JP3119579B2 - Surface acoustic wave resonator - Google Patents

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 having an interdigital electrode for surface acoustic wave excitation and two reflectors formed on a surface of a piezoelectric substrate.

[0002]

2. Description of the Related Art As shown in FIG. 24, a surface acoustic wave resonator generally has an interdigital electrode 2 formed on a surface of a substrate 1 made of a piezoelectric material such as quartz or piezoelectric ceramic, and has on both sides thereof. Grating reflector 31,
32 is formed. Interdigital electrode 2
Is a pair of comb-shaped electrodes 2 each having a plurality of electrode fingers.
Reference numerals a and 2b denote converters having a structure in which the respective electrode fingers are opposed to each other with the electrode fingers crossing each other, and for converting an electric signal into a surface acoustic wave. Each of the grating reflectors 31 and 32 has a structure in which a large number of strips are periodically arranged at a pitch of 弾 性 of the surface acoustic wave wavelength, and the surface acoustic waves excited by the interdigital electrode 2 and propagated on both sides thereof. Is formed repeatedly to form a standing wave.

In the above-described surface acoustic wave resonator, as shown in the example of FIG. 24, the cross width of the interdigital electrode 2, that is, the cross length of each pair of electrode fingers of the pair of comb-shaped electrodes 2a and 2b. In the case where it is constant in the propagation direction of the surface acoustic wave (the direction connecting the two reflectors 31 and 32) (referred to as a normal type), when the intersection 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.

[0004] The cause of such spurious is as follows.
As described in JP-B-7-28195, the energy distribution of the surface acoustic wave by the interdigital electrode 2 becomes rectangular, and higher-order transverse modes other than the zero-order transverse mode (fundamental wave) of the Fourier series expansion affect the distribution. For this reason, the above publication discloses a configuration for eliminating such an effect and reducing spurious.

[0005] That is, Japanese Patent Publication No. 7-28195 discloses a configuration in which the cross width of an interdigital electrode is reduced symmetrically from the center of the interdigital electrode toward the reflectors on both sides. A surface acoustic wave resonator free from spurious components is obtained in a wide band.

[0006]

In the above-mentioned proposal, however, a specific cross-section outer shape for reducing the cross-width of the interdigital electrode symmetrically as approaching the reflector is defined by a cosine curve. Good simulation results with less spurs are obtained by using the part (part of the tip or part of the base) or the entire cosine curve. Although it has been speculated that the mechanism for causing the transmission of energy in the 0th-order transverse mode (fundamental wave) becomes dominant, the mechanism 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-order modes.

The present invention has been made in view of such circumstances, and can further improve the spurious reduction effect as compared with the above-mentioned proposals. It is an object of the present invention to provide a surface acoustic wave resonator capable of suppressing spurious vibrations in modes other than the use order by using surface acoustic waves.

[0008]

DISCLOSURE OF THE INVENTION The surface acoustic wave resonator according to the present invention has a cross function of an interdigital electrode whose weight is such that the general transformation ratio Tr represented by the following equation is maximized with respect to the order of interest (the order to be used). It is characterized by being apodized according to F (x).

[0009]

(Equation 2)

[0010]

The present invention solves the wave equation to clarify the vibration distribution in each order in the waveguide, and then converts the conversion efficiency into the vibration of any order of interest (transformation ratio T
Maximizing r) is a result of finding that the vibration energy of other modes is relatively reduced.

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

The general metamorphic ratio T expressed by the above equation (1)
r is, in the symmetric mode, using the excitation energy distribution represented by F (x) and the vibration distribution 振動 (x) of the specific mode of the surface acoustic wave in the waveguide caused by the excitation energy distribution. It indicates the efficiency of conversion into the vibration of the specific mode. Therefore, ψ (x) in the equation (1) is calculated as the vibration distribution of the mode of the order of interest, and the equation (1) is calculated.
By obtaining F (x) that maximizes Tr and assigning a weight represented by F (x) to the intersection width of the interdigital electrode, the vibration energy of the mode of the order of interest in the waveguide is obtained. Propagation can be dominant, and a situation can be achieved in which vibrations of other modes are relatively suppressed.

Here, 着 目 (x) of the order mode of interest in the equation (1) is obtained by, for example, converting the wave equation represented by the following equation (2) to the waveguide formed by the interdigital electrode and the 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 propagation state is in the waveguide, and the outer region is in the attenuated state.

