Surface acoustic wave resonator, elastic wave filter, and multiplexer

Abstract

A surface acoustic wave resonator (1) has an IDT electrode and a reflector. The distance between electrode fingers Fe(k) and electrode fingers Fe(k+1) is defined as the kth electrode finger interval P(k). The difference between the electrode finger interval P(k) and the average of the electrode finger intervals P(k-1) and P(k+1) (the interval average electrode finger interval PM(k)) is divided by the overall average electrode finger interval PT, and the result is defined as the interval deviation rate D(k). The distribution obtained by calculating the interval deviation rate D(k) for all of the electrode fingers of the IDT electrode or the reflector is defined as a histogram of the interval deviation rate D(k). In this case, the standard deviation SD of the interval deviation rate D in the histogram is 0.2% or more in the IDT electrode or the reflector. This makes it possible to suppress the ripple generated on the higher frequency side than the anti-resonance frequency in the surface acoustic wave resonator.

Description

Technical Field

[0001] The present invention relates to a surface acoustic wave resonator, an elastic wave filter and a multiplexer. Background Art

[0002] Conventionally, a surface acoustic wave resonator is known that includes an interdigital transducer (IDT) electrode and a reflector positioned adjacent to the IDT electrode. The IDT electrode and the reflector each have multiple electrode fingers. Each of the multiple electrode fingers extends in a direction intersecting the direction of acoustic wave propagation and is arranged parallel to one another.

[0003] Patent Document 1 discloses a surface acoustic wave resonator having an IDT electrode with an electrode finger pitch that continuously varies in the direction of elastic wave propagation. The electrode finger pitch is the distance between the centers of two adjacent electrode fingers in the direction of elastic wave propagation. Patent Document 2 also discloses a surface acoustic wave resonator having an IDT electrode with an electrode finger pitch that continuously varies in the direction of elastic wave propagation. Patent Document 3 discloses a surface acoustic wave resonator comprising an IDT electrode having multiple regions in which the electrode finger pitch in the direction of elastic wave propagation is constant.

[0004] Prior art literature

[0005] Patent Literature

[0006] Patent Document 1: Japanese Patent Application Laid-Open No. 2018-182460

[0007] Patent Document 2: Japanese Patent Application Laid-Open No. 2013-85273

[0008] Patent Document 3: International Publication No. 2017 / 131170

[0009] Patent Document 4: International Publication No. 2021 / 010379

[0010] In the surface acoustic wave resonators disclosed in Patent Documents 1, 2, and 3, the reflection coefficient for frequencies higher than the antiresonance frequency of the surface acoustic wave resonator, that is, frequencies above a predetermined value, may decrease, and ripples may occur at frequencies higher than the antiresonance frequency.

[0011] Patent Document 4 discloses an elastic wave filter comprising a longitudinally coupled resonator containing multiple IDT electrodes. The technology disclosed in this document improves the attenuation characteristics of the elastic wave filter. However, this document does not disclose how to suppress the aforementioned ripple when the resonator comprises a single IDT electrode. Summary of the Invention

[0012] Problems to be solved by the invention

[0013] An object of the present invention is to provide a surface acoustic wave resonator or the like capable of suppressing ripples generated at a higher frequency than an antiresonance frequency when an IDT electrode included in the surface acoustic wave resonator is composed of a single IDT electrode.

[0014] Technical solutions to solve problems

[0015] In order to achieve the above-mentioned object, one embodiment of the present invention relates to a surface acoustic wave resonator comprising: a substrate having piezoelectricity; an IDT electrode provided on the substrate; and a reflector arranged adjacent to the IDT electrode in the direction of propagation of an elastic wave, wherein in the surface acoustic wave resonator, the IDT electrode included in the surface acoustic wave resonator is composed of a single IDT electrode, the IDT electrode and the reflector each having a plurality of electrode fingers extending in a direction intersecting the direction of propagation of the elastic wave and arranged parallel to each other, (1) a distance between a kth (k is an integer greater than or equal to 2)th electrode finger and a (k+1)th electrode finger in the direction of propagation of the elastic wave is defined as a kth electrode finger pitch, and (2) among three adjacent electrode fingers, namely, the (k-1)th electrode finger, the kth electrode finger, and the (k+1)th electrode finger, the kth electrode finger pitch is defined as a distance between the kth electrode finger pitch and the (k-1)th electrode finger. The value of the difference of the interval average electrode finger spacing divided by the overall average electrode finger spacing is defined as the spacing deviation rate of the kth electrode finger, wherein the interval average electrode finger spacing is the average of the (k-1)th electrode finger spacing and the (k+1)th electrode finger spacing, and the overall average electrode finger spacing is the average spacing of the entire electrode fingers of the IDT electrode or the reflector including the three adjacent electrode fingers, (3) the distribution of the spacing deviation rate obtained by calculating the spacing deviation rate of the kth electrode finger for all electrode fingers of the IDT electrode or the reflector including the three adjacent electrode fingers is defined as a histogram of the spacing deviation rate, in this case, in at least one of the IDT electrode and the reflector, the standard deviation of the spacing deviation rate in the histogram is greater than 0.2%.

[0016] In order to achieve the above-mentioned object, one embodiment of the present invention relates to a surface acoustic wave resonator comprising: a substrate having piezoelectricity; and an IDT electrode arranged on the substrate, wherein in the surface acoustic wave resonator, the IDT electrode included in the surface acoustic wave resonator is composed of a single IDT electrode, and the IDT electrode has a plurality of electrode fingers extending in a direction intersecting the direction of propagation of an elastic wave and arranged parallel to each other, (1) a distance between a kth (k is an integer greater than or equal to 2)th electrode finger and a (k+1)th electrode finger in the direction of propagation of the elastic wave is defined as a kth electrode finger pitch, and (2) among three adjacent electrode fingers, namely, the (k-1)th electrode finger, the kth electrode finger, and the (k+1)th electrode finger, the kth electrode finger pitch is aligned with the interval The value of the difference in average electrode finger spacing divided by the overall average electrode finger spacing is defined as the spacing deviation rate of the kth electrode finger, wherein the interval average electrode finger spacing is the average of the (k-1)th electrode finger spacing and the (k+1)th electrode finger spacing, and the overall average electrode finger spacing is the average spacing of the entire electrode fingers of the IDT electrode including the three adjacent electrode fingers. (3) The distribution of the spacing deviation rate obtained by calculating the spacing deviation rate of the kth electrode finger for all electrode fingers of the IDT electrode including the three adjacent electrode fingers is defined as a histogram of the spacing deviation rate. In this case, in the IDT electrode, the standard deviation of the spacing deviation rate in the histogram is greater than 0.2%.

