JPH01152809A - Piezoelectric vibrator - Google Patents

Abstract

PURPOSE:To eliminate the production of spurious radiation between series resonance and anti-resonance frequency being the operating region of main vibration by selecting properly the ratio of the long side to the thickness of the vibration chip, the ratio of the length to the thickness of the exciting electrode, the ratio of the width to the thickness of the vibration chip or the ratio of the width to the thickness of the exciting electrode. CONSTITUTION:A piezoelectric vibrator consists of a vibration chip 100 made by cutting a lithium tantalate single crystal in a specific azimuth and an exciting electrode 102 on the front and rear major faces of the vibration chip, the specific cut-off azimuth is expressed in terms of a rotation angle signal as xyt-50.3 deg.+ or -2 deg., and as the vibration mode of the vibration chip, the mode with fast thickness-shear vibration is used, and the ratio of the thickness T of the vibration chip to the length L in the direction of the long side is selected to be L/T<=32 or the ratio of the length Le of the exciting electrode with respect to the length Le in the direction of long side is selected to be Le/T<=32. Then a value OMEGA being the ratio of the anti-resonance frequency fFS of the face shear vibration mode with respect to the short side W of the vibration chip to the anti-resonance frequency fTS of the thickness-shear vibration mode of the vibration chip is selected to be OMEGA<0.9 and OMEGA<1 by selecting the ratio of the short side W of the vibrating chip to the thickness W/T or the ratio of the electrode width We in the direction of short side to the thickness We/T.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to the structure of a vibrating element of a piezoelectric vibrator made from a lithium tantalate single crystal, which is used as a frequency control element in a voltage controlled oscillator (VCO). Regarding.

[Conventional technology]

A conventional piezoelectric vibrator using an X-cut lithium tantalate single crystal was disclosed in JP-A-58-190115. Therefore, according to the patent, the long side of the vibrating piece is
When the short side is W and the thickness is T, the side ratio L/T=38.5, W/
A piezoelectric vibrator having an anti-resonant frequency of 20 MH2 with 'I'=9.629 was prototyped and its resonance characteristics were measured. As a result, the characteristics shown in FIG. 2 were obtained.

In the figure, the horizontal axis is the frequency, the vertical axis is the resonant current logarithm of the piezoelectric vibrator, 200 is the resonance characteristic curve, the series resonance of f r and fa, and the mode M1 expressed by the anti-resonance frequency is the originally required main vibration. , and M2, M3, and M observed in that pond are
The modes 4, M5, and M6 are resonance phenomena called spurious (unnecessary vibrations) that should be eliminated. In particular, it is explained that the M2 and M3 modes between the series resonance frequency and the anti-resonance frequency of the main vibration are generated due to higher-order modes (hereinafter referred to as inharmonic modes) of the fundamental wave of the thickness-shear vibration system. It is possible.

[Problem that the invention seeks to solve]

However, if there is a spurious generated by the above-mentioned prior art, the linearity of the output frequency with respect to the input voltage of C○ is impaired, and the output frequency is close to the spurious modes M2, M3, and If this happens, a sudden frequency jump will occur, causing a serious problem. The present invention is intended to solve these problems, and its purpose is to reduce the spurious mode existing between the series resonance and anti-resonance of the main vibration to the lower side of the series resonance frequency fr and the anti-resonance. The object of the present invention is to provide the market with a piezoelectric vibrator for a VCO whose characteristics are improved by eliminating frequencies above fa.

[Means for solving problems]

The piezoelectric vibrator of the present invention is characterized by the following items.

(1) In a piezoelectric vibrator comprising a vibrating piece cut in a specific direction from a lithium tantalate single crystal and excitation poles formed on the front and back main surfaces of the vibrating piece, the specific direction of the cut is a rotation angle. Expressed as a signal, it is xyt-50,3±2 degrees, the vibration mode of the vibrating piece uses a fast thickness shear vibration mode, and the length in the long side direction with respect to the thickness T of the vibrating piece L/T, which is the ratio of L/T hSL/T≦32, or Le/T, which is the ratio of the excitation w to the thickness T<the length Le in the long side direction of the electrode, is Le/T.
Must be ≦32.

