JPS6212684B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to dynamic impedance (reciprocal of conductance) of a tuning fork type crystal resonator. In particular, the present invention is directed to improving the dynamic impedance of second harmonic vibrations. An object of the present invention is to provide a stable oscillation circuit by appropriately selecting the dynamic impedance of a tuning fork type crystal resonator, and to provide a long-life crystal clock.

In recent years, electronic quartz clocks have become increasingly popular, and as a result, quartz crystal oscillators, which serve as time standards for quartz clocks, are being actively developed. Currently, a tuning fork crystal unit is commonly used as the time standard for quartz clocks. This type of crystal resonator is often used because of its stable characteristics. It is no exaggeration to say that the time accuracy of a crystal clock is determined by the stability of the crystal oscillation circuit. Recently, inexpensive crystal resonators, particularly crystal resonators using photomasking technology, have been developed. The external shape of this type of crystal resonator is produced by etching with a liquid such as hydrogen fluoride, which is different from the excitation method generally used in the past. For this reason, the electric field strength of tuning fork crystal resonators formed by etching is weaker than that of conventional tuning fork crystal resonators.
At the same time as the dynamic impedance increases, the oscillation region due to self-excited oscillation becomes smaller, and because a region with small capacity is used, harmonic oscillations are more likely to occur. The present invention provides a sufficiently stable oscillation circuit for a tuning fork crystal resonator formed by etching.

The explanation will be given below according to the drawings. FIG. 1 shows an overview of a conventional tuning fork type crystal resonator, 1 is a tuning fork type crystal, 2 is one electrode, 3 is the other electrode, and FIG. shows an electrode configuration diagram of the tuning fork type crystal resonator, and 5 and 6 are both terminal electrodes. FIG. 3 shows a general view of a tuning fork type crystal resonator according to the present invention, where 6 is a tuning fork type crystal, and 7 and 8 are electrodes. l is the length of the tuning fork arm, and le is the length of the excitation electrode.

FIG. 4 shows an electrode configuration diagram of a tuning fork type crystal resonator according to the present invention, and 9 and 10 are electrical terminal electrodes, which are formed into a tuning fork shape by etching.

Conventional tuning fork type crystal resonators have electrodes on the sides, so they have good electrical characteristics, but because they are mechanically processed and have electrodes on the sides, they have poor work efficiency, making it impossible to reduce costs. The tuning fork crystal resonator formed by etching according to the present invention has the advantage that electrodes can be easily formed, and since the tuning fork shape is formed by etching, work efficiency is high and costs can be reduced. FIG. 8 shows an oscillation circuit commonly used for watches, where 11 is an inverter, 12 is a crystal oscillator, Rf, Rd...resistors, Cg, Cd are variable capacitors, and _VDD is a power supply voltage. FIG. 9 shows the oscillation range of the crystal resonator when Cg and Cd are changed in the oscillation circuit, where 13 is a conventional tuning fork type crystal resonator and 14 is a tuning fork type crystal resonator according to the present invention. In this case, the oscillation region (Cg,
It can be seen that Cd=0 to 50PF) is much smaller than the conventional oscillation region. That is, when using the crystal resonator according to the present invention, it is necessary to use it in a place where the capacitance is small. However, if the capacitance is made small, a problem arises in that second harmonic vibration occurs. The present invention obviates the above-mentioned drawbacks. Next, the principle and means of the present invention will be explained.

FIG. 5 shows a cantilever beam having a length l, and FIG. 6 shows the vibration state of the beam. 15 is the vibration mode of the fundamental vibration in bending vibration, and 16 is the vibration mode of the second harmonic. Figure 7 shows the relationship between the length le/l of the excitation electrode and the conductance G (reciprocal of dynamic impedance) in each vibration state, 17 is the fundamental vibration state, and 18 is the second harmonic vibration state. This is the relationship between the excitation electrode le/l and the conductance G. Conventionally, the excitation electrode le/l of a commonly used tuning fork type crystal resonator was about 0.8. This was to make the conductance G in the basic vibration state as large as possible. However, as shown in Figure 7, when le/l is around 0.8, the conductance in the second harmonic is larger than the conductance in the fundamental vibration, and depending on the conditions of the oscillation circuit, it has the characteristic of sufficient oscillation. ing. The oscillation conditions will be described below. FIG. 8 shows the oscillation circuit, and the dotted line 19 shows the feedback circuit. Now, if the amplification factor of the inverter 11 is A and the feedback factor of the feedback circuit is B, the amplitude oscillation condition is A.B≧1. Furthermore, as an oscillation condition, the phase in the feedback circuit must be shifted by 180°. FIG. 10 shows the feedback circuit shown by the dotted line in FIG. 8, where Vd is the input voltage and Vg is the output voltage.
Figure 11 is a diagram that divides the crystal oscillator into real and imaginary components, and the impedance Z of the crystal oscillator is Z=
It is given by Re + jXe. Re is a real component and Xe is an imaginary component, which are expressed as functions of dynamic inductance Lo, dynamic capacitance Co, loss resistance Ro, parallel capacitance _C1 , and angular frequency ω, as shown below.

