JPH09270667A - Surface acoustic wave resonator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain the surface acoustic wave resonator with less spurious radiation by apotizing each crossing width of an interdigital electrode so as to maximize the transducing efficiency into its vibration mode with respect to a surface acoustic wave of an optional noted overtone. SOLUTION: An interdigital electrode 2 and grating reflectors 31, 32 made of an Al thin film are formed on the surface of a piezoelectric substrate. The crossing width of the interdigital electrode 2 is apotized symmetrically toward the reflectors 31, 32 at both sides according to a weight function F(x) to maximize a transformation ratio Tr of a fundamental wave mode being a noted overtone mode. That is, the crossing width of the interdigital electrode 2 is apotized along with a shape expressed by the weight function F(x) to maximize a general transformation ratio Tr shown in equation with respect to the noted overtone. In the equation, ϕ(x) is a vibration distribution of a surface acoustic wave in the noted overtone mode in a waveguide path, F(x) is a stimulation energy distribution by the interdigital electrode and x is a position of the waveguide path in the broadwise direction.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a surface acoustic wave resonator in which an interdigital electrode for exciting a surface acoustic wave and two reflectors are formed on the surface of a piezoelectric substrate.

[0002]

2. Description of the Related Art In general, a surface acoustic wave resonator has an interdigital electrode 2 formed on the surface of a substrate 1 made of a piezoelectric material such as crystal or piezoelectric ceramic, as shown in FIG. Grating reflector 31,
It has a structure in which 32 is formed. Interdigital electrode 2
Is a pair of comb-shaped electrodes 2 each having a plurality of electrode fingers.
Reference characters a and 2b are converters each having a structure in which the electrode fingers are arranged to face each other in a state where the electrode fingers cross each other and convert an electric signal into a surface acoustic wave. The grating reflectors 31 and 32 have a structure in which a large number of strips are periodically arranged at a pitch of 1/2 of the surface acoustic wave wavelength, and the surface acoustic waves are excited by the interdigital electrodes 2 and propagate to both sides thereof. To form a standing wave by repeatedly reflecting.

By the way, in the surface acoustic wave resonator as described above, as shown in the example of FIG. 24, the cross width of the interdigital electrodes 2, that is, the crossing length between the electrode fingers of the pair of comb-shaped electrodes 2a and 2b is set. When the surface acoustic waves are constant in the propagation direction (the direction connecting the two reflectors 31 and 32) (referred to as a normal type), if the crossing length of the electrode fingers is increased to reduce the impedance, There is a problem that spurious is generated in a frequency region higher than the fundamental frequency.

The cause of such spurious is
As described in Japanese Patent Publication No. 7-28195, the energy distribution of the surface acoustic wave due to the interdigital electrode 2 becomes rectangular, and the higher-order transverse modes other than the 0th-order transverse mode (fundamental wave) of the Fourier series expansion influence. This is because the above publication discloses a configuration for eliminating such an influence and reducing spurious.

That is, in Japanese Examined Patent Publication No. 7-28195, by adopting a configuration in which the cross width of the interdigital electrodes is symmetrically reduced from the center toward the reflectors on both sides, the fundamental frequency is centered. We have obtained a surface acoustic wave resonator with no spurious emission in a wide band.

[0006]

By the way, in the above-mentioned proposal, in order to symmetrically reduce the intersection width of the interdigital electrodes as it approaches the reflector, the outline of the specific intersection width is defined as one of the cosine curve. Good simulation results with less spurious are obtained by using the part (part of the tip part or part of the base end) or the entire cosine curve, but the contour of such cross width reduces spurious. It is speculated that the mechanism for causing this is because the propagation of energy of the 0th-order transverse mode (fundamental wave) is dominant, but it is not always clear, and the effect of reducing spurious is not yet sufficient. Also,
This proposal is effective when using the fundamental mode, but cannot be applied when using other higher modes.

The present invention has been made in view of the above circumstances, and can further improve the spurious reduction effect as compared with the above-mentioned proposal. Further, not only the fundamental wave mode but also any higher order mode. It is an object of the present invention to provide a surface acoustic wave resonator capable of suppressing spurious emission by suppressing the vibration of modes other than the used order by using the surface acoustic wave.

