Surface acoustic wave filter, boundary acoustic wave filter, and antenna duplexer using same

The present invention relates to a surface acoustic wave filter, a boundary acoustic wave filter, and an antenna duplexer including them and used in electronic devices, such as portable telephones.

FIGS. 28 and 29 are top views of surface acoustic wave resonator 3 of a conventional surface acoustic wave filter. Surface acoustic wave resonator 3 includes piezoelectric substrate 1 and interdigital transducer electrode 2 provided on an upper surface of piezoelectric substrate 1 . Interdigital transducer electrode 2 includes comb electrodes 2 A and 2 B facing each other on the upper surface of piezoelectric substrate 1 . Interdigital transducer electrode 2 of surface acoustic wave resonator 3 has a large apodized weighting factor. In other words, the ratio of the sum of the areas of regions 5 A, 5 B, 5 C, and 5 D where electrodes do not face to the area of excitation region 4 is large.

FIG. 30 shows frequency characteristics of a surface acoustic wave filter including surface acoustic wave resonator 3 as a series resonator electrically connected in series between input and output terminals. The propagation of the surface acoustic wave filter at anti-resonance frequency f AR is reduced to increase a Q factor, accordingly reducing a loss.

FIG. 31 shows frequency characteristics of a surface acoustic wave filter using surface acoustic wave resonator 3 as a parallel resonator electrically connected in parallel to input and output terminals. The propagation of the surface acoustic wave filter at anti-resonance frequency f AR is increased to reduce the loss.

The surface acoustic wave filter including surface acoustic wave resonator 3 as a series resonator has a large loss of transmission characteristics especially at resonance frequency f R .

A surface acoustic wave filter includes a piezoelectric substrate including lithium niobate, a series resonator including a first interdigital transducer electrode provided on the piezoelectric substrate, and a parallel resonator including a second interdigital transducer electrode provided on the piezoelectric substrate and being electrically connected to the series resonator. An apodized weighting factor of the first interdigital transducer electrode is smaller than an apodized weighting factor of the second interdigital transducer electrode.

This surface acoustic wave filter has a small loss.

FIG. 1 is a circuit diagram of a surface acoustic wave filter according to an exemplary embodiment of the present invention.

FIG. 2 is a top view of the surface acoustic wave filter according to the embodiment.

FIG. 3 shows characteristics of a series resonator of the surface acoustic wave filter according to the embodiment.

FIG. 4 shows characteristics of the series resonator of the surface acoustic wave filter according to the embodiment.

FIG. 5 shows characteristics of a parallel resonator of the surface acoustic wave filter according to the embodiment.

FIG. 6 shows characteristics of the parallel resonator of the surface acoustic wave filter according to the embodiment.

FIG. 7 shows the relation between an apodized weighting factor and a Q factor of the surface acoustic wave filter of the embodiment.

FIG. 8 shows the relation between an apodized weighting factor and a Q factor of the surface acoustic wave filter of the embodiment.

FIG. 9 is a top view of a resonator of a surface acoustic wave filter as a comparative example.

FIG. 10 shows transmission characteristics of the surface acoustic wave filter shown in FIG. 9 .

FIG. 11 shows transmission characteristics of the surface acoustic wave filter according to the embodiment.

FIG. 12 is a sectional view of the surface acoustic wave filter according to the embodiment.

FIG. 13 is a sectional view of another electrode of the surface acoustic wave filter according to the embodiment.

FIG. 14 is a sectional view of a boundary acoustic wave filter according to the embodiment.

FIG. 15 is a circuit diagram of an antenna duplexer according to the embodiment.

FIGS. 16A and 16B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIGS. 17A and 17B are sectional views of the surface acoustic wave filter according to the embodiment.

FIGS. 18A and 18B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIG. 19 is an enlarged plan view of the surface acoustic wave resonator according to the embodiment.

FIG. 20 shows the relation between a Q factor and a metallization ratio of the surface acoustic wave resonator according to the embodiment.

FIGS. 21A and 21B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIGS. 22 and 22B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIGS. 23A and 23B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIG. 24A shows the relation between the metallization ratio and a spurious of the transmission characteristics of the surface acoustic wave resonator according to the embodiment.