i ₁ and i ₂ are currents flowing in each loop. According to Kirchhock's law, the following formula holds true.

Rdi ₁ +1/jwCd(i ₁ −i ₂ )=Vd −(1) (i ₂ −i ₁ )1/jwCd+JXei ₂ +Rei ₂ +1/j
wCgi ₂ =0 −(2) 1/jwCgi ₂ =Vg −(3) From (1)(2)(3), Vd/Vg=1−wCgXe−w ² RdCdCgRe+jwCgRe +jwRdCg−jw ² RdCdCgXe+jwRdCd −(4) The phase is To invert 180°, the imaginary part becomes zero.
Rearranging equation (4), Xe=1/W{1/Cg+1/Cd(1+Re/R
d)}-(5) W=2πf f=frequency Equation (5) is the other oscillation condition.

In equation (5), in the conventional oscillation circuit, Cg and Cd are approximately
Since a large capacity of 25 ^PF to 60 ^PF is used, the effective L (inductance) component in the fundamental vibration is larger than the effective L component in the second harmonic, so oscillation occurs at the fundamental vibration. However, in an oscillation circuit in which the capacitance of Cg and Cd is reduced (5 ^PF to 10 ^PF ) and the dynamic impedance of the second harmonic vibration is smaller than the dynamic impedance of the fundamental vibration, the effective L of the second harmonic vibration Since the component becomes larger than the effective L component due to fundamental vibration, a problem arises in that second harmonic vibration occurs. More specifically, considering fundamental wave vibration and second harmonic vibration as an example, the equivalent circuit of the crystal resonator can be written as shown in FIG. However, LM ₁ , CM ₁ , and RM ₁ are the dynamic inductance, dynamic capacitance, and dynamic impedance at the fundamental vibration, respectively, and LM ₂ , CM ₂ , and RM ₂ are the dynamic inductance, dynamic capacitance, and dynamic at the second harmonic vibration. Indicates impedance, and Cs is the interelectrode capacitance. Further, if the real component and imaginary component in the fundamental vibration and second harmonic vibration are respectively Re ₁ , Re ₂ , Xe ₁ , and Xe ₂ , then they are expressed as follows.

However, ω ₁ and ω ₂ represent the angular frequencies of fundamental vibration and second harmonic vibration, respectively.

Furthermore, from equation (5), Xe ₁ and Xe ₂ are Xe ₁ = 1/ω ₁ {1/Cg+1/Cd(1+Re
₁ /Rd)} Xe ₂ =1/ω ₂ {1/Cg+1/Cd(1+Re
₂ /Rd)}......(6) Therefore, the angular frequencies ω ₁ and ω ₂ are determined by equations (0-1) and (6).

If the feedback rates of the return circuit for the fundamental vibration and the second harmonic vibration are β ₁ and β ₂ , the following equation is obtained from equation (4).

1/β ₁ =1−ω ₁ CgXe ₁ −ω ² ₁ RdCdRe ₁ 1/β ₂ =1−ω ₂ CgXe ₂ −ω ² ₂ RdCdRe ₂ ………(7) Substitute equation (6) into equation (7). Substituting the equation (7), 1/β ₁ = ω ₁ ² RdCgCdRe ₁ +Cg/Cd(1+Re ₁
/Rd) 1/β ₂ =ω ₂ ² RdCgCdRe ₂ +Cg/Cd(1+Re ₂
/Rd)...... (8) Next, considering the oscillation conditions for fundamental vibration and second harmonic vibration, suppose that the amplification factors for fundamental vibration and second harmonic vibration are A ₁ and A ₂ respectively. Then, the oscillation conditions for each are as follows.

