CN101257287A - Method for design piezoelectric resonator electrode shapes - Google Patents

Abstract

A piezoelectric resonator electrode shape design method is disclosed. The electrode shape at each direction can satisfy Bechmann number, thereby all the particle vibration covered by a same electrode are in the same phase. According to Y cutting quartz plate, At cutting quartz plate and Y cutting crystal plate thickness shearing resonator, the shaft x1 and the shaft x3 are coordinate axis in a place, x2 is a normal coordinate axis of the plate, Phi is a rotation angle from the shaft x1 to the shaft x3 in the plane, the electrode length L follows the expression (the above formula) of the angle Phi. The resonator structure of electrode after optimum design is portable, with good performance and high precision, which is propitious to miniaturization of device; meanwhile design method is simple and easy of bulk production.

Description

Method for design piezoelectric resonator electrode shapes

Technical field

The present invention relates to the Optimization Design of electrode in the piezoelectric resonator.

Background technology

Quartz-crystal resonator is the primary element of each electronic product, in various fields such as household electrical appliance, communication, navigation, accurately timing, transducers important application is arranged.Electrode is the important component part of resonator, and it has significant effects to the microminiaturization and the accuracy of resonator.

Electrode is used for exciting the mechanical oscillation of resonator, and its quality can realize falling into function, and along with the development of resonator microminiaturization, electrode shape research also more and more comes into one's own.Electrode shape in the existing quartz-crystal resonator is circle or rectangle, do not carry out sufficient optimal design, can not satisfy that electrode can fall into, resonator is microminiaturized and Bechmann counts requirement, wherein rectangular electrode causes easily that on the angle stress is concentrated, and the resonator overall performance is had adverse effect.Take into full account above factor, in conjunction with the theory of Mindlin, Steven and Tiesten, calculate the optimum shape and the size of several quartz-crystal resonator electrodes commonly used, electrode satisfies the Bechmann number that can fall on requirement, microminiaturized requirement and each direction.

Summary of the invention

For overcome conventional piezoelectric crystal resonator electrode can not satisfy can fall into, requirement such as microminiaturization and Bechmann number, the invention provides out the optimum electrode shape of several piezoelectric resonators commonly used, satisfy that electrode can fall into, resonator is microminiaturized and Bechmann counts requirement, improve the service behaviour of resonator.

The technical scheme that the present invention solves its technical problem employing is:

For Y cut quartz plate, At cuts quartz plate and Y Qie Lankesai crystal (1angasite) plate thickness shear mode resonator, x ₁Axle and x ₃Axle is a plane internal coordinate axle, x ₂Be the normal direction reference axis of plate,

Be x in the plane ₁Axle is to x ₃The corner of axle, optimum electrode length L is with angle

Expression formula be:

2h is the thickness of plate in the formula, and other parameter is expressed by following formula:

${\mathrm{\&gamma;}}_{11}=\frac{s_{33}}{s_{11}{s}_{33}-s_{13}^2}=c_{11}-\frac{{\mathrm{<figure-callout\; id="12"\; label="c"\; filenames="A20081003083300072.png,A20081003083300081.png"\; state="\{\{state\}\}">c</figure-callout>}}_{12}^2}{c_{22}}-\frac{{(c_{14}-\frac{c_{12}{c}_{24}}{c_{22}})}^2}{c_{44}-\frac{c_{24}^2}{c_{22}}},$

${\mathrm{\&gamma;}}_{55}=\frac{1}{s_{55}}=c_{55}-\frac{c_{25}^2}{c_{22}}-\frac{{(c_{45}-\frac{c_{24}{c}_{25}}{c_{22}})}^2}{c_{44}-\frac{c_{24}^2}{c_{22}}},$

${\widehat{\mathrm{\&gamma;}}}_{11}=\frac{{\mathrm{\&gamma;}}_{11}}{{3\mathrm{\&kappa;}}^2{c}_{66}},$ ${\widehat{\mathrm{\&gamma;}}}_{55}=\frac{{\mathrm{\&gamma;}}_{55}}{{3\mathrm{\&kappa;}}^2{c}_{66}},$ $\mathrm{\&alpha;}=\frac{1+3R}{1+R},---\left(2\right)$

${\mathrm{\&kappa;}}^2=(1+R-\frac{{8k}_{26}^2}{{\mathrm{\&pi;}}^2})\frac{{\mathrm{\&pi;}}^2{\stackrel{\&OverBar;}{c}}_{66}}{{12c}_{66}},$ $R=\frac{2{\mathrm{\&rho;}}^{\&prime;}{h}^{\&prime;}}{\mathrm{\&rho;h}},$