FIG. 24B shows the relation between the metallization ratio and a spurious of the admittance of the surface acoustic wave resonator according to the embodiment.

FIGS. 25A and 25B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIGS. 26A and 26B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIGS. 27A and 27B show transmission characteristics and an admittance of the surface acoustic wave resonator according to the embodiment, respectively.

FIG. 28 is a top view of a conventional surface acoustic wave filter.

FIG. 29 is a top view of the conventional surface acoustic wave filter.

FIG. 30 shows transmission characteristics of a series resonator of the conventional surface acoustic wave filter.

FIG. 31 shows transmission characteristics of a parallel resonator of the conventional surface acoustic wave filter.

FIG. 1 is a circuit diagram of surface acoustic wave filter 1001 according to an exemplary embodiment of the present invention. Surface acoustic wave filter 1001 includes input terminal 6 A, output terminal 6 B, series resonators 7 A, 7 B, and 7 C, and parallel resonators 8 A and 8 B electrically connected to series resonators 7 A, 7 B, and 7 C. Series resonators 7 A, 7 B, and 7 C are electrically connected in series between terminals 6 A and 6 B. Series resonators 7 A and 7 B are connected to each other at node 1001 B. Series resonators 7 B and 7 C are connected to each other at node 1001 C. Parallel resonator 8 A is connected between node 1001 B and ground 1001 A. Parallel resonator 8 B is connected between node 1001 C and ground 1001 A. Thus, parallel resonators 8 A and 8 B are connected in parallel to terminals 6 A and 6 B.

FIG. 2 is a top view of surface acoustic wave filter 1001 . Surface acoustic wave filter 1001 includes piezoelectric substrate 9 made of piezoelectric material. According to the embodiment, piezoelectric substrate 9 is made of −30° to +30° rotated Y-cut lithium niobate. Series resonator 7 A includes interdigital transducer electrode 10 provided on upper surface 9 A of piezoelectric substrate 9 . Interdigital transducer electrode 10 includes comb electrodes 10 A and 10 B facing each other on upper surface 9 A of piezoelectric substrate 9 . Plural electrode fingers of comb electrode 10 A are positioned interdigitally with plural electrode fingers of comb electrode 10 B. That is, the electrode fingers of interdigital transducer electrode 10 are located interdigitally with each other. This means that the electrode fingers of comb electrode 10 A face the electrode fingers of comb electrode 10 B in a direction perpendicular to directions in which the electrode fingers of comb electrodes 10 A and 10 B extend. The electrode fingers of comb electrode 10 A are positioned interdigitally with the electrode fingers of comb electrode 10 B by facing width 107 B at the ends of series resonator 7 A and by facing width 107 A at the center of series resonator 7 A. Facing width 107 B is smaller than facing width 107 A. As shown in FIG. 2 , the facing width of comb electrodes 10 A and 10 B of interdigital transducer electrode 10 decreases from the center toward the ends of series resonator 7 A. Parallel resonator 8 A includes interdigital transducer electrode 12 provided on upper surface 9 A of piezoelectric substrate 9 . Interdigital transducer electrode 12 includes comb electrodes 12 A and 12 B facing each other on upper surface 9 A of piezoelectric substrate 9 . Plural electrode fingers of comb electrode 12 A are positioned interdigitally with plural electrode fingers of comb electrode 12 B. That is, the electrode fingers of interdigital transducer electrode 12 are located interdigitally with each other. This means that the electrode fingers of comb electrode 12 A face the electrode fingers of comb electrode 12 B in a direction perpendicular to directions in which the electrode fingers of comb electrodes 12 A and 12 B extend. The electrode fingers of comb electrode 12 A face the electrode fingers of comb electrode 12 B by facing width 108 B at the ends of parallel resonator 8 A and by facing width 108 A at the center of parallel resonator 8 A. Facing width 108 B is smaller than facing width 108 A. As shown in FIG. 2 , the facing width of comb electrodes 12 A and 12 B of interdigital transducer electrode 12 decreases from the center toward the ends of parallel resonator 8 A.

