibration.

[0007]

As described above, the present invention is a crystal oscillator having a tuning-fork-shaped crystal unit that vibrates in a bending mode, and further, the structure of the tuning-fork-shaped groove and the electrode is improved, and the relationship between the amplifier circuit and the feedback circuit is improved. By indicating, it is possible to obtain a crystal oscillator that suppresses the second harmonic vibration and outputs a frequency that vibrates in the fundamental vibration mode.

In addition, the equivalent series resistance R ₁ is small and the Q value is small by providing a groove in the center of the neutral line of the tuning fork arm and arranging electrodes to optimize the dimension of the groove. high,
An ultra-small tuning fork-shaped bent crystal oscillator that vibrates in a bending mode with high electromechanical conversion efficiency can be obtained. At the same time, the load capacitance of the feedback circuit can be reduced. As a result, a crystal oscillator with low current consumption can be obtained.

[0009]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be specifically described below with reference to the drawings. FIG. 1 is an embodiment of a crystal oscillation circuit diagram constituting a crystal oscillator of the present invention. The crystal oscillation circuit 1 is composed of an amplifier (CMOS inverter) 2, a feedback resistor 4, a drain resistor 7, capacitors 5, 6 and a tuning fork-shaped bent crystal oscillator 3. The crystal oscillating circuit of this embodiment is composed of such circuit elements. That is, the crystal oscillation circuit 1 that constitutes the crystal oscillator is composed of the amplifier circuit 8 and the feedback circuit 9. Further, the tuning fork-shaped crystal oscillator that vibrates in the bending mode used in the crystal oscillator of the present invention will be described in detail with reference to FIGS.

FIG. 2 shows the feedback circuit diagram of FIG. The angular frequency of a tuning fork-shaped crystal unit that vibrates in the bending mode is now ω
_i , the resistance of the drain resistance 7 is R _d , and the capacitors 5 and 6 are
_Let C _{g be} the capacitance of C _d , C _{d be} the crystal impedance of the crystal be R _ei , be the input voltage be V ₁ and be the output voltage be V ₂ .
The feedback rate β is defined by β = | V ₂ | / | V ₁ |. However, i represents the vibration order of the bending vibration mode, for example, i
= 1, fundamental mode vibration, i = 2, second harmonic mode vibration, i = 3, third harmonic mode vibration. Further, the load capacitance C _L is C _L = C _g C _d / (C _g
+ C _d ), C _g = C _d = C _gs and Rd >> R
_{If ei} , the feedback rate β is given by β = 1 / (1 + kC _L ² ). However, k is represented by a function of ω _i , R _d , and R _ei . Also, R _ei is approximately equal to the equivalent series resistance R _i .

Thus, as is clear from the relationship between the feedback ratio β and the load capacitance C _L , as the load capacitance C _L becomes smaller, the feedback ratios at the resonance frequencies of the fundamental vibration mode and the harmonic vibration mode increase. I understand that it will be. Therefore, when the load capacitance C _L becomes smaller, the second harmonic mode vibration is more likely to oscillate than the fundamental wave mode vibration. The reason is that the maximum vibration amplitude of the second harmonic mode vibration is smaller than the maximum vibration amplitude of the fundamental wave mode vibration, so that the amplitude condition and the phase condition, which are oscillation continuation conditions, are satisfied at the same time.

An object of the crystal oscillator of the present invention is to provide a crystal oscillator which consumes less current and has an output frequency of the fundamental mode vibration. Therefore, in order to reduce the current consumption, the load capacitance C _L is 7p.
Use F or less. In order to further reduce the consumption current, the consumption current is proportional to the load capacitance, so that C _L = 6 pF or less is preferable. The capacitances C _g and C _{d mentioned} here are numerical values including the stray capacitance of the circuit. Further, in order to suppress the vibration of the second harmonic mode and the oscillator output signal obtains the frequency of the fundamental mode vibration, it is necessary to satisfy α ₁ / α ₂ > β ₂ / β ₁ and α ₁ β ₁ > 1. The oscillator circuit of this embodiment is constructed. Where α ₁ and α ₂ are the amplification factors of the amplification circuit for fundamental mode vibration and second harmonic mode vibration, and β ₁ and β ₂ are the feedback factors of the feedback circuit for fundamental mode vibration and second harmonic mode vibration. Is.

In other words, the amplification factor α ₁ of the fundamental mode vibration and the amplification factor α _{2 of the second} harmonic mode vibration of the amplifier circuit.
Is the feedback ratio β ₂ of the second harmonic mode vibration of the feedback circuit
And a feedback ratio β ₁ of the fundamental wave mode vibration, and a product of an amplification factor α ₁ of the fundamental wave mode vibration and a feedback factor β ₁ of the fundamental wave mode vibration is larger than 1. With this configuration, it is possible to realize a crystal oscillator that consumes less current and has an output signal at the frequency of fundamental mode vibration. The frequency is the reference frequency of the bent crystal oscillator or the frequency obtained by dividing the reference frequency.