[0017] To achieve the above object, an elastic wave filter according to one embodiment of the present invention includes the above-mentioned surface acoustic wave resonator.

[0018] To achieve the above object, a multiplexer according to one embodiment of the present invention includes a transmission filter and a reception filter, wherein the transmission filter includes the above-mentioned elastic wave filter.

[0019] Effects of the Invention

[0020] According to the present invention, it is possible to suppress ripples generated at a higher frequency side than the antiresonance frequency of a surface acoustic wave resonator. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 1 is a diagram schematically showing an IDT electrode of a surface acoustic wave resonator of Comparative Example 1.

[0022] Figure 2 This is a diagram schematically showing an IDT electrode of a surface acoustic wave resonator of Comparative Example 2.

[0023] Figure 3 This is a diagram schematically showing an IDT electrode of a surface acoustic wave resonator according to an embodiment.

[0024] Figure 4 It is a circuit configuration diagram of an elastic wave filter according to an embodiment.

[0025] Figure 5 It is a schematic plan view showing an electrode structure of a surface acoustic wave resonator according to an embodiment.

[0026] Figure 6 This is a graph showing the distribution of electrode finger pitches in a surface acoustic wave resonator.

[0027] Figure 7 This is a diagram for explaining the definitions of the section-average electrode finger pitch, the overall average electrode finger pitch, and the pitch deviation rate of a surface acoustic wave resonator.

[0028] Figure 8 This is a diagram illustrating the pitch deviation rate and its standard deviation in the irregular electrode finger pitch distribution of a surface acoustic wave resonator.

[0029] Figure 9 Graphs showing the insertion losses of the surface acoustic wave resonators in Comparative Example 3 and Examples 1, 2, and 3.

[0030] Figure 10 Graph showing the relationship between the standard deviation of the electrode finger pitch variation rate and the magnitude of the ripple.

[0031] Figure 11 It is a structural diagram of a multiplexer and its peripheral circuits according to an embodiment.

[0032] Description of Reference Numerals

[0033] 1: Surface acoustic wave resonator;

[0034] 2: Antenna;

[0035] 3: Inductor;

[0036] 11: IDT electrode;

[0037] 11a, 11b: comb-shaped electrodes;

[0038] 19A, 19B: reflectors;

[0039] 31s, 32s, 51s, 52s, 53s, 54s: series arm resonator;

[0040] 31p, 32p, 51p, 52p, 53p: parallel arm resonators;

[0041] 40: elastic wave filter;

[0042] 50: filter;

[0043] 60: substrate;

[0044] 100: Multiplexer;

[0045] 110, 120, 140, 150: input and output terminals;

[0046] 130: node;

[0047] 160: Common terminal;

[0048] D: spacing deviation rate;

[0049] Fe: electrode finger;

[0050] P: electrode finger spacing;

[0051] PM: average electrode finger spacing within the interval;

[0052] PT: overall average electrode finger spacing;

[0053] SD: standard deviation. DETAILED DESCRIPTION

[0054] Before describing the specific structure of the present invention, Figures 1 to 3 Problems of Comparative Examples 1 and 2 and an outline of the embodiment will be described.

[0055] Figure 1 1 is a diagram schematically showing an IDT electrode of a surface acoustic wave resonator of Comparative Example 1. Figure 2 This is a diagram schematically showing an IDT electrode of a surface acoustic wave resonator of Comparative Example 2. Figure 3 This is a diagram schematically showing an IDT electrode of a surface acoustic wave resonator according to an embodiment.

[0056] Figures 1 to 3 The IDT electrode shown has a plurality of electrode fingers. Each of the plurality of electrode fingers extends in a direction intersecting the direction of elastic wave propagation and is arranged parallel to one another. In this case, the direction of elastic wave propagation is orthogonal to the direction in which the electrode fingers extend.

[0057] like Figure 1 As shown, in the IDT electrode of Comparative Example 1, the distance between the centers of two adjacent electrode fingers in the direction of propagation of the elastic wave, i.e., the electrode finger pitch, becomes equal. In a surface acoustic wave resonator having such an IDT electrode, the reflection coefficient becomes large for frequencies less than a given value, but the reflection coefficient becomes sharply smaller for frequencies higher than the antiresonance frequency of the surface acoustic wave resonator, i.e., frequencies above a given value. As a result, there is a situation where large ripples are generated on the high-frequency side of the antiresonance frequency of the surface acoustic wave resonator. In addition, the so-called ripples in this specification refer to ripples in the reflection characteristics of the surface acoustic wave resonator (see Figure 9 (a), etc.).

[0058] like Figure 2 As shown, in the IDT electrode of Comparative Example 2, the electrode finger pitch remains constant within a certain range. In a surface acoustic wave resonator having such an IDT electrode, the reflection coefficient decreases sharply for frequencies above a predetermined value within the range where the electrode finger pitch is constant. This can cause large ripples at frequencies higher than the antiresonance frequency of the surface acoustic wave resonator.

[0059] like Figure 3 As shown, in the IDT electrode of the embodiment, the electrode fingers are arranged so that the electrode finger pitch varies irregularly. This irregular variation in the electrode finger pitch prevents the reflection coefficient from decreasing sharply at frequencies above a predetermined value. This also suppresses the generation of large ripple at frequencies higher than the antiresonance frequency.

[0060] Hereinafter, embodiments of the present invention will be described in detail using embodiments and drawings. In addition, the embodiments described below all illustrate general or specific examples. The numerical values, shapes, materials, constituent elements, configurations of constituent elements, and connection methods shown in the following embodiments are examples, and their purpose is not to limit the present invention. Among the constituent elements in the following embodiments, constituent elements that are not described in the independent claims are described as arbitrary constituent elements. In addition, the sizes or size ratios of the constituent elements shown in the drawings may not be rigorous.