Series resonator 7 A has excitation region 13 in which a surface acoustic wave propagates between comb electrodes 10 A and 10 B of interdigital transducer electrode 10 to excite comb electrodes 10 A and 10 B. Excitation region 13 includes region (electrode facing region) 14 E and regions (electrode non-facing regions) 14 A to 14 D. The electrode fingers of comb electrode 10 A are positioned interdigitally with the electrode fingers of comb electrode 10 B in electrode facing region 14 E, and are not positioned interdigitally with the electrode fingers of comb electrode 10 B in electrode non-facing regions 14 A to 14 D. The ratio of the sum of the areas of regions 14 A to 14 D to the area of excitation region 13 is defined as an apodized weighting factor of interdigital electrode 10 . Parallel resonator 8 A has excitation region 15 in which a surface acoustic wave propagates between comb electrodes 12 A and 12 B of interdigital transducer electrode 12 to excite comb electrodes 12 A and 12 B. Excitation region 15 includes region (electrode facing region) 16 E and regions (electrode non-facing regions) 16 A to 16 D. The electrode fingers of comb electrode 12 A are positioned interdigitally with the electrode fingers of comb electrode 12 B in electrode facing region 16 E, and are not positioned interdigitally with the electrode fingers of comb electrode 12 B in electrode non-facing regions 16 A to 16 D. Similar to series resonator 7 A, in parallel resonator 8 A, the ratio of the sum of the areas of regions 16 A to 16 D to the area of excitation region 15 is defined as an apodized weighting factor of interdigital electrode 12 . In surface acoustic wave filter 1001 according to the embodiment, the apodized weighting factor of series resonator 7 A is smaller than the apodized weighting factor of parallel resonator 8 A. According to the embodiment, the apodized weighting factors of series resonator 7 A and parallel resonator 8 A are about 0.3 and 0.5, respectively, but are not limited to these values.

Series resonators 7 B and 7 C shown in FIG. 1 have the same structure as series resonator 7 A. Parallel resonator 8 B has the same structure as parallel resonator 8 A.

In surface acoustic wave filter 1001 , series resonator 7 A can have a high Q factor at a resonance frequency while parallel resonator 8 A maintains a high Q factor at an anti-resonance frequency. Characteristics of surface acoustic wave filter 1001 will be described below.

FIG. 3 shows the relation between Q factor Qs 1 of each of series resonators 7 A, 7 B, and 7 C at the resonance frequency and the loss of surface acoustic wave filter 1001 . In FIG. 3 , the vertical axis represents a change of the loss. The loss at Q factor Qs 1 of 500 is determined as a reference loss, and the change of the loss is indicated as a ratio to the reference loss.

As shown in FIG. 3 , the loss of surface acoustic wave filter 1001 increases according to the decreasing of Q factor Qs 1 of series resonators 7 A, 7 B, and 7 C at the resonance frequency from 500 to 100.

FIG. 4 shows the relation between Q factor Qp 1 of series resonators 7 A, 7 B, and 7 C at the anti-resonance frequency and the loss of surface acoustic wave filter 1001 . In FIG. 4 , the vertical axis represents the change of the loss. The loss at Q factor Qp 1 of 500 is determined as a reference loss, and the change of the loss is indicated as a ratio to the reference loss.

As shown in FIG. 4 , Q factor Qp 1 of series resonators 7 A, 7 B, and 7 C at the anti-resonance frequency does not affect the loss of surface acoustic wave filter 1001 very much.

FIG. 5 shows the relation between Q factor Qs 2 of parallel resonators 8 A and 8 B at the resonance frequency and the loss of surface acoustic wave filter 1001 . In FIG. 5 , the vertical axis represents the change of the loss. The loss at Q factor Qs 2 of 500 is determined as a reference loss, and the change of the loss is indicated as a ratio to the reference loss.

As shown in FIG. 5 , Q factor Qs 2 of parallel resonators 8 A and 8 B at the resonance frequency does not affect the loss of surface acoustic wave filter 1001 very much.

FIG. 6 shows the relation between Q factor Qp 2 of parallel resonators 8 A and 8 B at the anti-resonance frequency and the loss of surface acoustic wave filter 1001 . In FIG. 6 , the vertical axis represents the change of the loss. The loss at Q factor Qp 2 of 500 is determined as a reference loss, and the change of the loss is indicated as a ratio to the reference loss.