Further, the amplifying portion of the amplifying circuit which constitutes the crystal oscillating circuit of this embodiment can exhibit its characteristic by the negative resistance -RL _i . When i = 1, it is a negative resistance of fundamental mode vibration, and when i = 2, it is a negative resistance of second harmonic mode vibration. In the crystal oscillator of this embodiment, the ratio between the absolute value of negative resistance | -RL ₁ | of the fundamental mode vibration of the amplifier circuit and the equivalent series resistance R ₁ of the fundamental mode vibration is the second harmonic mode of the amplifier circuit. negative absolute value of the resistance of the vibration | -RL 2 _| and the second harmonic mode vibration oscillator to be greater than the ratio of the equivalent series resistance R ₂ is configured. That is, | -RL ₁ | /
It is configured to satisfy R ₁ > | −RL ₂ | / R ₂ . By configuring the crystal oscillator circuit in this way,
The oscillation start of the second harmonic mode vibration is suppressed, and as a result, the oscillation start of the fundamental wave mode vibration is obtained, so that the frequency of the fundamental wave mode vibration is obtained as an output signal.

FIG. 3 shows an external view of a tuning fork-shaped crystal resonator 10 vibrating in a bending mode used in the crystal oscillator of the first embodiment of the present invention and its coordinate system. The coordinate system O, the electric axis x, the mechanical axis y, and the optical axis z constitute O-xyz. Tuning fork-shaped bent crystal unit 1 of the present embodiment
Reference numeral 0 includes a tuning fork arm 20, a tuning fork arm 26, and a tuning fork base portion 40, and the tuning fork arm 20 and the tuning fork arm 26 are connected to the tuning fork base portion 40. Further, a groove 21 is provided on the upper surface of the tuning fork arm 20 so as to sandwich the neutral line, and also on the upper surface of the tuning fork arm 26.
Similarly to the above, the groove 27 is provided, and further, the tuning fork base portion 40 is provided with the groove 32 and the groove 36. The angle θ is a rotation angle around the x-axis and is usually selected in the range of 0 to 10 °.

FIG. 4 is a cross-sectional view of the tuning fork base portion 40 of the bending quartz crystal resonator 10 of FIG. 4, the cross-sectional shape and electrode arrangement of the tuning fork base 40 of the crystal unit shown in FIG. 3 will be described in detail. Grooves 21 and 22 are provided in the tuning fork base portion 40 that is connected to the tuning fork arm 20. Similarly, the tuning fork base portion 40 connected to the tuning fork arm 26 is provided with grooves 27 and 28. Further, a groove 3 is further provided between the groove 21 and the groove 27.
2 and a groove 36 are provided. Further, a groove 33 and a groove 37 are also provided between the groove 22 and the groove 28. And
Electrodes 23 and 24 are provided in the grooves 21 and 22, and grooves 32 and 33,
Electrodes 34, 35, 38, 39 are provided on the grooves 36, 37 in the groove 27.
The electrodes 29 and 30 are arranged in the groove 28 and the groove 28, and the tuning fork base 40
Electrodes 25 and 31 are arranged on both side surfaces of. More specifically, electrodes are arranged on the side surfaces of the groove, and electrodes having different polarities are arranged opposite to the electrodes.

The tuning fork-shaped bent crystal oscillator 10 has a thickness t, and the groove has a thickness t ₁ . The thickness t _{1 mentioned} here means the thickness of the deepest part of the groove. The reason is that quartz is an anisotropic material, and therefore the etching speed differs depending on the direction of each crystal axis in the chemical etching method. Therefore, it is extremely difficult to process the groove into the uniform shape shown in FIG. 4 by the chemical etching method. In this embodiment, the groove is a tuning fork arm or a tuning fork arm such that the ratio (t ₁ / t) of the thickness t _{1 of} the groove and the thickness t of the tuning fork arm or the tuning fork arm and the tuning fork base is 0.01 to 0.79. And formed on the base of the tuning fork. In particular, in order to increase the distortion of the tuning fork base, the ratio of the thickness of the groove of the tuning fork base to the thickness of the tuning fork base is 0.01 to
It is preferably 0.025. By forming in this way, the electric field Ex between the tuning fork arm or the tuning fork arm and the groove side surface electrode of the tuning fork base and the side surface electrode opposite thereto becomes large. That is, it is possible to obtain a bending oscillator having a high electromechanical conversion efficiency. That is, a tuning fork-shaped bent crystal oscillator having a small capacitance ratio can be obtained. Further, in this embodiment, since the grooves 32, 33, 36 and 37 are further provided between the grooves of the tuning fork base portion, the electric field strength thereof is further increased and the electromechanical conversion efficiency is improved. . Further, in this embodiment, the grooves 32 and 36 are provided on the upper surface of the tuning fork base portion 40 and the grooves 33 and 37 are provided on the lower surface, but they may be provided only on one surface.