[0061] (Implementation Method)

[0062] [Structures of Surface Acoustic Wave Resonators and Elastic Wave Filters]

[0063] Reference Figure 4 as well as Figure 5 The structures of the surface acoustic wave resonator and the elastic wave filter are described.

[0064] Figure 4 1 is a circuit configuration diagram of an elastic wave filter 40 including the surface acoustic wave resonator 1 according to the embodiment.

[0065] like Figure 4 As shown, the elastic wave filter 40 includes series arm resonators 31 s and 32 s , parallel arm resonators 31 p and 32 p , and input / output terminals 110 and 120 .

[0066] Series-arm resonators 31s and 32s are elastic wave resonators arranged in series on the path connecting input / output terminal 110 and input / output terminal 120. Parallel-arm resonators 31p and 32p are elastic wave resonators connected between a node on the path and ground. A node is a point where a path branches off from another path.

[0067] The surface acoustic wave resonator 1 of this embodiment is applied to, for example, the parallel arm resonator 32p. The surface acoustic wave resonator 1 is disposed between the node 130 between the series kidney resonator 32s and the input / output terminal 120, and the ground. The surface acoustic wave resonator 1 includes an IDT (Interdigital Transducer) electrode 11 and reflectors 19A and 19B disposed on both outer sides of the IDT electrode 11. The IDT electrode 11 included in the surface acoustic wave resonator 1 consists of a single IDT electrode.

[0068] Figure 5 1 is a schematic top view showing the electrode structure of the surface acoustic wave resonator 1. Figure 5 The surface acoustic wave resonator 1 shown is used to illustrate a typical planar layout structure of the IDT electrode 11 and the reflectors 19A and 19B, and the number, length, and electrode finger pitch of the electrode fingers constituting the IDT electrode are not limited thereto.

[0069] like Figure 5 As shown, the IDT electrode 11 and the reflectors 19A and 19B are formed on a piezoelectric substrate 60. The IDT electrode 11 includes comb-shaped electrodes 11a and 11b. The comb-shaped electrode 11a is connected to the node 130, and the comb-shaped electrode 11b is connected to the ground.

[0070] The comb-shaped electrode 11a is an example of a first comb-shaped electrode and includes a portion of the electrode fingers that constitute the IDT electrode 11 and a busbar electrode that connects one end of the portion of electrode fingers. The comb-shaped electrode 11b is an example of a second comb-shaped electrode and includes another portion of the electrode fingers that constitute the IDT electrode 11 and a busbar electrode that connects the other ends of the portion of electrode fingers. The electrode fingers that constitute the comb-shaped electrode 11a and the electrode fingers that constitute the comb-shaped electrode 11b are interlaced with each other.

[0071] Reflectors 19A and 19B are positioned adjacent to IDT electrode 11 in the direction of elastic wave propagation. Specifically, reflectors 19A and 19B are positioned on either side of IDT electrode 11, sandwiching IDT electrode 11. Each reflector 19A and 19B has multiple electrode fingers. Furthermore, reflectors are not necessarily provided on both sides of IDT electrode 11; one reflector may be provided on a single side. In cases where the elastic wave propagating on substrate 60 is reflected at, for example, the ends of substrate 60, reflectors may not be provided on substrate 60.

[0072] In the above embodiment, the surface acoustic wave resonator 1 is used as the parallel arm resonator 32p, but the present invention is not limited thereto. The surface acoustic wave resonator 1 may be used as the series arm resonators 31s and 32s or the parallel arm resonator 31p.

[0073] In the elastic wave filter 40, the number of series arm resonators and the number of parallel arm resonators are arbitrary, and the series arm resonators 31s and 32s and the parallel arm resonator 31p may not be present. Figure 4 Other circuit elements, wiring, and the like are interposed between the disclosed elastic wave resonator, the input / output terminals, and the path connecting the ground.

[0074] Electrode finger spacing

[0075] Reference Figure 5 as well as Figure 6 The electrode finger pitch of the IDT electrode 11 and the reflectors 19A and 19B will be described.

[0076] like Figure 5 As shown, the IDT electrode 11 and the reflectors 19A and 19B each include a plurality of electrode fingers Fe extending in a direction intersecting the elastic wave propagation direction and arranged parallel to each other.

[0077] The surface acoustic wave resonator 1 according to this embodiment is characterized by the distribution of the electrode finger pitch P, where the electrode finger pitch P is the distance between adjacent electrode fingers Fe (the distance between the center lines of the electrode fingers Fe in the direction of propagation of the elastic wave). Figure 5 As shown, in the IDT electrode or reflector, the distance between the first electrode finger Fe(1) and the second electrode finger Fe(2) in the elastic wave propagation direction (the distance between the center line of the electrode finger Fe(1) and the center line of the electrode finger Fe(2) in the elastic wave propagation direction) is defined as the electrode finger pitch P(1) of the electrode finger Fe(1). Hereinafter, the electrode finger pitch P(2) of the electrode finger Fe(2), the electrode finger pitch P(3) of the electrode finger Fe(3), and the electrode finger pitch P(4) of the electrode finger Fe(4) are similarly defined. That is, the distance between the electrode finger Fe(k) and the electrode finger Fe(k+1) (the distance between the center line of the electrode finger Fe(k) and the center line of the electrode finger Fe(k+1) in the elastic wave propagation direction) is defined as the electrode finger pitch P(k) (k is a natural number) of the k-th electrode finger Fe(k) in the elastic wave propagation direction.

[0078] Figure 6 This graph shows the distribution of the electrode finger pitch P(k) of a surface acoustic wave resonator. The horizontal axis of the graph shows the positions of electrode fingers Fe(1) to Fe(k) that constitute the surface acoustic wave resonator 1, and the vertical axis shows the electrode finger pitch P(k) of the electrode fingers Fe(k).

[0079] like Figure 6As shown, the surface acoustic wave resonator 1 includes electrode finger sections where the electrode fingers Fe are arranged so that the electrode finger pitch P(k) is irregular. The term "irregular" means a state that varies randomly, not just a fixed state, a proportionally varying state, or a periodically varying state. By including electrode finger sections where the electrode finger pitch P(k) is irregular in the surface acoustic wave resonator 1, the frequency band of ripples generated by each electrode finger pitch P(k) can be appropriately dispersed.