[0008]

DISCLOSURE OF THE INVENTION In the surface acoustic wave resonator of the present invention, the crossing width of the interdigital electrodes is such that the general transformation ratio Tr represented by the following equation with respect to the order of interest (order to be used) becomes maximum. Characterized by being apodized according to F (x).

[0009]

[Equation 2]

Further, in the surface acoustic wave resonator of the present invention, the weighting function for apodization of the intersection width of the interdigital electrodes is replaced by the function F (x), and the function F
In order to emphasize the frequency component relating to the order of interest in the spectrum obtained by Fourier transforming (x), a function obtained by multiplying the Fourier transform result by a predetermined window function and then performing an inverse Fourier transform may be used. it can.

According to the present invention, the wave equation is solved to clarify the vibration distribution in each order in the waveguide, and then the conversion efficiency (transformation ratio T
Maximizing r) is the result of finding relatively small vibrational energies of other modes.

That is, the excitation energy by the interdigital electrodes on the piezoelectric substrate is uniquely determined by the weighting method of the intersection width of the interdigital electrodes (represented by the weight function F (x)). By making (x) a function that maximizes the conversion efficiency of the mode of interest into vibration, the vibration energy of the modes of other orders is relatively reduced, and the spurious reduction effect is further increased. It becomes possible to

The general transformation ratio T represented by the above-mentioned equation (1)
In the symmetrical mode, r is the excitation energy distribution expressed by F (x) and the vibration distribution ψ (x) of the specific mode of the surface acoustic wave in the waveguide, which is caused by the excitation energy distribution. It represents the efficiency converted into the vibration of the specific mode. Therefore, ψ (x) in equation (1) is used as the vibration distribution of the mode of interest, and this equation (1) is calculated,
By obtaining F (x) that maximizes Tr and giving a weight represented by F (x) to the cross width of the interdigital electrodes, the vibration energy of the mode of the focused order in the waveguide is It is possible to make the situation in which the propagation is dominant and the vibration of other modes is relatively suppressed.

Here, ψ (x) of the focused order mode in the equation (1) is obtained by using, for example, the wave equation represented by the following equation (2) as a waveguide formed by interdigital electrodes and a reflector. It can be obtained by setting and solving a boundary condition that displacement and stress are continuous at the boundary portion of the outer region, the waveguide is in a propagation state, and the outer region is in a damping state.

[0015]

(Equation 3)

Here, ψ _S and v _S are the potential and the sound velocity in the region where the sound velocity is slow (in the waveguide), and ψ _f and v _f are the potential and the sound velocity in the region where the sound velocity is fast. Further, z represents the waveguide direction of the waveguide (direction connecting the two reflectors), and ω is the angular velocity at the resonance frequency.

The boundary conditions described above are

[0018]

(Equation 4)

And the propagating wave is

[0020]

(Equation 5)

Given by where

[0022]

(Equation 6)

Where v is the velocity of the surface acoustic wave of a specific order mode in the waveguide. By solving the wave equation based on the above conditions, the velocity dispersion curve represented by the following equation can be obtained.

[0024]

(Equation 7)

In the equation (9), a is the width of the waveguide, and if this a is determined and vf and vs are determined based on the piezoelectric substrate or the like used, then in the waveguide having the width a. The velocity v of the surface acoustic wave in each of the modes can be obtained.

From the equation (5), the vibration distribution of the surface acoustic wave in the waveguide can be expressed by the general equation.

[0027]

(Equation 8)

By substituting the velocity v of the surface acoustic wave of the mode of interest into this equation (10), the vibration distribution of the mode of that order, that is, ψ (x ) Can be asked.

In equation (1), when ψ (x) that maximizes the transformation ratio Tr relating to the vibration of the mode of interest is obtained,

[0030]

[Equation 9]

## EQU1 ## Therefore, the wave equation is solved using each of the boundary conditions described above, and vf and vs are determined based on the material of the piezoelectric substrate to obtain the velocity dispersion curve of each mode of the order and the waveguide width a Is determined, the velocity v of the mode of interest is calculated to obtain ψ (x), and ψ (x) is calculated.
The range of x = -a / 2 to + a / 2 of the curve of (x) is defined as the weighting function F (x). And such a weighting function F
If the cross width of the interdigital electrodes is apodized by (x), a surface acoustic wave resonator in which the propagation of vibrations of the mode of interest is dominant and the propagation of vibrations of other orders is suppressed can be obtained.