Further, the electrodes 25, 29, 30, 34, 35
Has electrodes 23, 24, 31, 37, 38, and
39 is arranged so as to have the same polarity as the other, and constitutes a two-electrode terminal structure E-E '. That is, the groove electrodes facing the z-axis direction have the same polarity, and the electrodes facing the x-axis direction have the different poles. Now, 2 electrode terminal E-
When a DC voltage is applied to E '(E terminal is positive and E'terminal is negative), the electric field Ex acts as shown by the arrow in FIG.
The electric field Ex is extracted perpendicularly to the electrodes, that is, linearly by the electrodes arranged on the side surface of the crystal unit and the side surface inside the groove, so that the electric field Ex becomes large, and as a result, the amount of strain generated is also large. Become. Therefore, even when the tuning fork-shaped bent crystal unit is downsized, the equivalent series resistance R ₁ is small.
A tuning fork-shaped crystal unit having a high quality factor Q value and vibrating in a bending mode is obtained.

FIG. 5 is a tuning fork-shaped bent crystal unit 1 of FIG.
0 is a top view of FIG. In FIG. 5, the arrangement and dimensions of the grooves 21 and 27 will be described in detail. The groove 21 is provided so as to sandwich the neutral line 41 of the tuning fork arm 20. The other tuning fork arm 26 is also provided with a groove 27 so as to sandwich the neutral line 42. Further, in the tuning fork-shaped bent crystal oscillator 10 of the present embodiment, the groove 32 and the groove 36 are also provided in the portion of the tuning fork base portion 40 sandwiched between the groove 21 and the groove 27. By providing the grooves 21 and 27 and the grooves 32 and 36, as described above, the electric field Ex works in the tuning fork-shaped bent quartz crystal resonator 10 as shown by the arrow in FIG. Is drawn perpendicularly to the electrode, that is, linearly by the electrodes arranged on the side surface of the crystal unit and the side surface inside the groove, and especially the electric field Ex of the tuning fork base portion becomes large, and as a result, the amount of strain generated is also increased. growing. As described above, the shape and electrode configuration of the tuning fork-shaped bent crystal resonator 10 of this embodiment have excellent electrical characteristics even when the tuning fork-shaped bent crystal resonator is downsized, that is, the equivalent series resistance R. _A crystal unit having a small value of ₁ and a high quality factor Q value can be realized.

Further, when the partial widths W ₁ and W ₃ and the groove width W ₂ are set, the arm width W of the tuning fork arms 20 and 26 is W = W ₁ + W ₂ + W ₃
Given that, usually, some or all of W ₁ and W ₃ are W ₁ =
W ₃ and so as configured. Further, the groove width W ₂ is W ₂ ≧ W
₁ and W ₃ are satisfied. If described in further detail, in the present embodiment, a ratio of the groove width _{W 2} and the tuning fork arm width W _(W 2 / W) is from 0.35 to 0.95, the groove of the thickness _{t 1} and the thickness of the tuning fork arms The groove is formed in the tuning fork arm so that the ratio t (t ₁ / t) between t or the tuning fork arm and the thickness t of the tuning fork base is 0.01 to 0.79. By forming in this way, the moment of inertia from the neutral lines 41 and 42 of the tuning fork arm as a base point becomes large. That is, since the electromechanical conversion efficiency is improved, it is possible to obtain a bent quartz crystal resonator having a small equivalent series resistance R ₁ , a high Q value, and a small capacitance ratio.

On the other hand, regarding the length l ₁ of the groove 21 and the groove 27, in this embodiment, the grooves 21 and 27 have the tuning fork arm 2
It is dimensioned to extend from 0, 26 to the length l ₂ of the tuning fork base 40 and to have the groove length l ₃ of the base. Therefore, the length of the groove provided in the tuning fork arms 20 and 26 is (l ₁ −
l ₃ ), to obtain an oscillator with a small R ₁ ,
_{(L 1 -l 3) / (} l-l 2) it has a value of 0.4 to 0.8. Further, the total length l of the tuning fork-shaped bent crystal unit 10
Is determined by the required frequency and the size of the storage container. At the same time, in order to obtain a bent quartz oscillator having a good tuning fork shape that vibrates in the fundamental mode, there is a close relationship between the groove length l ₁ and the groove length l ₁ .

That is, the tuning fork arm 20, 26 or the tuning fork arm 2
0, 26 and the length l _{1 of the} groove provided in the tuning fork base 40 and the total length 1 of the bending fork-shaped quartz crystal in the tuning fork shape (l ₁ / l) are set so that the ratio is 0.2 to 0.78. Is provided.
The reason for forming in this way is, in particular, that it is possible to suppress unnecessary harmonic vibration of the second harmonic (a frequency that is about 6.3 times the fundamental frequency) and to increase the frequency stability of fundamental mode vibration. You can Therefore, a good tuning fork-shaped bent crystal unit that easily vibrates in the fundamental mode can be realized. More specifically, the equivalent series resistance R _{1 of} the tuning fork-shaped bent crystal oscillator vibrating in the fundamental mode is smaller than the equivalent series resistance R _{2 in the second} harmonic vibration. That is, R
₁ <R ₂ , and a crystal oscillator including an amplifier (CMOS inverter), a capacitor, a resistor, and a tuning fork-shaped bent crystal oscillator according to the present embodiment is a good crystal oscillator in which the oscillator easily vibrates in a fundamental wave mode. realizable. Further, the groove length l ₁ may be divided in the length direction of the tuning fork arm, and at least one of them may satisfy the side ratio (l ₁ / l).