[0080] The surface acoustic wave resonator 1 of this embodiment includes the following IDT electrode 11 and reflectors 19A and 19B, that is, there is no fixed electrode finger pitch P(k) between four or more adjacent electrode fingers Fe, and the electrode finger pitch P(k) between four or more adjacent electrode fingers Fe does not have a fixed slope (fixed increase or decrease rate).

[0081] For example, in the surface acoustic wave resonator 1, the electrode finger pitches of four electrode fingers adjacent to each other in the elastic wave propagation direction are set to P(k-1), P(k), and P(k+1) in the order of arrangement in the elastic wave propagation direction. In this case, in at least a portion of the electrode fingers having a

[0082] P(k-1)<P(k+1)<P(k) or

[0083] P(k-1)>P(k+1)>P(k)

[0084] relationship.

[0085] In addition, Figure 6 In the illustrated surface acoustic wave resonator 1, the electrode fingers Fe are arranged so that the electrode finger pitch P(k) is irregular in all of the IDT electrode 11 and reflectors 19A and 19B. However, the surface acoustic wave resonator 1 is not limited to this arrangement. In other words, the surface acoustic wave resonator 1 only needs to have an electrode finger section where the electrode finger pitch P(k) is irregular between four or more adjacent electrode fingers Fe in at least a portion of the IDT electrode 11 and reflectors 19A and 19B.

[0086] For example, in the surface acoustic wave resonator 1, some of the plurality of electrode fingers Fe may have a fixed electrode finger pitch, and the remaining electrode fingers excluding the some may have a pitch satisfying P(k-1)<P(k+1)<P(k) or

[0087] P(k-1)>P(k+1)>P(k)

[0088] relationship.

[0089] For example, the electrode fingers Fe included in the IDT electrode 11 may have a fixed electrode finger pitch, and the electrode fingers Fe included in the reflectors 19A and 19B may have a fixed electrode finger pitch.

[0090] P(k-1)<P(k+1)<P(k) or

[0091] P(k-1)>P(k+1)>P(k)

[0092] relationship.

[0093] For example, the plurality of electrode fingers Fe included in the reflectors 19A and 19B may have a fixed electrode finger pitch, and the plurality of electrode fingers Fe included in the IDT electrode 11 may have a fixed electrode finger pitch.

[0094] P(k-1)<P(k+1)<P(k) or

[0095] P(k-1)>P(k+1)>P(k)

[0096] relationship.

[0097] For example, in the surface acoustic wave resonator 1 , the electrode finger pitches P(k) between two electrode fingers adjacent to each other in the elastic wave propagation direction may all be different from each other.

[0098] [Spacing deviation rate and its standard deviation]

[0099] Reference Figure 7 as well as Figure 8 The pitch variation rate D and its standard deviation SD of the electrode fingers Fe(k) in the IDT electrode 11 and the reflectors 19A and 19B will be described.

[0100] Figure 7 This is a diagram for explaining the definitions of the section average electrode finger pitch PM(k), the overall average electrode finger pitch PT, and the pitch deviation rate D(k) of the surface acoustic wave resonator 1 .

[0101] exist Figure 7 This figure shows an example of the distribution of the electrode finger pitch P(k) of the IDT electrodes or reflectors that make up a surface acoustic wave resonator. The horizontal axis of the figure shows the positions of the electrode fingers Fe(k) that make up the IDT electrodes and reflectors, while the vertical axis shows the electrode finger pitch P(k) of the electrode fingers Fe(k).

[0102] As described above, first, (1) the distance between the kth (k is an integer greater than or equal to 2) electrode finger Fe(k) and the (k+1)th electrode finger Fe(k+1) in the direction of elastic wave propagation (the distance between the center line of the electrode finger Fe(k) in the direction of elastic wave propagation and the center line of the electrode finger Fe(k+1) in the direction of elastic wave propagation) is defined as the kth electrode finger pitch P(k).

[0103] Next, (2) in the three adjacent electrode fingers Fe(k-1), electrode finger Fe(k), and electrode finger Fe(k+1), the average of the electrode finger pitch P(k-1) and the electrode finger pitch P(k+1) is defined as the interval average electrode finger pitch PM(k) [={P(k-1)+P(k+1)} / 2]. At this time, the difference between the electrode finger pitch P(k) and the interval average electrode finger pitch PM(k) [=P(k)-PM(k)] divided by the overall average electrode finger pitch PT is defined as the pitch deviation rate D(k) of the electrode finger Fe(k) [={P(k)-PM(k)} / PT], where the overall average electrode finger pitch PT is the average pitch of the entire electrode fingers of the IDT electrode or reflector including the electrode fingers Fe(k-1), Fe(k), and Fe(k+1).

[0104] Next, (3) the spacing deviation rate D(k) of the electrode fingers Fe(k) of all the electrode fingers Fe of the IDT electrode or reflector including the electrode fingers Fe(k-1), Fe(k), and Fe(k+1) is calculated, and a histogram of the spacing deviation rate D(k) in the IDT electrode or reflector is calculated.

[0105] Figure 8 This is a diagram explaining the pitch variation rate D(k) and its standard deviation SD in the irregular electrode finger pitch distribution of the surface acoustic wave resonator 1 .

[0106] exist Figure 8 In (a), Figure 6 Similarly, a graph showing the distribution of the electrode finger pitch P(k) of the IDT electrode 11 and the reflectors 19A and 19B constituting the surface acoustic wave resonator 1 is shown. Figure 5 The electrode finger at the left end of the reflector 19A shown is an example of an electrode finger Fe(1). In the surface acoustic wave resonator 1 of this embodiment, the electrode finger pitch P(k) is dispersed within a range of 3.14 μm to 3.47 μm. In other words, the electrode finger pitch P(k) is dispersed such that the minimum value is 3.20 μm or less and the maximum value is 3.40 μm or more.

[0107] exist Figure 8(b) shows an example of the distribution of the pitch deviation rate D(k) of the electrode fingers Fe of the IDT electrode 11 and reflectors 19A and 19B. The horizontal axis shows the positions of the electrode fingers Fe(k) that constitute the IDT electrode 11 or reflectors 19A and 19B, and the vertical axis shows the pitch deviation rate D(k). In the surface acoustic wave resonator 1 of this embodiment, the pitch deviation rate D(k) is dispersed within a range of greater than -5% and less than 5%. In other words, the minimum value of the pitch deviation rate D(k) is less than -4% and the maximum value is greater than 4%.