As shown in FIG. 6 , the loss of the surface acoustic wave filter increases according to the decreasing of Q factor Qp 2 of parallel resonators 8 A and 8 B at the anti-resonance frequency from 500 to 100.

FIGS. 3 to 6 indicate that, in order to reduce the loss of surface acoustic wave filter 1001 at the resonance frequency and the anti-resonance frequency, it is necessary to increase Q factor Qs 1 of series resonators 7 A, 7 B, and 7 C at the resonance frequency and Q factor Qp 2 of parallel resonators 8 A and 8 B at the anti-resonance frequency.

FIG. 7 shows the relation between the apodized weighting factor of resonators 7 A to 7 C, 8 A, and 8 B and Q factors Qs 1 and Qs 2 at the resonance frequency. In FIG. 7 , the vertical axis represents Q factors Qs 1 and Qs 2 as normalized Q factor QsN. Normalized Q factor QsN indicates each of the ratios of Q factors Qs 1 and Qs 2 at the respective apodized weighting factors to Q factors Qs 1 and Qs 2 at the apodized weighting factor of 0.5, respectively.

As shown in FIG. 7 , normalized Q factor QsN, i.e., Q factors Qs 1 and Qs 2 , decreases according to the increasing of the apodized weighting factor. In view of the relation between Q factor Qs 1 of series resonators 7 A to 7 C and the loss shown in FIG. 3 , the apodized weighting factor of series resonators 7 A to 7 C is as small as possible to increase Q factor Qs 1 , thereby reducing the loss at the resonance frequency.

FIG. 8 shows the relation between the apodized weighting factor of resonators 7 A to 7 C, 8 A, and 8 B and Q factors Qp 1 and Qp 2 at the anti-resonance frequency. In FIG. 8 , the vertical axis represents Q factors Qp 1 and Qp 2 as normalized Q factor QpN. Normalized Q factor QpN is the ratio of each of Q factors Qp 1 and Qp 2 at the respective apodized weighting factors to Q factors Qp 1 and Qp 2 at the apodized weighting factor of 0.5, respectively.

As shown in FIG. 8 , normalized Q factor QpN, i.e., Q factors Qp 1 and Qp 2 , increases according to the increasing of the apodized weighting factor. In view of the relation between Q factor Qp 2 of parallel resonators 8 A, 8 B and the loss shown in FIG. 6 , the apodized weighting factor of parallel resonators 8 A and 8 B is as large as possible and as close to 0.5 as possible to increase Q factor Qp 2 , thereby reducing the loss at the anti-resonance frequency.

As shown in FIGS. 7 and 8 , the apodized weighting factor of interdigital transducer electrode 10 of each of series resonators 7 A, 7 B, and 7 C is smaller than the apodized weighting factor of interdigital transducer electrode 12 of each of parallel resonators 8 A and 8 B. This arrangement allows series resonators 7 A, 7 B, and 7 C to have a high Q factor at the resonance frequency while allowing parallel resonators 8 A and 8 B to maintain a high Q factor at the anti-resonance frequency, accordingly reducing the loss in the transmission characteristics of surface acoustic wave filter 1001 .

The apodized weighting factor is also related to the reducing of spurious of a transverse mode. FIG. 9 is a top view of surface acoustic wave resonator 51 as a comparative example. Surface acoustic wave resonator 51 includes piezoelectric substrate 59 and interdigital transducer electrode 17 provided on substrate 59 . Piezoelectric substrate 59 is made of the same material as piezoelectric substrate 9 . Interdigital transducer electrode 17 includes comb electrodes 17 A and 17 B provided on piezoelectric substrate 59 . In excitation region 53 of interdigital transducer electrode 17 , the area of an electrode non-facing region in which the electrode fingers of comb electrodes 17 A and 17 B are not positioned interdigitally with each other is zero. In other words, the apodized weighting factor is zero.

FIG. 10 shows transmission characteristics of resonator 51 . Interdigital transducer electrode 17 is provided over an SiO 2 thin layer having a thickness not less than 15% of the wavelength of a surface acoustic wave propagating through excitation region 53 . As shown in FIG. 10 , surface acoustic wave resonator 51 produces spurious of a transverse mode at frequencies ranging from 1900 MHz to 2100 MHz.