In this embodiment, the tuning fork base 40 is the entire lower part of the length l ₂ of the vibrator 10 in FIG.
Further, the tuning fork arm 20 and the tuning fork arm 26 are the vibrator 10 in FIG.
From the length l ₂ portion to the entire upper portion. In the present embodiment, the tuning fork has a rectangular shape, but the present invention is not limited to the above-mentioned shape, and the tuning fork may have a U shape. In this case as well, similar to the rectangular shape, the dimensional relationship between the tuning fork arm and the tuning fork base is the same as the above relationship. Further, in the present embodiment, the groove is provided in the tuning fork arm and the tuning fork base, but the present invention is not limited to this, and the groove may be provided only in the tuning fork arm, and the same effect can be obtained. . In this case, the groove length l ₃ = 0. The groove length l _{1 referred} to in the present invention is a groove provided in the tuning fork arm, and the ratio (t ₁ / t) of the groove thickness t ₁ to the tuning fork arm thickness t is 0.
01 to 0.79, the ratio of the groove width W ₂ to the tuning fork arm width W (W ₂
/ W) is the length of the groove configured to be 0.35 to 0.95. Along with the above, when the groove provided on the tuning fork arm extends to the tuning fork base, the ratio of the thickness of the groove of the tuning fork base to the thickness of the tuning fork base is within the range of 0.01 to 0.025. A length including a groove length l ₃ is l ₁ .

In other words, at least one groove is provided in the length direction on the upper and lower surfaces of the central portion in the width direction sandwiching the neutral line of the tuning fork arm, and electrodes are arranged on both side surfaces of the groove. And the electrodes on the side surfaces of the groove and the electrodes on the side surfaces of the tuning fork arm that oppose the electrodes have different polarities.
The groove width W _{2 of} at least one of the at least one groove so that the moment of inertia generated in the tuning fork arm is increased.
And the ratio of the tuning fork arm width _{W (W} 2 / W) is from 0.35 to 0.95
And the ratio of the thickness t _{1 of the} groove to the thickness t of the tuning fork arm (t ₁ /
t) is 0.01 to 0.79, and further, the tuning fork arm or the tuning fork arm and the groove length l ₁ provided in the tuning fork base and the total length l of the tuning fork-shaped crystal resonator are Ratio (l
_The groove is formed so that ₁ / l) is within the range of 0.2 to 0.78.

[0025] Is satisfied, and the distance W ₄ is 0.05 mm to
In 0.35mm, the groove width _{W 2} is 0.03mm~0.068
It has a value of mm. The reason for configuring in this way is that it is a very small bending crystal oscillator, and the tuning fork shape and the groove of the tuning fork arm can be formed separately (separate steps) using photolithography technology. The stability can be made higher than the frequency stability of the second harmonic mode vibration. In this case, the thickness t of the vibrator is 0.05 mm to 0.1
A 2 mm crystal wafer is used.

[0026] If More specifically, the ratio of full Iga of merit M _i is the quality factor Q _i value and the capacitance ratio r _i representing the inductive electromechanical conversion efficiency and the quality factor of the flexural crystal resonator (Q _i
/ R _i ) (fundamental oscillation when i = 1,
i = 2 harmonic vibration when 2, the third harmonic vibration when i = 3), a difference Δf of the series resonance frequency f _r, including mechanical series resonance frequency f _s and the parallel capacitance of the flexural crystal oscillator off Inversely proportional to the iger of merit M _i , the larger the value M _{i, the} more Δ
f becomes small. Therefore, as M _i is larger, the resonance frequency of the bent crystal unit is not affected by the parallel capacitance, and the frequency stability of the bent crystal unit is improved.

For example, the frequency of fundamental mode vibration is 3
In the case of 2.768 kHz, due to the configuration of the tuning fork shape, the groove, and the dimensions thereof, the figurer of merit M ₁ of the fundamental mode vibration is derived from the figurer of merit M ₂ and M _{3 of the second} and third harmonic mode vibrations. growing. In this embodiment,
M ₁ , M ₂ and M ₃ are respectively M ₁ > 50, M ₂ <30,
M ₃ <18. That is, it is possible to obtain a bent quartz oscillator having high inductive property and good electromechanical conversion efficiency (small equivalent series resistance R ₁ ) and vibrating in a fundamental wave mode having a large quality factor. As a result, the frequency stability of the fundamental mode vibration becomes better than the frequency stability of the second and third harmonic mode vibrations, and the second and third harmonic mode vibrations can be suppressed. The reference frequency of the fundamental mode vibration of the present invention is 10 kHz to 200 kHz. In this embodiment, the groove width _{W 2} is 0.03Mm～0.068Mm, by increasing the groove width _{W 2} to 0.12 mm, it is possible to obtain larger _{M 1.}