[0108] exist Figure 8 Figure (c) shows an example of a histogram of the pitch deviation rate D(k) of the electrode fingers Fe of the IDT electrode 11 and reflectors 19A and 19B. Based on this histogram of the pitch deviation rate D(k), the standard deviation SD of the pitch deviation rate of the electrode fingers Fe can be calculated. According to the above definition, the more regular the electrode finger pitch P(k), the smaller the standard deviation SD of the pitch deviation rate becomes, and the more irregular the electrode finger pitch P(k), the larger the standard deviation SD of the pitch deviation rate becomes.

[0109] In this embodiment, the standard deviation SD of the pitch variation rate in the above-mentioned histogram is 0.2% or greater in at least one of the IDT electrode 11 and reflectors 19A and 19B. This structure prevents the reflection coefficient from decreasing sharply at frequencies higher than the antiresonance frequency. This prevents the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency. The effects of the surface acoustic wave resonator 1 having the above-mentioned structure are described below.

[0110] [Effects, etc.]

[0111] Figure 9 This is a graph showing the insertion loss of the surface acoustic wave resonators in Comparative Example 3 and Examples 1, 2, and 3. This graph shows that the reflection loss increases toward the lower side of the vertical axis.

[0112] Figure 9 (a) is Comparative Example 3. This figure shows an example in which the electrode finger pitch P(k) of the plurality of electrode fingers Fe is uniform and the standard deviation SD of the pitch variation rate is 0.0%. In Comparative Example 3, large ripples are generated at frequencies higher than the antiresonance frequency (959 MHz) of the surface acoustic wave resonator, specifically around a frequency of 1110 MHz.

[0113] Figure 9(b) is Example 1, which is an example of an embodiment. This figure shows an example in which the standard deviation SD of the pitch variation rate is set to 0.2%. In Example 1, compared to Comparative Example 3, the generation of ripples at frequencies higher than the antiresonance frequency of the surface acoustic wave resonator 1 can be suppressed.

[0114] Figure 9 (c) is Example 2, an example of an implementation. This figure shows an example in which the standard deviation SD of the pitch variation rate is set to 0.7%. In Example 2, compared to Comparative Example 3 and Example 1, the generation of ripples at frequencies higher than the antiresonance frequency of the surface acoustic wave resonator 1 can be suppressed.

[0115] Figure 9 (d) is Example 3, which is an example of an embodiment. This figure shows an example in which the standard deviation SD of the pitch variation rate is set to 0.9%. In Example 3, the generation of ripples at a frequency higher than the antiresonance frequency of the surface acoustic wave resonator 1 can be suppressed.

[0116] Figure 10 : is a graph showing the relationship between the standard deviation SD of the pitch deviation rate of the electrode fingers Fe and the magnitude of the ripple. Figure 10 The figure shows the magnitude of each ripple when the standard deviation SD of the pitch variation rate of the electrode fingers Fe changes from 0.0% to 1.45%. The magnitude of the ripple is the difference between the upper and lower limits of the ripple when the insertion loss is used as the vertical axis (see Figure 9 (a), etc.).

[0117] like Figure 10 As shown in FIG. 1 , when the standard deviation SD of the pitch variation rate of the electrode fingers Fe is 0.2% or greater, the ripple is reduced compared to when the standard deviation SD is 0.1%. Thus, by setting the standard deviation SD of the pitch variation rate to 0.2% or greater, it is possible to suppress the generation of large ripples at frequencies higher than the antiresonance frequency of the surface acoustic wave resonator 1.

[0118] Furthermore, when the standard deviation SD of the pitch variation rate of the electrode fingers Fe is 0.7% or greater, the ripple is further reduced compared to when the standard deviation SD is 0.2%. Thus, by setting the standard deviation SD of the pitch variation rate to 0.7% or greater, the generation of ripple at frequencies higher than the antiresonance frequency of the surface acoustic wave resonator 1 can be further suppressed.

[0119] Furthermore, when the standard deviation SD of the pitch variation rate of the electrode fingers Fe is 0.95% or greater, the ripple is further reduced, and the ripple magnitude remains almost constant. This trend is thought to persist even when the standard deviation SD of the pitch variation rate is 1.4%, and even when the standard deviation SD is 3% or 10%. Thus, by setting the standard deviation SD of the pitch variation rate to 0.95% or greater, the generation of ripple at frequencies higher than the antiresonance frequency of the surface acoustic wave resonator 1 can be further suppressed.

[0120] [Structure of multiplexer]

[0121] Figure 11 This is a structural diagram of a multiplexer 100 and its peripheral circuits according to an embodiment. As shown in the figure, the multiplexer 100 includes an elastic wave filter 40, a filter 50, and a common terminal 160. The multiplexer 100 is connected to the antenna 2 at the common terminal 160. An inductor 3 for impedance matching is connected between the connection path between the common terminal 160 and the antenna 2 and the ground. Alternatively, the inductor 3 may be connected in series between the common terminal 160 and the antenna 2. The inductor 3 may be included in the multiplexer 100 or may be external to the multiplexer 100. Furthermore, the inductor 3 may be a capacitor or a composite circuit including an inductor and a capacitor.

[0122] The input / output terminal 110 of the elastic wave filter 40 and the input / output terminal 140 of the filter 50 are connected to the common terminal 160 .

[0123] The elastic wave filter 40 utilizes Love waves as elastic waves. The IDT electrode 11 and the reflectors 19A and 19B included in the surface acoustic wave resonator 1 of the elastic wave filter 40 have Figure 6 The distribution of electrode finger pitch P(k) is shown.

[0124] Filter 50 is a ladder-type elastic wave filter having input / output terminals 140 and 150 and composed of a plurality of elastic wave resonators. Filter 50 includes series-arm resonators 51s, 52s, 53s, and 54s and parallel-arm resonators 51p, 52p, and 53p. Series-arm resonators 51s, 52s, 53s, and 54s are arranged in series on a path connecting input / output terminals 140 and 150. Parallel-arm resonators 51p, 52p, and 53p are each connected between a node on the path and ground.