When A ₁ β ₁ > A ₂ β ₂ , it oscillates at the fundamental vibration.

When A ₁ β ₁ > A ₂ β ₂ , it oscillates with second harmonic vibration. ......(9) To explain these things more specifically, at the same time, in order to make the explanation easier to understand, the following assumption can be made in equation (8).

Cg=Cd=C Re ₁ /Rd Re ₂ /Rd≪1……(10) Therefore, equation (8) is 1/β ₁ =1+ω ² ₁ RdC ² Re ₁ 1/β ₂ =1+ω ² ₂ RdC ² Re ₂ ......(11) These are the angular frequencies ω ₁ , ω ₂ and output resistance, respectively.
This means that the larger Rd, load capacitance C, and real number components Re ₁ and Re ₂ in the equivalent circuit of the crystal resonator become, the smaller the feedback factors β ₁ and β ₂ become.

Furthermore, to explain with a specific example, in the case of a tuning fork type bent crystal resonator, the frequencies ω ₁ and ω
Since there is a relationship between _{ω 2 =} 6ω ₁ , if we substitute this into equation (11) and further assume that Rd and C are constant, equation (11) becomes as follows.

1/β ₁ = 1+ω ₁ ² RdC ² Re ₁ 1/β ₂ = 1+36ω ² ₁ RdC ² Re ₂ ......(12) In equation (12), the fundamental vibration and the second harmonic vibration have the same feedback rate. In order to have the following relationship, Re ₂ =Re ₁ /36 (13).

Equation (13) can be rewritten using dynamic impedances RM ₁ and RM ₂ as follows: have the following relationship. Also, since the amplification factors A ₁ and A ₂ can be the same up to a frequency of about 400 KHz, and the term on the right side of equation (14) can be almost 1, taking these into consideration, the second harmonic When the dynamic impedance RM ₂ of wave vibration has a value smaller than 1/36 times the dynamic impedance RM ₁ of fundamental vibration, oscillation occurs as a second harmonic vibration.

However, although only the power conditions have been explained here, in reality, oscillation is determined only after the phase conditions are taken into consideration.

Next, the phase conditions will be described.

Although the load capacitances Cg and Cd are not directly related to the fundamental vibration and second harmonic vibration under power conditions, they greatly contribute to the phase conditions. Now, if the minute phases in which the phase of the feedback section deviates from 180° are fundamental vibration and second harmonic vibration, Δβ ₁ and Δβ ₂ are given.
From formula (4), Δβ ₁ = tan ^-1 ω ₁ (CgRe ₁ +RdCg+RdCd-ω ₁ RdCdCgXe ₁ )/1-ω ₁ ²
CgXe ₁ −ω ₁ ² RdCgCdRe ₁ Δβ ₂ =tan ⁻¹ ω ₂ (CgRe ₂ +RdCg+RdCd−ω ₂ RdCdCgXe ₂ )/1−ω ₂ ²
CgXe ₂ −ω ₂ ² RdCgCdRe ₂ ......(15) When the load capacity is large between 25 ^PF and 50 ^PF ,
The second harmonic, the phase angle Δβ ₂ of the vibration, is of the same order of magnitude or larger than the phase angle Δβ ₁ of the fundamental vibration, and therefore, unless the power conditions mentioned above, i.e. RM ₂ are made considerably smaller than RM ₁ , the second harmonic It does not oscillate due to harmonic vibration. However, when the load capacitances Cg and Cd become smaller than 25PF as considered in the present invention, even if the second harmonic vibration is inferior to the fundamental wave vibration under power conditions, the phase angle Δβ ₂ and Δβ ₁ becomes smaller. Become,
It becomes easier to oscillate due to second harmonic vibration. Therefore, in the present invention, when the oscillation conditions of the fundamental vibration and the second harmonic vibration are determined by considering the power conditions and phase conditions described above, the dynamic impedance RM ₁ in the fundamental vibration becomes the dynamic impedance in the second harmonic vibration. When RM is smaller than ₂ , fundamental wave vibration will occur even if the load capacitances Cg and Cd are small.