FIG. 6 is a top view of a tuning fork-shaped crystal oscillator 45 that vibrates in a bending mode used in the crystal oscillator of the second embodiment of the present invention. Tuning fork-shaped bent crystal unit 45
Is composed of tuning fork arms 46 and 47 and a tuning fork base portion 48. That is, one end of each tuning fork arm 46, 47 is connected to the tuning fork base 48. In the present embodiment, the tuning fork base portion 48 is provided with cutout portions 53 and 54. Also, tuning fork arm 4
Grooves 49 and 50 are provided in 6, 47 with the neutral lines 51 and 52 sandwiched therebetween. Further, in this embodiment, the grooves 49 and 50 are provided in a part of the tuning fork arms 46 and 47, and the grooves 49 and 50 are provided.
Each have a width W ₂ and a length l ₁ . More specifically, the area of the groove is represented by S = W ₂ × l ₁ , and S is 0.025.
Configured to have a value of ˜0.12 mm ² . The reason for forming the groove area in this way is that the groove can be easily formed by the chemical etching method, and further the groove can be formed so that the electromechanical conversion efficiency is improved. At the same time, a tuning-fork-shaped crystal oscillator that vibrates in a bending mode having a high quality factor Q value of fundamental mode vibration can be obtained. As a result, it is possible to realize a crystal oscillator in which the output signal is the frequency of fundamental mode vibration.

With the groove area S, the groove and the tuning fork arm can be processed in separate steps. However, in order to simultaneously process the tuning fork arm and the groove provided therein, it is necessary to optimize the thickness t of the tuning fork arm, the groove width W ₂ , the spacing W _{4 of the} tuning fork arm, and the area S. That is, the thickness t of the tuning fork arm is 0.06 mm to 0.15 m.
When m, the groove width W ₂ is within the range of 0.02 mm to 0.068 mm, and the area S is 0.023 mm ^{2 to} 0.08.
It is in the range of 8 mm ² , and the interval W ₄ is 0.05 mm to
It is configured to be 0.35 mm. The reason for configuring in this way is to utilize the crystallinity of quartz, and due to its crystallinity, a groove that is not a through hole (including a groove divided in the length direction of the tuning fork arm).
And the tuning fork shape can be formed at the same time. In addition, FIG.
Although not shown in FIG. 3, grooves are also provided on the lower surfaces of the tuning fork arms 46 and 47 at positions facing the grooves 49 and 50.

Further, the width dimension of the notch portions 53, 54 provided on the tuning fork base portion 48 on the tuning fork portion side is given by W ₅ , and the dimension of the notch portions 53, 54 on the end portion side is given by W _6. . When the end portion of the tuning fork base portion 48 is fixed to a surface mounting type case or a cylindrical type case with solder or adhesive, in order to reduce the loss of vibration energy of the vibrator, The energy loss of the vibrating part can be reduced. The arm width W, partial widths W ₁ and W ₃ , of the tuning fork arm shown in FIG.
Since the relationship between the total length l of the groove width W ₂ and the spacing W ₄ and the length of the groove l ₁ and the tuning fork vibrator is described in FIG. 5, description thereof will be omitted.

FIG. 7 is a sectional view of a crystal unit used in the crystal oscillator of the third embodiment of the present invention. The crystal unit 170 includes a tuning fork-shaped bent crystal oscillator 70, a case 71, and a lid 72. In more detail,
The vibrator 70 is fixed to the fixing portion 74 provided on the case 71 with a conductive adhesive 76 or solder. Also, case 7
1 and the lid 72 are joined via a joining member 73. In the present embodiment, the oscillator 70 is the same oscillator as one of the tuning fork-shaped crystal oscillators 10 and 45 that oscillates in the bending mode described in detail in FIGS. 3 and 6. In the crystal oscillator of this embodiment, the circuit element is connected to the outside of the crystal unit. That is, only the tuning fork-shaped bent crystal oscillator is stored in the unit. At this time, the bent crystal unit is housed in a unit in vacuum.

Further, the case member is made of ceramics or glass, the lid member is made of metal or glass, and the joining member is made of metal or low melting glass. The relationship between the vibrator, the case, and the lid described in this embodiment is shown in FIG.
Also applied to the crystal oscillator.

FIG. 8 is a sectional view of a crystal oscillator according to the fourth embodiment of the present invention. The crystal oscillator 190 includes a crystal oscillation circuit, a case 91, and a lid 92. In this embodiment,
The crystal oscillator circuit is housed in a crystal unit including a case 91 and a lid 92. Further, the crystal oscillator circuit comprises a tuning fork-shaped bent crystal oscillator 90, an amplifier 98 including a feedback resistor, a capacitor (not shown), and a drain resistor (not shown).
A MOS inverter is used.

Further, in this embodiment, the vibrator 90 is fixed to the fixing portion 94 provided on the case 91 with the adhesive 96 or solder. On the other hand, the amplifier 98 has a case 91.
It is fixed to. Further, the case 91 and the lid 92 are joined via a joining member 93. Transducer 90 of this embodiment
The oscillators in the tuning fork-shaped bent crystal oscillators 10 and 45 described in detail with reference to FIGS. 3 and 6 are used.