[0125] For example, elastic wave filter 40 is used as a transmission filter, and filter 50 is used as a reception filter. The passband of elastic wave filter 40 is located on the lower frequency side than the passband of filter 50.

[0126] For example, the elastic wave filter 40 is applied to a transmission filter of LTE (Long Term Evolution), and the filter 50 is applied to a reception filter of LTE.

[0127] (Summarize)

[0128] As described above, the surface acoustic wave resonator 1 according to this embodiment includes a piezoelectric substrate 60, an IDT electrode 11 provided on the substrate 60, and reflectors 19A and 19B arranged adjacent to the IDT electrode 11 in the direction of acoustic wave propagation. The IDT electrode 11 included in the surface acoustic wave resonator 1 consists of a single IDT electrode. The IDT electrode 11 and reflectors 19A and 19B each have a plurality of electrode fingers Fe extending in a direction intersecting the direction of acoustic wave propagation and arranged parallel to each other.

[0129] (1) The distance between the kth (k is an integer greater than or equal to 2)th electrode finger and the (k+1)th electrode finger in the direction of elastic wave propagation is defined as the kth electrode finger pitch.

[0130] (2) Among the three adjacent electrode fingers, namely the (k-1)th electrode finger, the kth electrode finger, and the (k+1)th electrode finger, the value obtained by dividing the difference between the kth electrode finger pitch and the interval average electrode finger pitch by the overall average electrode finger pitch is defined as the pitch deviation rate D(k) of the kth electrode finger, wherein the interval average electrode finger pitch is the average of the (k-1)th electrode finger pitch and the (k+1)th electrode finger pitch, and the overall average electrode finger pitch is the average pitch of the entire electrode fingers of the IDT electrode 11 or the reflectors 19A and 19B including the three adjacent electrode fingers.

[0131] (3) The distribution of the pitch deviation rate D(k) obtained by calculating the pitch deviation rate D(k) of the k-th electrode finger for all electrode fingers of the IDT electrode 11 or reflectors 19A and 19B including three adjacent electrode fingers is defined as a histogram of the pitch deviation rate D(k). In this case,

[0132] In at least one of the IDT electrode 11 and the reflectors 19A and 19B, the standard deviation SD of the pitch variation rate D(k) in the histogram is 0.2% or more.

[0133] By keeping the standard deviation SD of the pitch variation rate D(k) of the electrode fingers Fe(k) at 0.2% or greater, it is possible to suppress the reflection coefficient from rapidly decreasing at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0134] Alternatively, in the surface acoustic wave resonator 1, the electrode finger pitches of four electrode fingers adjacent to each other in the elastic wave propagation direction may be set to P(k-1), P(k), and P(k+1) in the order of arrangement in the elastic wave propagation direction. In this case, in at least a portion of the electrode fingers having a

[0135] P(k-1)<P(k+1)<P(k) or

[0136] P(k-1)>P(k+1)>P(k)

[0137] relationship.

[0138] The surface acoustic wave resonator 1 having the electrode finger pitch relationship described above can suppress the reflection coefficient from rapidly decreasing at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0139] Alternatively, some of the plurality of electrode fingers may have a fixed electrode finger pitch, and the remaining electrode fingers may have a fixed electrode finger pitch.

[0140] P(k-1)<P(k+1)<P(k) or

[0141] P(k-1)>P(k+1)>P(k)

[0142] relationship.

[0143] By having the electrode finger pitches of the remaining electrode fingers, except for a portion, maintain the relationship shown above, it is possible to suppress the reflection coefficient from decreasing rapidly at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0144] Alternatively, the plurality of electrode fingers included in the IDT electrode 11 may have a fixed electrode finger pitch, and the plurality of electrode fingers included in the reflector (for example, the reflector 19A) may have a fixed electrode finger pitch.

[0145] P(k-1)<P(k+1)<P(k) or

[0146] P(k-1)>P(k+1)>P(k)

[0147] relationship.

[0148] By having the electrode finger pitches of the multiple electrode fingers included in the reflector have the relationship shown above, it is possible to suppress the reflection coefficient from decreasing sharply at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0149] Alternatively, the plurality of electrode fingers included in the reflectors 19A and 19B may have a fixed electrode finger pitch, and the plurality of electrode fingers included in the IDT electrode 11 may have a fixed electrode finger pitch.

[0150] P(k-1)<P(k+1)<P(k) or

[0151] P(k-1)>P(k+1)>P(k)

[0152] relationship.

[0153] By having the electrode finger pitches of the multiple electrode fingers included in the IDT electrode 11 have the relationship shown above, it is possible to suppress the reflection coefficient from decreasing sharply at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0154] The surface acoustic wave resonator 1 according to this embodiment includes a piezoelectric substrate 60 and an IDT electrode 11 provided on the substrate 60. The IDT electrode 11 included in the surface acoustic wave resonator 1 is composed of a single IDT electrode. The IDT electrode 11 has a plurality of electrode fingers extending in a direction intersecting the direction of propagation of the elastic wave and arranged parallel to each other.

[0155] (1) The distance between the kth (k is an integer greater than or equal to 2)th electrode finger and the (k+1)th electrode finger in the direction of elastic wave propagation is defined as the kth electrode finger pitch.

[0156] (2) For the three adjacent electrode fingers, namely the (k-1)th electrode finger, the kth electrode finger, and the (k+1)th electrode finger, the value obtained by dividing the difference between the kth electrode finger pitch and the interval average electrode finger pitch by the overall average electrode finger pitch is defined as the pitch deviation rate D(k) of the kth electrode finger, wherein the interval average electrode finger pitch is the average of the (k-1)th electrode finger pitch and the (k+1)th electrode finger pitch, and the overall average electrode finger pitch is the average pitch of the entire electrode fingers of the IDT electrode 11 including the three adjacent electrode fingers.

[0157] (3) The distribution of the pitch deviation rate D(k) obtained by calculating the pitch deviation rate D(k) of the k-th electrode finger for all electrode fingers of the IDT electrode 11 including three adjacent electrode fingers is defined as a histogram of the pitch deviation rate D(k). In this case,

[0158] In the IDT electrode 11 , the standard deviation SD of the pitch variation rate D(k) in the above-mentioned histogram is 0.2% or more.