Next, this relationship is expressed as the effective L (inductance)
To explain in terms of components, the equivalent circuit of a crystal resonator is the first
It can be written as shown in Figure 2. However, this circuit can be equivalently written as shown in FIG. Here, since it is the inductance component that actually contributes greatly to oscillation, the effective LM ₂ in Fig. 13, the effective
LM ₁ is the effective L of second harmonic vibration and fundamental vibration, respectively.
It's called an ingredient. By the way, effective LM ₁ , effective
LM ₂ can be expressed using the circuit constants shown in Figure 12, and is as follows.

In addition, the oscillation conditions are determined by the power conditions and phase conditions described above, but in equation (16), if the resonator oscillates with the fundamental wave, the equivalent circuit constant and the equivalent of the second harmonic vibration When calculating by substituting circuit constants, it can be seen that effective LM ₁ >effective LM ₂ , and the larger the effective L component is, the easier it is to oscillate.
Conversely, when effective LM ₂ >effective LM ₁ , the problem of second harmonic vibration occurs. Furthermore, since the capacitance is large, the current consumption is also large. (The current consumption is proportional to the capacity.) The present invention eliminates the above drawbacks. That is, the present invention is to select the dynamic impedance of the crystal resonator, and more specifically, by making the dynamic impedance of the second harmonic vibration larger than the dynamic impedance of the fundamental vibration, the oscillation circuit is improved.
Even when Cg and Cd are reduced, the effective L component in the oscillation circuit in the fundamental vibration is increased, and stable oscillation of the fundamental vibration is achieved. In other words, a large effective L component increases the Q value of the resonator in the oscillation circuit.
Therefore, dependence on the oscillation circuit elements becomes extremely small, and as a result, stable oscillation can be maintained despite deterioration of the circuit elements. Therefore, Cg,
It has the advantage of low current consumption due to the small capacitance of Cd. (The current consumption is proportional to the capacity.) In order to make the dynamic impedance of the second harmonic vibration larger than the dynamic impedance of the fundamental vibration in the present invention, the seventh step is to
As shown in the figure, this can be easily achieved by setting le/l to 0.65 or less. As described above, the present invention enables stable oscillation with fundamental vibration even when the capacity of the oscillation circuit is reduced, making it possible to provide a long-life quartz watch.

[Brief explanation of the drawing]

FIG. 1 shows an overview of a conventional tuning fork type crystal resonator, and FIG. 2 is a diagram showing the electrode structure of the conventional tuning fork type crystal resonator. FIG. 3 shows a tuning fork type crystal resonator according to the present invention, and FIG. 4 is an electrode configuration diagram of the tuning fork type crystal resonator according to the present invention. FIG. 5 shows the vibration direction of the cantilever beam, and FIG. 6 shows the vibration state of the cantilever beam. FIG. 7 shows the relationship between the electrode length and conductance (reciprocal of dynamic impedance) in fundamental vibration and second harmonic vibration. FIG. 8 is a crystal oscillation circuit diagram, and FIG. 9 is a diagram showing oscillation regions in the oscillation circuit of a conventional tuning fork type crystal resonator and a tuning fork type crystal resonator according to the present invention. 10 and 11 are feedback circuit diagrams in a crystal oscillation circuit. FIG. 12 and FIG. 13 are equivalent circuit diagrams of the crystal resonator, respectively. 1, 6,... Tuning fork crystal, 2, 3, 7, 8...
Electrode, 11... Inverter, 12... Crystal resonator, 15... Fundamental vibration mode, 16... Second harmonic vibration mode, 4, 5, 9, 10... Electrode terminal, 17
...Fundamental vibration, 18...Second harmonic vibration, 19...
...Feedback circuit.

Claims (1)

[Claims] 1 In a crystal clock using a crystal oscillation circuit consisting of a C-MOSIC, a capacitor, a resistor, and a tuning fork crystal resonator, Cg and Cd of the crystal oscillation circuit are selected from 5-10PF, Cg is larger than Cd, and The dynamic impedance of the fundamental wave vibration of a tuning fork crystal resonator is expressed as the dynamic impedance of the second harmonic vibration.
A crystal clock characterized by using a tuning fork crystal resonator smaller than 36 times as the time standard for the crystal clock.