FIG. 11 shows transmission characteristics of a surface acoustic wave filter including an interdigital transducer electrode having an apodized weighting factor of 0.225. As shown in FIG. 11 , this surface acoustic wave filter is prevented from allowing the spurious of the transverse mode at frequencies ranging from 1900 MHz to 2100 MHz.

Thus, the apodized weighting factor of interdigital transducer electrode 10 of series resonators 7 A to 7 C shown in FIG. 2 is determined to be larger than zero to prevent the spurious.

The apodized weighting factor of interdigital transducer electrode 12 of parallel resonators 8 A and 8 B is preferably not smaller than 0.5. This reduces the spurious of the transverse mode and increases the Q factor of parallel resonators 8 A and 8 B at the anti-resonance frequency, thereby reducing the loss of transmission characteristics of surface acoustic wave filter 1001 .

Piezoelectric substrate 9 is preferably made of −30° to +30° rotated Y-cut lithium niobate. Cut angles within this range provides surface acoustic wave filter 1001 with a wide bandwidth.

FIG. 12 is a sectional view of surface acoustic wave filter 1001 . Electrode fingers 101 of interdigital transducer electrodes 10 and 12 may be covered with dielectric layer 31 . Dielectric layer 31 is provided on upper surface 9 A of piezoelectric substrate 9 and upper surfaces 101 A of electrode fingers 101 . Dielectric layer 31 may be preferably made of SiO 2 and have a thickness not less than 15% of the wavelength of the surface acoustic wave which propagates through the excitation region, thereby reducing the loss of the surface acoustic wave and improving temperature characteristics.

Dielectric layer 31 has upper surface 31 A including projection 31 C and flat portion 31 D. Projection 31 C covers electrode finger 101 along finger 101 . Flat portion 31 D is connected with projection 31 C and provided on upper surface 9 A of piezoelectric substrate 9 . Projection 31 C has upper surface 31 E located directly above electrode finger 101 and slanting portion 31 F extending slantingly from upper surface 31 E to flat portion 31 D and flat portion 31 A. Upper surface 31 E is parallel to upper surface 101 A of electrode finger 101 . Upper surface 31 E of projection 31 C have a width smaller than that of upper surfaces 101 A of electrode fingers 101 , thereby reducing spurious caused by Rayleigh waves.

Interdigital transducer electrodes 10 and 12 are made of material, such as Al or Cu, having a high conductivity. Interdigital transducer electrodes 10 and 12 are made of heavy material, such as Au, Ag, or Cu, to have so large weights that the surface acoustic wave can be confined in piezoelectric substrate 9 , thereby reducing the loss of surface acoustic wave filter 1001 .

FIG. 13 is a sectional view of another interdigital transducer electrode 201 of surface acoustic wave filter 1001 . Interdigital transducer electrode 201 includes lower layer 211 provided on upper surface 9 A of piezoelectric substrate 9 and upper layer 221 provided on lower layer 211 . Lower layer 211 is made of Ti. Upper layer 221 is made of Al-based alloy. This electrode can improve withstanding characteristics of surface acoustic wave filter 1001 against high power.

FIG. 14 is a sectional view of boundary acoustic wave filter 1002 according to the embodiment. Boundary acoustic wave filter 1002 further includes medium layer 109 provided on upper surface 9 A of piezoelectric substrate 9 and on interdigital transducer electrodes 10 and 12 of surface acoustic wave filter 1001 shown in FIG. 2 . A propagation speed of transverse waves through medium layer 109 is lower than that of transverse waves in piezoelectric substrate 9 . This arrangement causes acoustic waves to be confined on the boundary between piezoelectric substrate 9 and medium layer 109 . If piezoelectric substrate 9 is made of lithium niobate, medium layer 109 is made of SiO 2 . Thereby, the boundary acoustic wave filter with excellent temperature characteristics is provided.