(2) The value of Ω, which is the ratio of the anti-resonance frequency f ps of the plane shear vibration mode in the short side W direction of the vibrating element to the anti-resonance frequency fT8 of the thickness-shear vibration mode of the vibrating element, is Ω<o, The ratio W/T of the short side W and the thickness of the vibrating piece that satisfies Ω>1 or the electric current in the short side direction! h%, W
The piezoelectric vibrator according to claim 1, having a ratio of e to thickness W e /T.

〔Example〕

FIG. 1 is a conceptual diagram of a vibrating piece having a piezoelectric vibrator in an embodiment of the present invention. To explain the names of each part in the diagram,
The coordinate axes x, y, and z axes are the reference coordinate system of the trigonal lithium tantalate single crystal, the X axis is one of the two-fold rotational symmetry axes, and the Z-axis is the three-fold rotational symmetry axis, Furthermore, the y-axis is orthogonal to the One of the excitation electrodes on the front and back sides, 103 is an axis indicating the long side direction of the vibrating piece 100. Further, L and W are the length of the vibrating piece in the long side direction (length) and the size of the short side (width), respectively, and Le and We are the size of the excitation electrode 102 in the long side direction (length). This is the size in the short side direction (width). Further, let T be the thickness of the vibrating piece. The cutting direction of the vibrating piece 100 from the lithium tantalate single crystal was I in 1949.

Using the notation determined by R, E, xyt-50,
It can be written as 3±2 degrees. However, here, the above notation is -50 when the plate in which the X axis is the thickness direction and the y axis is the long side direction is rotated around t (thickness direction axis) with the counterclockwise direction being positive in the pre-rotation state.
, which means that the plate obtained by rotating 3±2 degrees is set as the orientation of the vibrating element.

The rotation angle φ=-50.3 degrees is determined by an elastic constant matrix (Cij ;i, j=1 to 6
) is the angle at which the C46 component becomes zero. Furthermore, it can be proven that at this angle, pure thickness shear vibration that satisfies the stress-free boundary condition exists on the two main surfaces 101 of the vibrating element 100 and the four side surfaces surrounding the main surfaces. The thickness shear vibration is caused by resonance of an elastic wave having a faster propagation speed among the two transverse waves, and its anti-resonance frequency constant KTI is approximately K'rs=1880 Hzm. Furthermore, the displacement of the vibration is directed in the long side direction of the vibrating piece 100, and furthermore, the meaning of the pure thickness shear vibration is that the displacement vector is orthogonal to the propagation direction of the wave structure, that is, the thickness direction of the vibrating piece 100. Add that it is.

Next, the reason why the spurious in FIG. 1 can be eliminated in the piezoelectric vibrator of the present invention will be explained with reference to IIM.

First, spurious removal in M2 and M3 modes will be explained. The modes M2 and M3 are thickness-slip inharmonic modes (j, 1.O) and (
5,1,O) mode.

The inharmonic mode is a mode in which the amplitude of the thickness-shear vibration displacement changes vibrationally in the long side direction of the vibrating piece, and M
The (3,1,0> mode of 2 has an 8-width distribution or approximately three half wavelengths in the long side direction, and the (5,1°0) mode has approximately five half wavelengths in the long side direction, and This means that the amplitude distribution in the short side (width) direction of the vibrating element is uniform.An anti-resonant frequency fa of these modes is given by the following equation.

However, ρ is the density, p, q, and r are integers (p.

The inharmonic mode is represented by a set of q, r'). Also, C++=2.638XI O”, C66=
1.053X1012, Cs5=0.847X10 I
2 (dyne/ad), both of which are elastic constants.

The ratio of elastic constants expressed in equation (1) is C+ l/C6
6=2.505, Css/Cas=0,804.

Generally, equation (1) gives the anti-resonance frequency of thickness shear vibration in an infinite flat plate with thickness T, where q=l or the fundamental wave, q=3.5.7.
Odd numbers of . . . give antiresonant frequencies of harmonic modes such as 3rd, 5th, 7th, etc., respectively. For convenience, Ω= f / f a
It is easier to understand if it is expressed as a ratio to fao as o,
As an example, let's calculate Ω for a conventional piezoelectric vibrator1
If L/T=38°51 and W/T=9.629 are taken as side ratios, the values in the left column of Table 1 below are obtained.