The cross width of the interdigital electrodes is F
As a specific example of apodizing using (x), the center of the waveguide in the waveguiding direction (z direction) is z = 0, and the cross width of the interdigital electrodes is F (x) on both sides of the positive and negative sides. A method of applying an apotize can be mentioned. In that case, the weighting function F (x) corresponding to the range of −a / 2 ≦ x ≧ + a / 2 of ψ (x) is k _xS · x in the function ψ (x) when the fundamental mode is taken as an example. However, they do not reach ± π / 2 at x = ± a / 2, that is, −π / 2 <−k _xs · a / 2 k _xS · a / 2 <π / 2. On both sides of the center of the surface acoustic wave propagating direction (z direction), regions having the maximum crossing length of the electrode fingers are formed with a predetermined spread. When the length of the region from the center in the z direction to one side is represented by Pc, when the total length from the center in the z direction to the one side of the interdigital electrode is 1,

[0033]

(Equation 10)

It should be noted that the specific method of apodizing the intersection width of the interdigital electrodes by the function F (x) is not limited to the apodization to both sides as described above, and the point is that it is excited by the interdigital electrodes. It suffices if the method of apodization is such that the order vibration distribution is F (x).

The above-mentioned ψ (x) is an example calculated using the boundary condition represented by the above equation (3), and the region where the sound velocity is slow and the region where the sound velocity is fast are appropriately distributed. If so, the boundary condition is calculated accordingly. No matter what boundary condition is used to calculate ψ (x), when ψ (x) is applied to equation (1) and F (x) that maximizes Tr is obtained, F (x By matching) with ψ (x), the intended purpose can be achieved.

By the way, the weighting function F (x) for maximizing the transformation ratio Tr for the focused order mode thus obtained maximizes the conversion efficiency of the excitation energy into the vibration of the focused order mode. This suppresses the propagation of vibrations of other modes. However, in the invention according to claim 2, the excitation energy distribution based on the weighting function F (x) is further focused after the Fourier transform. The influence of frequencies other than the frequency is reduced, and the vibration distribution itself of the other mode, which is an extra frequency component, is suppressed.

That is, in the vibration spectrum obtained by Fourier transforming the excitation energy distribution represented by the weighting function F (x), the frequency component of the mode of the focused order is dominant, but of other orders. There are some frequency components. Therefore, in order to emphasize the focused order mode and relatively reduce the frequency components of other orders, the Fourier transform result is multiplied by a predetermined window function to emphasize the necessary frequency component, and then the inverse Fourier transform is performed. The vibration distribution of the extra frequency component itself is suppressed as a whole, the attenuation amount of the vibration of the other order mode is increased with respect to the vibration of the mode of the focused order, and as a result, spurious can be reduced. Although this process may reduce the conversion efficiency of the vibration of the order mode of interest, comparing the degree of reduction and the degree of damping of the vibration of the other mode, the damping effect of the vibration of the other mode If it is larger, the effect of reducing spurious is increased.

Here, the window function used in the present invention is
There is no particular limitation as long as frequency components other than the order of interest can be suppressed, but specific examples include known window functions such as Hamming functions, Hanning functions, Bartlett functions, and square wave window functions. Or can be windowed by any other function that can achieve the above objectives.

[0039]

BEST MODE FOR CARRYING OUT THE INVENTION A surface acoustic wave resonator to which the present invention is applied will be specifically described below. FIG. 1 is a plan view of an embodiment of the present invention.

In this example, quartz is used as the piezoelectric substrate, and the interdigital electrode 2 and the grating reflectors 31 and 32 each made of an Al thin film are formed on the surface thereof.