[0015]

(Equation 3)

Here, ψ _S and v _S are the potential and the sound velocity in a region where the sound speed is low (in the waveguide), and ψ _f and v _f are the potential and the sound speed in the region where the sound speed is high. Z represents the waveguide direction of the waveguide (the direction connecting the two reflectors), and ω is the angular velocity at the resonance frequency.

The above boundary condition is

[0018]

(Equation 4)

And the propagating wave is

[0020]

(Equation 5)

Where: where

[0022]

(Equation 6)

And v is the velocity of the surface acoustic wave of the mode of a specific order in the waveguide. By solving the wave equation based on the above conditions, a 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 determined based on the piezoelectric substrate to be used are determined, the width of the waveguide having the width a is obtained. , The velocity v of the surface acoustic wave in each order mode can be obtained.

From the above equation (5), the vibration distribution of the surface acoustic wave in the waveguide is represented by a general equation.

[0027]

(Equation 8)

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

In equation (1), when 変 (x) at which the transformation ratio Tr regarding the vibration of the mode of the order of interest is maximized is obtained,

[0030]

(Equation 9)

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

Note that the intersection width of the interdigital electrodes is F
As a specific example of apotizing using (x), the center in the waveguide direction (z direction) of the waveguide is set to z = 0, and on both the positive and negative sides, the intersection width of the interdigital electrode is represented by F (x). And a method of performing apotizing by using 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), taking the fundamental mode as an example. but, x = ± a / 2 but did not make it into the respective ± [pi / 2 in, that is, to become a _{-π / 2 <-k xs · a} / 2 k xS · a / 2 <π / 2, interdigital electrodes On both sides of the center in the surface acoustic wave propagation direction (z direction) of FIG. When the length of the region from the center in the z direction to one side from the center in the z direction is represented by Pc, when the total length of the interdigital electrode from the center in the z direction to one side is 1,

[0033]

(Equation 10)

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

The above-mentioned ψ (x) is an example calculated using the boundary condition expressed by the above equation (3), and the region where the sound speed is low and the region where the sound speed is high are appropriately distributed in the waveguide. In such a case, the calculation is performed using the boundary condition corresponding to that. Whatever boundary condition is used to calculate ψ (x), when ψ (x) is applied to equation (1) to find F (x) that maximizes Tr, F (x) By matching) with ψ (x), the intended purpose can be achieved.

By the way, the weighting function F (x) which is obtained in this way and maximizes the transformation ratio Tr with respect to the order mode of interest maximizes the conversion efficiency of the excitation energy into the vibration of the mode of the order of interest. is intended, whereby it is intended to suppress the propagation of the vibration of the other order mode, the
In the present invention, the influence of frequencies other than the frequency of interest after the Fourier transform of the excitation energy distribution based on the weighting function F (x) is reduced, and the vibration distribution itself of other modes, which are extra frequency components, 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 interest is dominant, but the frequency components of the other orders are dominant. There are also some frequency components. Therefore, in order to emphasize the order mode of interest and relatively reduce the frequency components of other orders, the required frequency components are enhanced by multiplying the Fourier transform result by a predetermined window function, and then the inverse Fourier transform is performed. The vibration distribution of the extra frequency component itself is suppressed as a whole, and the attenuation of the vibration of the other mode with respect to the vibration of the mode of the order of interest increases, and as a result, the spurious can be reduced. Note that this process may reduce the conversion efficiency of the vibration of the order mode of interest, but in comparing the degree of the decrease with the degree of attenuation of the vibration of the other mode, the effect of damping the vibration of the other mode is reduced. If it is larger, the spurious reduction effect increases.

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. Specific examples include well-known window functions such as a Hamming function, a Hanning function, a Bartlett function, and a function of a square wave window. Alternatively, they can be windowed by any function that can achieve the above objectives.

[0039]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 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 electrodes 2 made of an Al thin film and the grating reflectors 31 and 32 are formed on the surface thereof.

In this example, the mode of the order of interest is the fundamental mode, and the transformation ratio Tr of the fundamental mode is set.
Is apodized symmetrically toward both of the reflectors 31 and 32 on both sides by the weight function F (x) that maximizes. That is, the outer shape of the intersection width of the interdigital electrode 2 is determined by the reflectors 31 on both sides,
Both sides have a shape represented by a function F (x). In this example, a dummy electrode 4 that does not contribute to the excitation is provided at a portion other than the intersection of the electrode fingers in order to prevent 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 each of the interdigital electrodes 2a and 2b of the interdigital electrode 2 were set to 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.
1.14 μm. Further, the film thickness of the interdigital electrode 2 is 3000 °, and the width a of the waveguide is 334.2 μm.
And This is equivalent to 3 of the wavelength λ of the surface acoustic wave in the waveguide.
It corresponds to 0 times.