$k_{26}^2=\frac{e_{26}^2}{c_{66}{\mathrm{\&epsiv;}}_{22}},$ ${\stackrel{\&OverBar;}{c}}_{66}=(1+k_{26}^2)c_{66}.$

C wherein ₁₁, c ₁₂, c ₁₄, c ₂₂, c ₂₄, c ₂₅, c ₄₄, c ₄₅, c ₆₆Be piezoelectric elastic constant, s ₁₁, s ₁₃, s ₃₃, s ₅₅Be the flexible constant of piezoelectric, ε ₂₂Be dielectric constant, e ₂₆For piezoelectric constant, ρ are that piezoelectric board density, ρ ' are that battery lead plate density, 2h ' are that battery lead plate thickness, R are the mass ratio of battery lead plate and piezoelectric board.

For the slow thickening degree of dual rotation pattern quartz plate piezo-electric resonator, if x ₂Axle is the normal direction reference axis of plate primary flat, x ₁The axle edge is rotating shaft direction reference axis for the second time,

Be x in the plane ₁Axle is to x ₃The corner of axle, optimum electrode length L is with angle

Relational expression be

Wherein n is the mode number, gets odd number mode, M _n, P _nAnd Q _nBe material parameter, c ⁽¹⁾Be a characteristic value in the equation of motion, in the formula 3

Expression formula is:

${\hat{c}}^{\left(1\right)}={\stackrel{\&OverBar;}{c}}^{\left(1\right)}(1-\frac{{8\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A20081003083300071.png,A20081003083300072.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20081003083300071.png,A20081003083300072.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2}-2R),$ (4)

${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A20081003083300071.png,A20081003083300072.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2=\frac{e_{26}^2}{{\stackrel{\&OverBar;}{c}}^{\left(1\right)}{\mathrm{\&epsiv;}}_{22}},$ $R=\frac{2{\mathrm{\&rho;}}^{\&prime;}{h}^{\&prime;}}{\mathrm{\&rho;h}}.$

ε wherein ₂₂Be dielectric constant, e ₂₆For piezoelectric constant, ρ are that piezoelectric board density, ρ ' are that electrode density, 2h are that piezoelectric board thickness, 2h ' are that battery lead plate thickness, R are the mass ratio of battery lead plate and piezoelectric board.

The present invention compares with existing piezoelectric resonator electrode and has the following advantages: structure is light, performance good, highly sensitive, helps the microminiaturization development of device.

Description of drawings

Fig. 1 piezoelectric resonator profile of the present invention;

Fig. 2 Y cuts quartz, At cuts quartz and the optimum electrode shape figure of three kinds of resonators of Y Qie Lankesai plate;

Fig. 3 Y cut the quartz plate resonator at different quality than optimum electrode shape comparison diagram under the situation;

Fig. 4 SC cuts the optimum electrode shape figure of quartz resonator under different modalities;

Fig. 5 SC cuts the quartz resonator different quality than optimum electrode shape comparison diagram under the situation.

The present invention is further illustrated below in conjunction with accompanying drawing.

Embodiment

As shown in Figure 1, piezoelectric resonator by middle one deck piezoelectric board 1 and up and down two plate electrode plates 2 form.x ₁Axle and x ₃Axle is a plane internal coordinate axle, x ₂Be the normal direction reference axis of plate: piezoelectric board 1 thickness is 2h, and density is ρ; Each battery lead plate 2 thickness is 2h ', and density is ρ ', and tangent plane length is 2L.

In calculating, choose: 2h=1mm, analyzed dimensionless polar radius r=L/ (4h) and angle that cartesian coordinate system is represented among Fig. 2-Fig. 5

The relation of two parameters.

As can be seen from Figure 2, cut quartz plate, Y for At and cut the optimum electrode shape of quartz plate resonator near oval, but be not standard ellipse, major axis is than the about length 25% of minor axis; For Y Qie Lankesai plate resonator and elliptical shape disparity.As can be seen from Figure 2, do not meet the shearing distribution for rectangle or circular electrode.

Fig. 3 has analyzed the influence of mass ratio variation to the optimum electrode shape of piezo-electric resonator.As can be seen from Figure 3, optimum electrode size increases along with mass ratio and reduces.

Fig. 4 has analyzed SC and has cut the optimum electrode shape of quartz resonator under different modalities.As can be seen from Figure 4, electrode shape approaches ellipse, but the major axis of electrode and minor axis no longer overlap with reference axis, and electrode size reduces along with the increase of mode number.