Next, a method of manufacturing the crystal oscillator of the present invention will be described. The tuning fork-shaped bent crystal oscillator is formed by a photolithography method and a chemical etching method using semiconductor technology. First, a metal film (for example,
Chromium and gold thereon is formed by sputtering or vapor deposition. Next, a resist is applied on the metal film. Then, after the resist and the metal film are removed by the photolithography process while leaving the tuning fork shape, a tuning fork shape including a tuning fork arm and a tuning fork base is formed by a chemical etching method. When forming this tuning fork shape, a notch may be formed in the tuning fork base. Further, the metal film and the resist shown in the above step are applied on the tuning fork-shaped surface, and grooves are formed in the tuning fork arm or the tuning fork arm and the tuning fork base by the photolithography step and the chemical etching method.

Next, a metal film and a resist are applied again in the shape of a tuning fork having a groove, and an electrode is formed by a photolithography process. That is, the electrode on the side surface of the tuning fork arm and the electrode on the side surface of the groove are arranged so as to have opposite polarities. More specifically, the side electrode of the first tuning fork arm and the groove electrode of the second tuning fork arm have the same polarity, and the groove electrode of the first tuning fork arm and the side electrode of the second tuning fork arm have the same polarity. The electrodes of the groove of the first tuning fork arm and the side electrodes are configured to have different polarities. That is, Two-electrode terminals are formed on the vibrator. As a result, when an alternating voltage is applied to the two-electrode terminals, the tuning fork arm flexurally vibrates in reverse phase. In this embodiment, the groove is formed in the tuning fork arm or the tuning fork arm and the tuning fork base after forming the tuning fork shape, but the present invention is not limited to the above embodiment, and first, the groove is formed. May be formed into a tuning fork shape. Alternatively, the tuning fork shape and the groove may be formed at the same time. Further, the dimensions and the like of the grooves in this step are the same as those described above and have already been described, so they are omitted here.

According to the process of this embodiment, a large number of tuning fork-shaped bent crystal oscillators are formed on the crystal wafer.
Therefore, in the next step, in this wafer state, the first frequency adjustment is performed by laser or plasma etching or vapor deposition. At the same time, the defective oscillator is marked or removed from the wafer. In this process, 10 kHz-
The frequency deviation is -9 with respect to the reference frequency of 200 kHz.
The frequency is adjusted so that it is within the range of 000 PPM to +5000 PPM. Further, in the next step, the formed vibrator is fixed to the lead wire of the surface mount type case or the cylindrical type case with an adhesive or solder. After the fixing, the second frequency adjustment is performed by laser or plasma etching or vapor deposition. In this step, the frequency adjustment is performed so that the frequency deviation is within the range of -50PPM to + 50PPM.

Further, after the frequency adjustment, the vibrator is housed in a unit that is a case and a lid in a vacuum. When the lid is made of glass, the third frequency adjustment is performed by the laser after the housing. In this step, the frequency adjustment is performed so that the frequency deviation is within the range of -30PPM to + 30PPM. In this embodiment, the frequency adjustment is performed three times, but it may be performed at least twice. For example, the third frequency adjustment need not be performed. In the next step,
Two-electrode terminals of the above-mentioned vibrator are electrically connected to the amplifier, the capacitor and the resistor. In other words, the amplifier circuit is composed of a CMOS inverter and a feedback resistor, and the feedback circuit is connected so as to be composed of a tuning fork-shaped bent crystal oscillator, a drain resistor, a gate side capacitor and a drain side capacitor. The third frequency adjustment may be performed after the crystal oscillation circuit is constructed.

Although the present invention has been described above based on the illustrated example, the present invention is not limited to the above-described example, and the tuning fork-shaped bent crystal oscillator used in the crystal oscillators of the first to fourth embodiments. in, it is provided with the groove on the tuning fork arm or fork arms and fork base, for example, through holes in the fork arms (t 1 _{= 0)}
May be provided. Alternatively, a groove and a through hole may be provided in the tuning fork base. Further, the groove of the tuning fork base portion connected to the groove provided in the tuning fork arm of this embodiment may be configured as a through hole,
By arranging the electrode on the side surface of the groove or the through hole and arranging the electrode having a polarity different from that of the electrode on the side surface opposed to the electrode, the same effect as described above can be obtained.

Further, in FIG. 4 shown in this embodiment, the tuning fork arm and the tuning fork base are provided with grooves having substantially the same depth, but the present invention is not limited to this, and for example, the tuning fork base is provided. It is also possible to provide all the grooves in the above and change the thickness of the groove on the lower side of the fork and the thickness of the grooves on both sides thereof. That is, grooves having different thicknesses may be provided. As an example, the thickness of the groove in the central portion of the tuning fork base may be formed to be smaller or larger than the thickness of the grooves on both sides thereof. As another example, the depth of the groove provided in the tuning fork arm may be changed. In particular, when a plurality of tuning fork-shaped bent quartz crystal resonators are connected at the tuning fork base through the connecting portion and those resonators are electrically connected in parallel, the groove of the tuning fork arm of each resonator is By changing the thickness (depth), the peak temperature of each vibrator can be changed, and the frequency temperature characteristic can be improved.

Further, the crystal oscillators of the first to fourth embodiments and the tuning fork-shaped bent crystal oscillators used therein have been described. The crystal oscillators used in the crystal oscillators of these embodiments are cases. It is housed in a so-called unit composed of a lid and constitutes a crystal unit. That is, the vibrator of the present embodiment is fixed to the fixing portion provided on the case with a conductive adhesive or solder, and the case and the lid are joined via a joining member.
The inside of the case is configured to be a vacuum. With this configuration, it is possible to realize a microminiature crystal unit having a small equivalent series resistance R ₁ .