[0159] By keeping the standard deviation SD of the pitch variation rate D(k) of the electrode fingers Fe(k) at 0.2% or greater, it is possible to suppress the reflection coefficient from rapidly decreasing at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0160] Alternatively, the electrode finger pitches of four adjacent electrode fingers in the elastic wave propagation direction may be set to P(k-1), P(k), and P(k+1) in the order of arrangement in the elastic wave propagation direction. In this case, at least a portion of the electrode fingers may have a

[0161] P(k-1)<P(k+1)<P(k) or

[0162] P(k-1)>P(k+1)>P(k)

[0163] relationship.

[0164] The surface acoustic wave resonator 1 having the electrode finger pitch relationship described above can suppress the reflection coefficient from rapidly decreasing at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0165] Alternatively, some of the plurality of electrode fingers may have a fixed electrode finger pitch, and the remaining electrode fingers may have a fixed electrode finger pitch.

[0166] P(k-1)<P(k+1)<P(k) or

[0167] P(k-1)>P(k+1)>P(k)

[0168] relationship.

[0169] By having the electrode finger pitches of the remaining electrode fingers, except for a portion, maintain the relationship shown above, it is possible to suppress the reflection coefficient from decreasing rapidly at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0170] Alternatively, the electrode finger pitches between any two electrode fingers adjacent to each other in the elastic wave propagation direction may all be different from each other.

[0171] By making all the electrode finger pitches different in this way, the reflection coefficient can be prevented from decreasing sharply at frequencies higher than the antiresonance frequency. This can suppress the generation of unnecessary standing waves in the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0172] The elastic wave filter 40 according to the present embodiment is an elastic wave filter including the above-described surface acoustic wave resonator 1 .

[0173] Thus, it is possible to provide the elastic wave filter 40 including the surface acoustic wave resonator 1 capable of suppressing the generation of large ripples at a frequency higher than the antiresonance frequency.

[0174] Alternatively, the elastic wave filter 40 may be formed of a ladder circuit including series-arm resonators and parallel-arm resonators, and at least one of the parallel-arm resonators may be formed of the surface acoustic wave resonator 1 .

[0175] This can suppress the generation of large ripples at higher frequencies than the antiresonance frequency of the parallel arm resonator, and can suppress the increase in insertion loss in the passband of the elastic wave filter 40 .

[0176] The multiplexer 100 according to the present embodiment includes a transmission filter and a reception filter, and the transmission filter includes the elastic wave filter 40 described above.

[0177] This can suppress the generation of ripples outside the passband of the transmission filter. This can suppress the increase in insertion loss in the passband of the reception filter outside the passband of the transmission filter.

[0178] Here, the point that the pitch deviation rate of the surface acoustic wave resonators disclosed in the aforementioned Patent Documents 1 to 3 is greatly different from the pitch deviation rate of the surface acoustic wave resonator 1 of the present embodiment will be described.

[0179] The pitch deviation rates in Patent Documents 1 to 3 can be calculated using the respective pitches disclosed in Patent Documents 1 to 3 and in accordance with the definitions of (1), (2), and (3) in the (Summary) column of this specification. The pitch deviation rate in Comparative Example 2A of Patent Document 1 is 0.008%. The pitch deviation rate in Comparative Example 2B of Patent Document 1 is 0.016%. The pitch deviation rate in Comparative Example 2C of Patent Document 1 is 0.025%. The pitch deviation rate in Comparative Example 3A of Patent Document 1 is 0.027%. The pitch deviation rate in Comparative Example 3B of Patent Document 1 is 0.048%. The pitch deviation rate in Comparative Example 3C of Patent Document 1 is 0.068%. The pitch deviation rate in Patent Document 2 is 0.045%. The pitch deviation rate in Patent Document 3 is 0.183%.

[0180] As described above, the pitch deviation ratios of the surface acoustic wave resonators of Patent Documents 1 to 3 are similar to the pitch deviation ratio of the surface acoustic wave resonator 1 of the present embodiment (see Figure 8 Compared to the maximum and minimum values ​​of (b)), the values ​​of the pitch deviation rate D(k) of the electrode fingers Fe(k) are significantly smaller in the surface acoustic wave resonator 1 of this embodiment. By making the values ​​of the pitch deviation rate D(k) of the electrode fingers Fe(k) highly dispersed, it is possible to suppress the reflection coefficient from decreasing sharply at frequencies higher than the antiresonance frequency. This prevents the generation of unnecessary standing waves within the surface acoustic wave resonator 1 and the generation of large ripples at frequencies higher than the antiresonance frequency.

[0181] (Other modifications, etc.)

[0182] While the surface acoustic wave resonator, elastic wave filter, and multiplexer according to the present invention have been described above by way of examples, the surface acoustic wave resonator, elastic wave filter, and multiplexer according to the present invention are not limited to the above-described examples. Other examples implemented by combining arbitrary components of the above-described examples, variations of the above-described examples that occur to those skilled in the art without departing from the spirit of the present invention, and various devices incorporating the surface acoustic wave resonator, elastic wave filter, and multiplexer according to the above-described examples are also encompassed by the present invention.

[0183] For example, in the surface acoustic wave resonator 1, the standard deviation SD of the pitch variation rate of at least one of the IDT electrode 11 and the reflectors 19A and 19B may be 0.2% or greater. Alternatively, the standard deviation SD of the pitch variation rate of the IDT electrode 11 may be 0.2% or greater, and the standard deviation SD of the pitch variation rate of each of the reflectors 19A and 19B may be less than 0.2%. Alternatively, the standard deviation SD of the pitch variation rate of at least one of the reflectors 19A and 19B may be 0.2% or greater, and the standard deviation SD of the pitch variation rate of the IDT electrode 11 may be less than 0.2%.

[0184] The multiplexer can be applied not only to duplexers but also to triplexers in which three filters are commonly connected to an antenna, hexaplexers in which three duplexers are commonly connected via a common terminal, etc. In other words, the multiplexer only needs to have two or more filters.

[0185] Furthermore, the multiplexer according to the present invention is not limited to a configuration including both a transmission filter and a reception filter, and may be a configuration including only a plurality of transmission filters or only a plurality of reception filters.