In this example, the mode of the focused order is the fundamental wave mode, and the transformation ratio Tr of the fundamental wave mode is
The crossing width of the interdigital electrode 2 is symmetrically apodized toward both the reflectors 31 and 32 on both sides by the weighting function F (x) that maximizes. That is, the outer shape of the cross width of the interdigital electrode 2 is defined by the reflectors 31 on both sides.
Both of the 32 sides have the shape represented by the function F (x). Further, in this example, a dummy electrode 4 that does not contribute to the excitation is provided at a position other than the intersection of the electrode fingers so as to prevent the disturbance of the phase of the surface acoustic wave.

The weighting function F (x) used in this example
Was calculated based on the following conditions. The width and pitch of the electrode fingers of the comb-shaped electrodes 2a and 2b of the interdigital electrode 2 were 2.78 μm and 11.14 μm, respectively, and the design resonance frequency was set to 280 MHz. Also,
The width and pitch of each strip of the grating reflectors 31 and 32 are also 2.78 μm and 1 respectively.
It is 1.14 μm. Further, the film thickness of the interdigital electrode 2 is 3000 Å, and the width a of the waveguide is a = 334.2 μm.
And This is 3 of the wavelength λ of the surface acoustic wave in the waveguide.
It corresponds to 0 times.

From the above, the angular velocity ω = at the resonance frequency
1.759 × 10 ⁹ rad / s, v _f = 3148.8 m
/ S, v _S = 3118.5 m / s, the velocity dispersion curve is obtained, and the fundamental wave mode propagation velocity v = 3118.9 m / s
I got

Ψ (x) is calculated from these specific numerical values,

[0045]

[Equation 11]

Was obtained. The graph of the function F (x) is as shown in FIG. 2, and the cross width of the interdigital electrodes 2 of the resonator shown in FIG. 1 is directed toward the reflectors 31 and 32 on both sides thereof. It has been apoted to the shape represented by the graph in 2.

The frequency characteristics in the above embodiment are
As shown in FIG. Further, FIG. 4 shows the frequency characteristics of a normal type in which the intersection width of the interdigital electrodes is not apodized, assuming that other conditions are the same as those in the above-described embodiment, and FIG. As a substitute for the above weighting function F (x), apodization is performed according to a simple cosine curve with a crossing length of 0 at both ends in the width direction of the waveguide, that is,

[0048]

(Equation 12)

The frequency characteristic of the crossing width of the interdigital electrodes apodized to both sides by the weighting function F (x) represented by 3 to 5, the horizontal axis represents the normalized frequency (F / F ₀₀ ). When standardizing, the speed of sound in the crystal in the absence of metal V
₀ and the interdigital electrode period is λ,
A value obtained by dividing the actual frequency F by F ₀₀ = V ₀ / λ was used.

As is clear from FIGS. 3 to 5, it was confirmed that the effect of reducing spurious emission according to the embodiment of the present invention is extremely large. Further, [Table 1] shows the attenuation rates of the second to fifth modes (S1 to S5) with respect to the fundamental mode (S1), which is the focused order mode, for the embodiment of the present invention and the two comparative examples. That is, the attenuation rate of the non-focused order is shown. It should be noted that the sixth and higher order modes do not appear in the relationship a / λ = 30 between the width a of the waveguide and the wavelength λ.

[0051]

[Table 1]

As is apparent from [Table 1], in the embodiment of the present invention, the attenuation factors of all higher-order modes with respect to the fundamental wave mode are significantly improved as compared with each comparative example. I was confirmed.

Further, in the above-described embodiment of the present invention, the width a of the waveguide is variously changed to calculate the transformation ratio Tr of each of the fundamental mode S1 and the higher modes S2 to S6, which are the orders of interest. The graph plotted in FIG. 6 is shown in FIG. 6, and the results of the same calculation for each of the comparative examples weighted according to the normal type and the simple cosine curve described above are shown in FIGS. 7 and 8, respectively. In each graph, the horizontal axis is a value obtained by dividing the width a of the waveguide by the wavelength λ.

As is apparent from FIGS. 6 to 8,
In the embodiment of the present invention, even if the waveguide a is widened to reduce the impedance, the ratios of the transformation ratios of all non-focused orders to the transformation ratios of the focused order are always small in comparison with the comparative examples. It was confirmed that the damping ratio of the higher modes was high.