[0042]

As described above, it has been described that many effects can be obtained by providing the crystal oscillator of the present invention. Among them, the following remarkable effects can be obtained. (1) Since a plurality of grooves are provided in the tuning fork base and electrodes having different polarities are arranged on their side surfaces, an electric field works vertically. As a result, the electromechanical conversion efficiency is improved, so that a crystal oscillator having a bent quartz crystal resonator having a small equivalent series resistance R _{1 and} a high quality factor Q value can be obtained. (2) The secondary moment of inertia is increased by optimizing the relationship between the groove width, the tuning fork arm width dimension, the groove thickness, and the tuning fork arm thickness dimension. That is, it is possible to realize a crystal oscillator having a tuning fork-shaped bent crystal resonator having a small equivalent series resistance R ₁ , a high Q value, and a small capacitance ratio. (3) The equivalent series resistance R ₁ of the fundamental wave mode vibration of the tuning fork-shaped oscillator is smaller than the equivalent series resistance R _{2 of the second} harmonic mode vibration, and the figurer of merit M ₁ of the fundamental wave mode vibration is 2 The crystal oscillator is configured with a vibrator larger than the Figger of Merit M ₂ of the second harmonic mode vibration, and the fundamental mode vibration of the amplification circuit of the crystal oscillator is further configured including an amplification circuit and a feedback circuit. The ratio of the absolute value of negative resistance | -RL ₁ | to the equivalent series resistance R _{1 of} fundamental mode vibration is the absolute value of negative resistance | -RL ₂ | Since it is configured to be larger than the ratio of the harmonic mode vibration to the equivalent series resistance R ₂ , the output signal of the crystal oscillator is obtained as the output of the frequency of the fundamental mode vibration even if the load capacitance is small. , Power consumption A crystal oscillator with less current can be realized. (4) Furthermore, the amplification factor α ₁ of the fundamental mode vibration of the amplifier circuit
And the amplification factor α ₂ of the second harmonic mode vibration is larger than the ratio of the feedback factor β ₂ of the second harmonic mode vibration of the feedback circuit to the feedback factor β ₁ of the fundamental mode vibration, and Since the product of the amplification factor α ₁ of the wave mode vibration and the feedback factor β ₁ of the fundamental mode vibration is larger than ₁ , it is possible to suppress the second harmonic mode vibration even if the load capacity is small. As a result, the output signal of the crystal oscillator is
The frequency of fundamental mode vibration can be obtained as an output, and a crystal oscillator with low current consumption can be realized. (5) The tuning fork shape and the groove can be formed by the photolithography method and the chemical etching method, which is excellent in mass productivity, and moreover, a large number of vibrators can be formed on one crystal wafer at a time by batch processing, which is inexpensive. It is possible to obtain a bending quartz oscillator having a simple tuning fork shape. At the same time, an inexpensive crystal oscillator equipped with it can be realized. (6) Since the full Iga of merit M ₁ of the fundamental wave mode vibration is a crystal oscillator comprises a full Iga of merit M ₂ is larger than transducers of the second harmonic mode vibration is configured, the output signal is the fundamental mode vibration With the frequency of
A crystal oscillator having high frequency stability can be realized.

[Brief description of drawings]

FIG. 1 is an embodiment of a crystal oscillation circuit diagram constituting a crystal oscillator of the present invention.

FIG. 2 shows a feedback circuit diagram of FIG.

FIG. 3 shows an external view and a coordinate system of a tuning fork-shaped crystal resonator that vibrates in a bending mode used in the crystal oscillator of the first embodiment of the present invention.

4 is a cross-sectional view of the tuning fork base portion of the tuning fork-shaped bent crystal resonator of FIG.

5 shows a top view of the tuning fork-shaped bent crystal oscillator of FIG. 3. FIG.

FIG. 6 is a top view of a tuning fork-shaped crystal resonator that vibrates in a bending mode used in the crystal oscillator of the second embodiment of the present invention.

FIG. 7 is a sectional view of a crystal unit used in a crystal oscillator according to a third embodiment of the present invention.

FIG. 8 shows a sectional view of a crystal oscillator according to a fourth embodiment of the present invention.

FIG. 9 shows a perspective view of a conventional tuning fork-shaped bent crystal unit and its coordinate system.

FIG. 10 is a cross-sectional view of a tuning fork arm of the tuning fork crystal oscillator shown in FIG.