Table 1 By the way, mode M1 in Figure 2 is <p, q, r) = (1,
1,0), and the resonant frequency fr is given by 0°97 when the anti-resonant frequency fa=1.

Therefore, the antiresonance frequencies of modes M1, M2, and M3 are all close enough to be considered to be 1. On the other hand, the resonance frequencies of modes M2 and M3 with respect to mode M1 are f2=fa-1/3Δf, fs=fa 115Δ, respectively, as shown in FIG.
f. However, Δf=fa−fr. The reason for this is due to the displacement distribution of the modes (3, 1, 0) and (5, 1, 0) as described above, and the total charge Q on the excitation electrode 101 obtained in each mode is the main vibration (1, 1°0), mode (3, 1, 0) is Q./3, mode <5.
1. O) becomes C015. As a result, the dynamic capacitance of the piezoelectric vibrator is (3
, 1, 0) mode is C1/3, and the (5, 1, 0) mode is C115, so that the above-mentioned resonance frequency relationship is obtained.

On the other hand, in the case of the embodiment of the present invention shown in FIG. 1, the relationship between the dimensions and T that give the shape of the vibrating element is a side ratio, and is given so as to satisfy the relational expression L/T≦32. This makes it possible to bring the spurious modes M2 and M3 above the anti-resonance frequency fa of the main vibration. The reason for this will be explained next. From equation (1) giving the series resonance frequency of the inharmonic mode (p, q, r) and the anti-resonance frequency of the main vibration, the above condition needs to satisfy the relationship of the following equation.

Considering the case where the first term of equation (3) takes the minimum value, it is sufficient to set r=0, so that the following can be obtained. Substituting the actual value of fa/△f=30, the fundamental wave of q=1 that maximizes the right side of (4), and P=3, we get (
4) The right side of the equation is 31.85.

Also, from the third-order overtone ci = 3, the right side of equation (4) is 10
．． 62, 6.37 is obtained for ct=5.0 or more As explained above, if the ratio L/T of the long side and the thickness T of the vibrating element 100 of the present invention is 32, the spurious M2 and M3 will be equal to or greater than fa. frequency. However, if the above side ratio conditions are maintained, problems may occur. For example, if the anti-resonance frequency fa is 201Z and the length of the long side of the vibrating piece 100 is L = 4, then the thickness T = 0, 1. m
Since the side ratio L/T is 40, the above condition cannot be satisfied. Making the long sides even shorter is not preferable because it increases the series resonance resistance of the piezoelectric vibrator due to the support of the vibrating element and causes deterioration of characteristics.

Therefore, in the present invention, the same effect is achieved by focusing on the large electromechanical coupling coefficient (k=0.45> of the lithium tantalate vibrator and appropriately adjusting the dimension Le in the long side direction of the vibrating electrode 102. - In the thickness shear vibration mode that has a high electromechanical coupling coefficient in boat fishing, a confinement effect of vibration energy occurs due to the electric field and mass effect of the excitation electrode 102. In this case, the vibration displacement is almost at the bottom of the electrode. , and has the same distribution as above (p, q, r). Therefore, the conditional expression of the side ratio L/T≦32
The inequality is Le/T≦3 instead of L.
It can be rewritten as 2.

Next, another method of eliminating spurious M6 between the resonance frequency and the anti-resonance frequency of the main vibration in the conventional example shown in FIG. 2 will be described. This mode is known to move the series resonance point of M6 by changing the side ratio W/T of the vibrating element 100, and is generally known as a plane-slip vibration mode (Fs).

Since the plane slip mode is excited quite strongly, it is necessary to keep it away from the region between fr and fa, which is the operating region of the vibrator.

For this purpose, the side ratio W/ of the plane-slip vibration mode is
I theoretically derived a relational expression (referred to as a mode chart) between anti-resonant frequency and T. The vibrating piece 10
In the coordinate system x'y'z' attached to The perfect frequency can be obtained. fKs is the frequency of thickness-shear vibration (
2) Normalization using equation 2) yields. However, m is an integer and gives the order of the facing verimode. Figure 3 illustrates equation (6).
Since the plane slip mode is strongly excited when m is an odd number, FIG. 3 illustrates the orders of m=1 to 13 for odd values of m.