As described 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, a velocity dispersion curve is determined, and the fundamental mode propagation velocity v = 318.9 m / s
I got

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

[0045]

[Equation 11]

Was obtained. FIG. 2 shows the function F (x) as a graph. The intersection width of the interdigital electrode 2 of the resonator shown in FIG. 1 is shifted toward the reflectors 31 and 32 on both sides thereof. That is, it is apotized to the shape represented by the graph of FIG.

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

[0048]

(Equation 12)

The frequency characteristics of the inter-digital electrode intersection widths apodized on both sides by the weight function F (x) expressed by In FIGS. 3 to 5, the horizontal axis represents the normalized frequency (F / F ₀₀ ). When standardizing, the sound velocity in the crystal where no metal exists is V
₀ and the period of the interdigital electrode is λ,
The value obtained by dividing the actual frequency F by F ₀₀ = V ₀ / λ was used.

[0050] As can be seen from the FIGS. 3 to 5, this
It was confirmed that the spurious reduction effect by the form was extremely large. Table 1 shows that the second to fifth-order modes (S1) with respect to the fundamental mode (S1), which is the order mode of interest, for the embodiment of the present invention and the above two comparative examples.
1 to S5), that is, the non-order of interest. The higher-order mode of the sixth or higher order does 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, this form
In the state , it was confirmed that the attenuation rates of all higher-order modes with respect to the fundamental mode were significantly improved for each comparative example.

[0053] Further, in the above shape state, the width a of the waveguide
FIG. 6 is a graph in which the transformation ratio Tr of each of the fundamental mode S1 and the higher-order modes S2 to S6, which are the order of interest, is calculated and plotted. 7 and 8 show the results of performing the same calculation for each of the comparative examples weighted according to. 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 this embodiment , even if the impedance is reduced by widening the waveguide a, the ratio of the transformation ratio of all non-orders of interest to the transformation ratio of the order of interest is always small in comparison with each comparative example. It was confirmed that the decay rate was high.

Further, the width a of the waveguide is set to 10λ, 20
λ, 40λ, and 50λ, and the frequency characteristics when the intersection width of the interdigital electrodes is apodized by F (x) = ψ (x) of the present invention are shown in FIGS. 9 to 12, respectively. As a comparative example, the frequency characteristics of the normal type in which a is 10λ, 20λ, 40λ, and 50λ are shown in FIGS.
Where a is also 10λ, 20λ, 40λ and 50λ
Then, the intersection width of the interdigital electrode is set to
FIGS. 17 to 20 show the frequency characteristics of those apotized by a simple cosine curve represented by the equation.

As can be seen from these figures, the resonator apotized according to the present embodiment has a larger thickness than the resonator of each comparative example regardless of how the width a of the waveguide is changed. It was confirmed that spurious was improved.

Next, an embodiment according to the present invention will be described. In the previous shape state, the weighting of the cross width of the interdigital electrode, the crossing width of the interdigital electrodes with a general transformation ratio Tr is maximum F (x) = ψ (x ) becomes the weighting function for the interest order However, in the present invention , the weighting function F (x) is Fourier-transformed to obtain a frequency spectrum, and the spectrum is emphasized in the spectrum to emphasize the frequency component of the mode of interest. Is multiplied by a predetermined window function, and then the intersection width of the interdigital electrodes is apodized by a function obtained by inverse Fourier transform.

Hereinafter, a specific calculation example will be described. In this example, except that the width a of the waveguide was set to 28 times the wavelength λ, ψ (x) (= F
After (x)) was obtained, Fourier transform was performed by FFT to obtain a frequency spectrum as shown in FIG. This FIG.
In the graph, the horizontal axis indicates the data number relating to the frequency, the vertical axis indicates the power density, and the convex portion at the center of the curve indicates the position of the frequency component of the fundamental mode whose order is the order of interest.

Next, with respect to the curve of FIG.

[0060]

(Equation 13)

By multiplying by the window function expressed by the following equation, a spectrum curve from which frequency components related to orders other than the order of interest are almost removed is obtained as shown in FIG. Then, the resulting curve is subjected to inverse Fourier transform. The curve W (x) obtained in this way has almost no extra frequency components contained in F (x) = ψ (x).
FIG. 23 is a graph showing the curve W (x). In FIG. 23, the graph of F (x) = ψ (x) is also indicated by a broken line, and it is apparent that the shape is different particularly at both ends of the waveguide.