Fig. 5 has analyzed SC and has cut the influence of quartz resonator mass ratio variation to the optimum electrode shape of piezo-electric resonator.For a fixing mode (among Fig. 5 fixedly n=1), optimum electrode size increases along with mass ratio and reduces, this and Fig. 3 is resulting comes to the same thing.

In sum, for the different materials parameter, the piezoelectric resonator electrode shape under the different geometrical size need calculate optimum electrode shape; The optimum electrode shape of piezoelectric resonator approaches ellipse, and rectangle or the circular electrode used in this and the tradition all have very big gap on shape still is size; Optimum electrode size reduces along with the increase of mass ratio and mode number.

Claims (1)

1. method for design piezoelectric resonator electrode shapes is characterized in that: for Y cut quartz plate, At cuts quartz plate and Y Qie Lankesai crystal slab thickness-shear-mode resonators, x ₁Axle and x ₃Axle is a plane internal coordinate axle, x ₂Be the normal direction reference axis of plate,

Be x in the plane ₁Axle is to x ₃The corner of axle, electrode length L is with angle

Expression formula be:

2h is the thickness of plate in the formula, and other parameter is expressed by following formula:

${\mathrm{\&gamma;}}_{11}=\frac{s_{33}}{s_{11}{s}_{33}-s_{13}^2}=c_{11}-\frac{c_{12}^2}{c_{22}}-\frac{{(c_{14}-\frac{c_{12}{c}_{24}}{c_{22}})}^2}{c_{44}-\frac{c_{24}^2}{c_{22}}}$

${\mathrm{\&gamma;}}_{55}=\frac{1}{s_{55}}=c_{55}-\frac{c_{25}^2}{c_{22}}-\frac{{(c_{45}-\frac{c_{24}{c}_{25}}{c_{22}})}^2}{c_{44}-\frac{c_{24}^2}{c_{22}}}$

${\widehat{\mathrm{\&gamma;}}}_{11}=\frac{{\mathrm{\&gamma;}}_{11}}{{3\mathrm{\&kappa;}}^2{c}_{66}}$ ${\widehat{\mathrm{\&gamma;}}}_{55}=\frac{{\mathrm{\&gamma;}}_{55}}{{3\mathrm{\&kappa;}}^2{c}_{66}}$ $\mathrm{\&alpha;}=\frac{1+3R}{1+R}$

${\mathrm{\&kappa;}}^2=(1+R-\frac{{8k}_{26}^2}{{\mathrm{\&pi;}}^2})\frac{{\mathrm{\&pi;}}^2{\stackrel{\&OverBar;}{c}}_{66}}{{12c}_{66}}$ $R=\frac{2{\mathrm{\&rho;}}^{\&prime;}{h}^{\&prime;}}{\mathrm{\&rho;h}}$

$k_{26}^2=\frac{e_{26}^2}{c_{66}{\mathrm{\&epsiv;}}_{22}}$ ${\stackrel{\&OverBar;}{c}}_{66}=(1+k_{26}^2)c_{66}$

C wherein ₁₁, c ₁₂, c ₁₄, c ₂₂, c ₂₄, c ₂₅, c ₄₄, c ₄₅, c ₆₆Be piezoelectric elastic constant, s ₁₁, s ₁₃, s ₃₃, s ₅₅Be the flexible constant of piezoelectric, ε ₂₂Be dielectric constant, e ₂₆For piezoelectric constant, ρ are that piezoelectric board density, ρ ' are that battery lead plate density, 2h ' are that battery lead plate thickness, R are the mass ratio of battery lead plate and piezoelectric board;

Slowly become the thickness mode resonator for dual rotation, electrode length L is with angle

Relational expression be

Wherein n is the mode number, gets odd number mode, M _n, P _nAnd Q _nBe material parameter, c ⁽¹⁾Be a characteristic value in the equation of motion,

Expression formula is:

${\hat{c}}^{\left(1\right)}={\stackrel{\&OverBar;}{c}}^{\left(1\right)}(1-\frac{{8k}_1^2}{n^2{\mathrm{\&pi;}}^2}-2R)$

$k_1^2=\frac{e_{26}^2}{{\stackrel{\&OverBar;}{c}}^{\left(1\right)}{\mathrm{\&epsiv;}}_{22}}$ $R=\frac{2{\mathrm{\&rho;}}^{\&prime;}{h}^{\&prime;}}{\mathrm{\&rho;h}}$

ε wherein ₂₂Be dielectric constant, e ₂₆Be piezoelectric constant, ρ is a piezoelectric board density, and ρ ' is an electrode density, and 2h is a piezoelectric board thickness, and 2h ' is a battery lead plate thickness, and R is the mass ratio of battery lead plate and piezoelectric board.

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