[Explanation of symbols]

1 amplifier circuit 9 feedback circuit V ₁ input voltage V ₂ output voltage 20, 26, 46, 47 tuning fork arm W ₂ groove width W tuning fork arm width W ₁ , W ₃ tuning fork arm partial width W ₄ tuning fork arm interval l Length of ₁ groove ₁ Length of ₂ tuning fork base 1 Total length of tuning fork-shaped bent crystal unit t Thickness of tuning fork arm or tuning fork arm and tuning fork base t ₁ Groove thickness

Claims (2)

[Claims] 1. A crystal oscillator comprising a crystal unit, an amplifier, a capacitor and a resistor, wherein the crystal unit comprises a tuning fork-shaped crystal unit including a tuning fork arm and a tuning fork base that vibrate in a bending mode. Further, the amplifier is composed of a CMOS inverter, and at least one groove is provided in the longitudinal direction on the upper and lower surfaces of the central portion in the width direction sandwiching the neutral line of the tuning fork arm. Electrodes are arranged on both sides of the groove, and the electrodes on the side surfaces of the groove and the electrodes on the side surfaces of the tuning fork arm that oppose the electrodes are configured to have different polarities so that the inertia moment generated in the tuning fork arm becomes large. The ratio (W ₂ / W) of the groove width W ₂ of at least one of the at least one groove to the tuning fork arm width W is 0.
35 to 0.95, the thickness t _{1 of the} groove and the thickness t of the tuning fork arm
And the ratio (t ₁ / t) of the tuning fork arm or the tuning fork arm and the groove length l ₁ provided in the tuning fork base to the tuning fork arm and the tuning fork crystal. The ratio (l ₁ / l) to the total length 1 of the oscillator is in the range of 0.2 to 0.78, and the tuning fork-shaped bent crystal oscillator is housed in a surface mount type or cylindrical type unit. The equivalent series resistance R ₁ of the fundamental mode vibration of the tuning fork-shaped bent crystal oscillator is smaller than the equivalent series resistance R _{2 of the second} harmonic mode vibration, and the figurer of merit M ₁ of the fundamental mode vibration is Figuer of Merit M of second harmonic mode vibration
_The crystal oscillator is configured with a bent crystal oscillator larger than ₂ , and the amplification factor α ₁ and the second harmonic of the fundamental mode vibration of the amplification circuit of the crystal oscillator configured with the amplification circuit and the feedback circuit. The ratio of the amplification factor α ₂ of the wave mode vibration is larger than the ratio of the feedback factor β ₂ of the second harmonic mode vibration of the feedback circuit to the feedback factor β ₁ of the fundamental wave mode vibration, and The crystal oscillator is configured such that the product of the amplification factor α ₁ and the feedback factor β ₁ of the fundamental mode vibration is greater than ₁ , and the crystal oscillator is configured to include the tuning fork-shaped bent crystal oscillator. A crystal oscillator, wherein the output signal is the frequency of fundamental mode vibration. 2. A method of manufacturing a crystal oscillator comprising a crystal resonator, an amplifier, a capacitor and a resistor, wherein the crystal resonator is a tuning fork-shaped crystal vibration composed of a tuning fork arm vibrating in a bending mode and a tuning fork base. At least one groove is provided in the length direction on the upper and lower surfaces of the central portion in the width direction sandwiching the neutral line of the tuning fork arm, and electrodes are arranged on both side surfaces of the groove. The electrode on the side surface of the groove and the electrode on the side surface of the tuning fork arm that opposes the electrode are configured to have different polarities, and at least one of the at least one groove is formed so that the moment of inertia generated in the tuning fork arm becomes large. the ratio of the number of the groove width _{W 2} and the tuning fork arm width W _(W 2 / W) is from 0.35 to 0.95, the ratio of the thickness t of the thickness _{t 1} and the tuning fork arms of said grooves _(t 1 / t ) Is 0.01 to 0.79, and The ratio (l ₁ / l) of the length l _{1 of the} fork arm or the tuning fork arm and the groove provided in the tuning fork base to the total length l of the tuning fork-shaped crystal unit is in the range of 0.2 to 0.78. A step of forming a groove and an electrode so as to be inside, a step of adjusting the frequency of the crystal resonator after fixing the bending crystal resonator with an adhesive or solder to a case of the unit, and a bending of the tuning fork shape. The step of accommodating the crystal unit in a surface mount type or cylindrical type unit, and the CMO as the amplifier.
Using the S inverter, the bent crystal unit and the CMO
Electrically connecting an S inverter, a capacitor, and a resistor, wherein the equivalent series resistance R ₁ of the fundamental mode vibration of the tuning fork-shaped bent crystal resonator is the equivalent series resistance of the second harmonic mode vibration. less than R _2, and, together with the the crystal oscillator comprises a full Iga of merit M ₂ greater flexural quartz crystal full Iga of merit M ₁ of the fundamental wave mode vibration second harmonic mode vibration constituted, second harmonic ratio feedback circuit amplification factor alpha ₁ and the amplification factor alpha ₂ of the second harmonic mode vibration of the fundamental wave mode oscillation of the amplifier circuit of the crystal oscillator constituted comprising an amplifier circuit and a feedback circuit Feedback ratio β ₂ of modal vibration and feedback ratio β ₁ of fundamental mode vibration
And the product of the amplification factor α ₁ of the fundamental mode vibration and the feedback factor β ₁ of the fundamental mode vibration is greater than ₁ , and the crystal oscillator has the tuning fork shape. A method of manufacturing a crystal oscillator, wherein an output signal of the crystal oscillator configured to include a bent crystal oscillator is a frequency of fundamental mode vibration.