Using the curve W (x) obtained by performing the Fourier transform, windowing, and inverse Fourier transform of ψ (x) as a weight function, the intersection width of the interdigital electrode is set on the reflector side on both sides thereof. For the surface acoustic wave resonator apodized for the second direction, the second- to fourth-order attenuation rates for the fundamental mode are expressed by F
Table 2 shows the surface acoustic wave resonators apotized by the weight function of (x) = ψ (x). When the width a of the waveguide is set to 28λ, higher-order modes S5 and higher do not appear.

[0063]

[Table 2]

As is apparent from Table 2, W (x)
It was confirmed that the resonators apoptized in have improved attenuation rates of all higher-order modes S2 to S4 compared to the resonator apodized in ψ (x).

Note that the window function is not limited to the above-mentioned equation (13), and any window function such as the above-mentioned well-known window function such as the Hamming function or the Hanning function may be used as long as it can emphasize the frequency component of the order of interest. Things can be used.

[0066]

[0067]

According to the present invention, with respect to the Fourier transform result of the weighting function, such as conversion efficiency to focus order vibration mode is maximized, to remove other frequency components emphasized the required frequency component After applying a window function like this, the weighting function obtained by the inverse Fourier transform apodizes the intersection width of the interdigital electrodes, which results in a spurious response.
And a surface acoustic wave resonator having a small surface acoustic wave can be obtained.

[Brief description of the drawings]

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

FIG. 2 is a graph showing an apotize curve of the embodiment of FIG. 1;

3 is a graph showing a frequency characteristic of the embodiment

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 a frequency characteristic of a surface acoustic wave resonator having an IDT in which a weight function for apotizing is a simple cosine function;

Graph 6 and the width of the waveguide in the embodiment, each of the transformation ratio of the fundamental wave mode S1 and the higher order modes S2 to S6

FIG. 7 shows the width of the waveguide in the surface acoustic wave resonator having the normal type IDT, and the fundamental mode S1 and the higher order mode S.
Graph showing each metamorphic ratio of 2 to S6

FIG. 8 is an IDT in which an apotize curve is a simple cosine curve.
Is a graph showing the width of the waveguide in the surface acoustic wave resonator having the above, and the transformation ratios of the fundamental mode S1 and the higher modes S2 to S6.

FIG. 9 is a graph showing frequency characteristics of a resonator subjected to the apotization of the present invention with a waveguide having a width of 10λ.

Figure 10 is a graph of the width of the waveguide as a 20λ shows the frequency characteristic of the resonator which has been subjected to A Potaizu

Figure 11 is a graph of the width of the waveguide as a 40λ shows the frequency characteristic of the resonator which has been subjected to A Potaizu

Figure 12 is a graph of the width of the waveguide as a 50λ shows the frequency characteristic of the resonator which has been subjected to A Potaizu

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

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

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

FIG. 16 is a graph showing frequency characteristics of a normal type resonator having 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 having a width of 10λ.

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

FIG. 19 is a graph showing frequency characteristics of a resonator apodized according to a simple cosine curve with a waveguide having a 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 a result of Fourier transform of ψ (x) as one procedure for obtaining a weighting function for apodizing according to the 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 weight function according to the embodiment of the present invention;

23 is a graph showing a weighting curve W (x) for apodizing according to the embodiment of the present invention obtained by performing an inverse Fourier transform on the curve of FIG. 10;

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

[Explanation of symbols]

 Reference Signs List 1 piezoelectric substrate 2 interdigital electrode 2a, 2b comb-shaped electrode 31, 32 grating reflector

──────────────────────────────────────────────────続 き Continuation of the front page (56) References Japanese Patent Publication No. 7-28195 (JP, B2) IEICE Technical Report Vol. 263, p. 15-22 (US76-67), March 28, 1977 (58) Fields investigated (Int. Cl. ⁷ , DB name) H03H 9/25 H03H 9/145

Claims (1)

(57) [Claims] 1. An interdigital electrode for converting an electric signal into a surface acoustic wave on a surface of a piezoelectric substrate, and reflections on both sides of the interdigital electrode for reflecting surface acoustic waves excited by the interdigital electrode. Weighting function F (x) in which the intersection width of the interdigital electrode is the maximum in the general transformation ratio Tr represented by the following equation with respect to the order of interest in the surface acoustic wave resonator including the resonator
A surface acoustic wave resonator characterized by being apodized according to the following. (Equation 1)