Furthermore, the width a of the waveguide is 10λ, 20
9 and 12 show the frequency characteristics when the cross widths of the interdigital electrodes are apodized with F (x) = ψ (x) of the present invention, where λ, 40λ, and 50λ. Further, as comparative examples, FIGS. 13 to 16 show the frequency characteristics of the normal type in which a is 10λ, 20λ, 40λ and 50λ.
Similarly, a is 10λ, 20λ, 40λ and 50λ.
Then, the intersection width of the interdigital electrodes is set to the above (12).
The frequency characteristics of the apodized simple cosine curve expressed by the formula are shown in FIGS.

As is clear from each of these figures, no matter how the width a of the waveguide is changed, the apodized resonator according to the present invention is compared with the resonator of each comparative example. It was confirmed that spurious was improved.

Next, another embodiment of the present invention will be described. In the above embodiment, the crossing width of the interdigital electrodes is weighted by using the weighting function F (x) = ψ (x) that maximizes the general transformation ratio Tr related to the order of interest. In this example, the weighting function F (x) is Fourier-transformed to obtain a frequency spectrum, and a predetermined frequency is specified for the spectrum in order to emphasize the frequency component of the mode of the focused order in the spectrum. After the window function is multiplied, an inverse digital transform function is used to apotize the cross width of the interdigital electrodes.

A specific calculation example will be described below. In this example, the condition is exactly the same as in the previous example except that the width a of the waveguide is 28 times the wavelength λ, and ψ (x) (= F
After obtaining (x), Fourier transform was performed by FFT to obtain a frequency spectrum as shown in FIG. This FIG.
Shows the data number related to frequency on the horizontal axis, the power density on the vertical axis, and the convex portion at the center of the curve indicates the position of the frequency component of the fundamental wave mode of the focused order.

Next, with respect to the curve of FIG.

[0060]

(Equation 13)

By multiplying by the window function represented by, as shown in FIG. 22, a spectrum curve in which most frequency components relating to orders other than the target order are removed is obtained. Then, the curve thus obtained is subjected to inverse Fourier transform. The curve W (x) obtained as a result contains almost no extra frequency component contained in F (x) = ψ (x).
The curve W (x) is shown graphically in FIG. In FIG. 23, the graph of F (x) = ψ (x) is also shown by a broken line, and it is clear that the shapes are different especially at both ends of the waveguide.

Using the curve W (x) obtained by Fourier transform-windowing-inverse Fourier transform of such ψ (x) as a weighting function, the cross width of the interdigital electrodes is set to the reflector side on both sides thereof. For the surface acoustic wave resonator apodized towards, the second- to fourth-order attenuation factors for the fundamental mode are
Table 2 shows the surface acoustic wave resonator apotized by the weighting function of (x) = ψ (x). When the width a of the waveguide is 28λ, higher-order modes of S5 and above do not appear.

[0063]

[Table 2]

As is clear from this [Table 2], W (x)
It was confirmed that the resonator apodized in [4] is improved in the attenuation rate of all higher-order modes of S2 to S4 as compared with the resonator apodized by [psi] (x).

The window function is not limited to the equation (13), and any known window function such as the Hamming function or the Hanning function can be used as long as it can emphasize the frequency component of the focused order. Things can be used.

[0066]

According to the present invention, for a surface acoustic wave of an arbitrary focused order, the cross width of the interdigital electrodes is apodized so that the conversion efficiency into the vibration mode is maximized. It is possible to relatively reduce the vibrational energy of the mode, thereby increasing the attenuation rate of the vibration of the other modes with respect to the focused order mode as much as possible, and to obtain the surface acoustic wave resonator with less spurious.

Further, the Fourier transform result of the weighting function that maximizes the conversion efficiency into the vibration mode of the focused order is multiplied by the window function that emphasizes the required frequency component and removes other frequency components. Then, if the crossing width of the interdigital electrodes is apodized by a weighting function obtained by inverse Fourier transform, it is possible to further increase and reduce spurious.

[Brief description of drawings]

FIG. 1 is a schematic plan view of an embodiment of the present invention.