[0186] Furthermore, in the elastic wave filters and multiplexers in the above-described embodiments, other circuit elements, wiring, etc. may be inserted between paths connecting the circuit elements (and components) and signal paths disclosed in the drawings.

[0187] Industrial applicability

[0188] The present invention can be widely used in a transmission / reception filter and a multiplexer used at the front end of a wireless communication terminal requiring high attenuation outside a passband.

Claims

1. A surface acoustic wave resonator comprising: a substrate having piezoelectric properties; An IDT electrode is provided on the substrate; as well as a reflector arranged adjacent to the IDT electrode in the direction of propagation of the elastic wave, In the surface acoustic wave resonator, The IDT electrode included in the surface acoustic wave resonator is composed of one IDT electrode. The IDT electrode and the reflector each have a plurality of electrode fingers extending in a direction intersecting the elastic wave propagation direction and arranged parallel to each other. (1) The distance between the kth electrode finger and the (k+1)th electrode finger in the propagation direction of the elastic wave is defined as the kth electrode finger pitch, where k is an integer greater than 2. (2) Among three adjacent electrode fingers, namely, the (k-1)th electrode finger, the kth electrode finger, and the (k+1)th electrode finger, a value obtained by dividing the difference between the kth electrode finger pitch and the interval average electrode finger pitch by the overall average electrode finger pitch is defined as the pitch deviation rate of the kth electrode finger, wherein the interval average electrode finger pitch is the average of the (k-1)th electrode finger pitch and the (k+1)th electrode finger pitch, and the overall average electrode finger pitch is the average pitch of the entire electrode fingers of the IDT electrode or the reflector including the three adjacent electrode fingers. (3) A distribution of the pitch deviation rate obtained by calculating the pitch deviation rate of the k-th electrode finger for all electrode fingers of the IDT electrode or the reflector including the three adjacent electrode fingers is defined as a histogram of the pitch deviation rate. In this case, In at least one of the IDT electrode and the reflector, a standard deviation of the pitch variation rate in the histogram is 0.2% or more.

2. The surface acoustic wave resonator according to claim 1, wherein The electrode finger pitches of four electrode fingers adjacent to each other in the elastic wave propagation direction are set to P(k-1), P(k), and P(k+1) in the order of arrangement in the elastic wave propagation direction. In this case, at least one portion of the electrode fingers has P(k-1)<P(k+1)<P(k) or P(k-1)>P(k+1)>P(k) relationship.

3. The surface acoustic wave resonator according to claim 2, wherein A portion of the electrode fingers of the plurality of electrode fingers have a fixed electrode finger pitch, The remaining electrode fingers except for the portion have the P(k-1)<P(k+1)<P(k) or P(k-1)>P(k+1)>P(k) relationship.

4. The surface acoustic wave resonator according to claim 3, wherein The plurality of electrode fingers included in the IDT electrode have a fixed electrode finger pitch. The plurality of electrode fingers included in the reflector have P(k-1)<P(k+1)<P(k) or P(k-1)>P(k+1)>P(k) relationship.

5. The surface acoustic wave resonator according to claim 3, wherein The plurality of electrode fingers included in the reflector have a fixed electrode finger pitch. The plurality of electrode fingers included in the IDT electrode have P(k-1)<P(k+1)<P(k) or P(k-1)>P(k+1)>P(k) relationship. The surface acoustic wave resonator according to claim 1 , wherein: The electrode finger pitches between two electrode fingers adjacent to each other in the elastic wave propagation direction are all different from each other.

7. A surface acoustic wave resonator comprising: a substrate having piezoelectricity; and IDT electrodes, provided on the substrate, In the surface acoustic wave resonator, The IDT electrode included in the surface acoustic wave resonator is composed of one IDT electrode. The IDT electrode includes a plurality of electrode fingers extending in a direction intersecting the elastic wave propagation direction and arranged parallel to each other. (1) The distance between the kth electrode finger and the (k+1)th electrode finger in the propagation direction of the elastic wave is defined as the kth electrode finger pitch, where: k is an integer greater than or equal to 2, (2) Among three adjacent electrode fingers, namely, the (k-1)th electrode finger, the kth electrode finger, and the (k+1)th electrode finger, a value obtained by dividing the difference between the kth electrode finger pitch and the interval average electrode finger pitch by the overall average electrode finger pitch is defined as the pitch deviation rate of the kth electrode finger, wherein the interval average electrode finger pitch is the average of the (k-1)th electrode finger pitch and the (k+1)th electrode finger pitch, and the overall average electrode finger pitch is the average pitch of the entire electrode fingers of the IDT electrode including the three adjacent electrode fingers. (3) A distribution of the pitch deviation rates obtained by calculating the pitch deviation rates of the k-th electrode finger for all electrode fingers of the IDT electrode including the three adjacent electrode fingers is defined as a histogram of the pitch deviation rates. In this case, In the IDT electrode, a standard deviation of the pitch variation rate in the histogram is 0.2% or more.

8. The surface acoustic wave resonator according to claim 7, wherein The electrode finger pitches of four electrode fingers adjacent to each other in the elastic wave propagation direction are set to P(k-1), P(k), and P(k+1) in the order of arrangement in the elastic wave propagation direction. In this case, at least one portion of the electrode fingers has P(k-1)<P(k+1)<P(k) or P(k-1)>P(k+1)>P(k) relationship.

9. The surface acoustic wave resonator according to claim 8, wherein A portion of the electrode fingers of the plurality of electrode fingers have a fixed electrode finger pitch, The remaining electrode fingers except for the portion have the P(k-1)<P(k+1)<P(k) or P(k-1)>P(k+1)>P(k) relationship.

10. The surface acoustic wave resonator according to claim 7, wherein The electrode finger pitches between two electrode fingers adjacent to each other in the elastic wave propagation direction are all different from each other. 11 . An elastic wave filter comprising the surface acoustic wave resonator according to claim 1 .

12. The elastic wave filter according to claim 11, wherein The elastic wave filter is composed of a ladder circuit having series-arm resonators and parallel-arm resonators. At least one of the parallel arm resonators is formed of the surface acoustic wave resonator.

13. A multiplexer, wherein: Equipped with transmission filter and reception filter, The transmission filter includes the elastic wave filter according to claim 11 or 12.

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