In the figure, the vertical axis is the normalized frequency according to equation (6), and Ω = 1
However, it can be considered that this corresponds to half vibration (1° 1.0) of thickness shear vibration, and the horizontal axis is the side ratio W/T. 30 again
1 is the mode chart 1 curve according to equation (6), and the f
The anti-resonant frequency position of the face-to-face vibration with respect to ao is shown.

It is clear that in order for frs not to be located between the series and anti-resonant frequencies of the main vibration, the relationships Ω>1 and Ω<frZfa need to be satisfied. The value of frZfa is determined by the cutting direction of the vibrating piece from the lithium tantalate single crystal, and in the case of the piezoelectric vibrator of the present invention, it is about 0°97, so it is preferable that Ω<0.9. It is a condition. straight line 30
2 gives Ω=0.9. Therefore, when selecting a range of side ratio W/T that satisfies the above condition, W/T<0.9.1<
W/T<2.6.3<W/T<4.4.5<W/T<6
．． 2.7ku W/T<8.0.9<W/T<9.8.11
Therefore, W/T<11.6, . . . is obtained.

Furthermore, looking at the relationship between Le and L mentioned above, the energy confinement phenomenon of thickness shear torsional waves (TT waves) also exists in the width direction of the vibrating element, so the conditions for W/T are the same as the conditions for We/T. It can be easily inferred that it can be regarded as 0-order. FIG. In the figure, 401 is the resonance characteristic curve, Ml is the main vibration of the thickness-shear vibration with the series resonance frequency fr and anti-resonance frequency fa, and M2 and M3 are the inharmonic modes (3, 1, O
), (5,1,O) mode, and M6 is the shear vibration mode.

It should be added that M4 is considered to be a thickness shear vibration due to the slow horizontal axis.The ratio of the antiresonant frequency of M2, M3, and M6 to the main vibration fa is 1.038 (M2
), 1.103 (M3), and 0°82 (M6), however, as the dimensions of the components of the vibrating piece, L = 4 cities, W =
1 kaku, T=0.1 fin, Le=1.7 city, We=0.9m
m was used.

[Effects of the Invention] As described above, according to the present invention, the ratio L/T between the long side of the vibrating element and its thickness or the ratio L between the length Le and the thickness of the excitation electrode
By appropriately selecting e/T and the ratio W/T between the width and thickness of the vibrating element, or the ratio We/T between the width We and the thickness of the excitation pole, it is possible to counteract the series resonance, which is the operating region of the main vibration. Since there is no spurious between resonance frequencies, good CO frequency control characteristics with a wide range of variable frequencies can be obtained, and great benefits can be expected in the future.

[Brief explanation of the drawing]

FIG. 1 is a conceptual diagram of the vibrating element of the piezoelectric vibrator of the present invention,
Fig. 2 is a resonance characteristic diagram of a conventional piezoelectric vibrator, Fig. 3 is a mode chart of face-edge vibration mode, and Fig. 4 is a resonance characteristic diagram of a piezoelectric vibrator which is an embodiment of the present invention. be. 100... Vibration piece 102... Excitation electrode 101... Principal surface 401... Resonance characteristic curve or higher

Claims (2)

[Claims] (1) In a piezoelectric vibrator having a vibrating piece cut in a specific direction from a lithium tantalate single crystal and having excitation electrodes formed on the front and back main surfaces of the vibrating piece, the specific direction of the cut is rotated. Expressed as an angular signal, it is xyt-50.3±2 degrees, the vibration mode of the vibrating piece uses a fast thickness shear vibration mode, and the length in the long side direction with respect to the thickness T of the vibrating piece is L/T, which is the ratio of the length L, is L/T≦32, or the length L in the long side direction of the excitation electrode with respect to the thickness T
A piezoelectric vibrator characterized in that a ratio of e, Le/T, satisfies Le/T≦32. (2) The value of Ω, which is the ratio of the anti-resonant frequency F_K_S of the plane-slip vibration mode in the short side W direction of the vibrating element to the anti-resonant frequency F_T_S of the thickness-shear vibration mode of the vibrating element, is Ω<0.9 and Ω Claim 1, characterized in that the vibrating element has a ratio W/T between the short side W and the thickness of the vibrating element or a ratio We/T between the electrode width We in the short side direction and the thickness satisfying >1. Piezoelectric vibrator.