FIG. 2 is a graph showing an apodization curve according to the embodiment shown in FIG.

FIG. 3 is a graph showing frequency characteristics according to the embodiment of the present invention.

FIG. 4 is a graph showing an example of frequency characteristics of a conventional surface acoustic wave resonator having a normal type IDT.

FIG. 5 is a graph showing an example of frequency characteristics of a surface acoustic wave resonator having an IDT in which a weighting function for apodization is a simple cosine function.

FIG. 6 is a graph showing the width of the waveguide and the transformation ratios of the fundamental mode S1 and the higher-order modes SS2 to S6 in the embodiment of the present invention.

FIG. 7 shows a width of a waveguide in a surface acoustic wave resonator having a normal type IDT, and a fundamental wave mode S1 and a higher mode S.
The graph which shows each metamorphic ratio of S2-S6

FIG. 8 is an IDT in which the apodization curve is a simple cosine curve.
A graph showing the width of the waveguide in the surface acoustic wave resonator with and the respective metamorphic ratios of the fundamental wave mode S1 and the higher-order modes SS2 to S6.

FIG. 9 is a graph showing the frequency characteristics of the apodized resonator of the present invention with the waveguide width of 10λ.

FIG. 10 is a graph showing the frequency characteristic of the apodized resonator of the present invention with the waveguide width of 20λ.

FIG. 11 is a graph showing frequency characteristics of the apodized resonator of the present invention with the waveguide width of 40λ.

FIG. 12 is a graph showing the frequency characteristics of the apodized resonator of the present invention with the waveguide width of 50λ.

FIG. 13 is a graph showing frequency characteristics of a normal type resonator with a waveguide width of 10λ.

FIG. 14 is a graph showing frequency characteristics of a normal type resonator with a waveguide width of 20λ.

FIG. 15 is a graph showing frequency characteristics of a normal type resonator with a waveguide width of 40λ.

FIG. 16 is a graph showing frequency characteristics of a normal type resonator with a waveguide width of 50λ.

FIG. 17 is a graph showing frequency characteristics of a resonator apodized according to a simple cosine curve with a waveguide width of 10λ.

FIG. 18 is a graph showing the frequency characteristic of a resonator apotized according to a simple cosine curve with the waveguide width of 20λ.

FIG. 19 is a graph showing a frequency characteristic of a resonator apodized according to a simple cosine curve with a waveguide width of 40λ.

FIG. 20 is a graph showing frequency characteristics of a resonator apodized according to a simple cosine curve with a waveguide width of 50λ.

FIG. 21 is a graph showing the result of Fourier transform of ψ (x) as one procedure for obtaining a weighting function for apodization according to another embodiment of the present invention.

FIG. 22 is a graph showing a curve obtained by multiplying the curve of FIG. 9 by a window function as one procedure for obtaining the weighting function of another embodiment of the present invention.

23 is a graph showing a weighting curve W (x) for apodizing according to another embodiment of the present invention, which is obtained by performing an inverse Fourier transform on the curve in FIG.

FIG. 24 is a plan view of a conventional surface acoustic wave resonator having a normal type IDT.

[Explanation of symbols]

 1 piezoelectric substrate 2 interdigital electrodes 2a, 2b comb-shaped electrodes 31, 32 grating reflector

Claims (2)

[Claims] 1. An interdigital electrode for converting an electric signal into a surface acoustic wave on the surface of a piezoelectric substrate, and reflection for reflecting surface acoustic waves excited by the interdigital electrode on both sides of the interdigital electrode. In a surface acoustic wave resonator formed by forming a container, the crossing width of the interdigital electrodes is a weighting function F (x) that maximizes the general transformation ratio Tr represented by the following equation for the order of interest.
A surface acoustic wave resonator characterized in that it is apodized according to. [Equation 1] 2. The weight function for apodization of the intersection width of the interdigital electrodes is replaced by the function F (x), and the order of interest in a spectrum obtained by Fourier transform of the function F (x) is related to To emphasize the frequency component,
A surface acoustic wave resonator, characterized in that the Fourier transform result is multiplied by a predetermined window function and then the inverse Fourier transform is performed.