FIG. 15 is a circuit diagram of antenna duplexer 1003 according to the embodiment. Antenna duplexer 1003 includes antenna terminal 18 arranged to be connected to an antenna, transmitting terminal 19 arranged to connected to a transmitting circuit, receiving terminal 20 arranged to be connected to an receiving circuit, transmitting filter 21 , and receiving filter 22 . Transmitting filter 21 is connected between antenna terminal 18 and transmitting terminal 19 . Receiving filter 22 is connected between antenna terminal 18 and receiving terminal 20 . At least one of transmitting filter 21 and receiving filter 22 is surface acoustic wave filter 1001 or boundary acoustic wave filter 1002 , providing antenna duplexer 1002 with low loss.

Surface acoustic wave filter 1001 shown in FIG. 2 includes series resonators 7 A to 7 C and parallel resonators 8 A and 8 B on single piezoelectric substrate 9 . According to the embodiment, series resonators 7 A to 7 C may be formed on a piezoelectric substrate different from the piezoelectric substrate having parallel resonators 8 A and 8 B formed thereon.

Surface acoustic wave filter 1001 includes three series resonators 7 A to 7 C and two parallel resonators 8 A and 8 B. Alternatively, the surface acoustic wave filter may include at least one series resonator and at least one parallel resonator, having the same effects to reducing loss.

In the surface acoustic wave resonator including the dielectric layer 31 made of SiO 2 , the interdigital transducer electrodes 11 and 12 , and the piezoelectric substrate 9 made of lithium niobate shown in FIG. 12 , the apodized weighting factor may be determined to suppress the spurious in the transverse mode, however, the resonator do not suppress a spurious due to a Rayleigh mode may occur in a frequency region lower than the resonance frequency. FIGS. 16A and 16B show transmission characteristics and an admittance of the surface acoustic wave resonator, respectively. The spurious 1801 shown in FIG. 16A has a large level of 0.2 dB, and the spurious 1802 of the admittance shown in FIG. 16B has a large level of 1.0 dB. Upon being utilized in a ladder-type filter and an antenna duplexer, this surface acoustic wave resonator may cause the spurious to have the characteristics deteriorate in the region.

The spurious due to the Rayleigh mode can be suppressed by making a metallization ratio of a surface acoustic wave resonator of a surface acoustic wave filter having a high resonance frequency be larger than a metallization ratio of a surface acoustic wave resonator having a low resonance frequency.

FIGS. 17A and 17B are sectional views of the surface acoustic wave filter 1001 . The dielectric layer 31 provided on the upper surface 9 A of the piezoelectric substrate 9 and on the upper surface 101 A of the electrode finger 101 has a shape along the upper surface 9 A of the piezoelectric substrate 9 and the upper surface 101 A of the electrode finger 101 . The width LB of the upper surface 31 E of the projection 31 C of the dielectric layer 31 directly above the upper surface 101 A of the electrode finger 101 shown in FIG. 17B is smaller than the width LA of the upper surface 31 E of the projection 31 C of the dielectric layer 31 directly above the upper surface 101 A of the electrode finger 101 shown in FIG. 17A . The projection 31 C of the dielectric layer 31 may be formed by, for example, applying a bias voltage to the piezoelectric substrate when the dielectric layer 31 is formed. The bias voltage is increased to reduce the width of the upper surface 31 E of the projection 31 C.

FIGS. 18A and 18B show transmission characteristics and an admittance of the surface acoustic wave resonator having the width LB of the upper surface 31 E shown in FIG. 17B . The spurious 201 of the transmission characteristics shown in FIG. 18A is suppressed to 0.05 dB. The spurious 202 of the admittance shown in FIG. 18B is suppressed to 0.1 dB. Thus, the condition for forming the dielectric layer 31 may be controlled to suppress the spurious. However, this method may have characteristics of the resonator slightly deteriorate. In particular, the Q factor at the anti-resonance frequency is reduced from 180 to 120, and the level at the pole of the attenuation deteriorates from 24.5 dB to 22.0 dB. This may cause the transmission loss to deteriorate if the surface acoustic wave resonator is used as the parallel resonator of the ladder-type surface acoustic wave filter.

The characteristics of the resonator depending on the metallization ratio of the comb electrodes were evaluated. FIG. 19 is an enlarged plan view of each of the surface acoustic wave resonators 7 A to 7 C shown in FIG. 2 . The comb electrodes 10 A and 10 B ( 12 A and 12 B) facing each other have the electrode fingers 101 extending in a direction 91 A. The electrode fingers 101 faces in a direction 91 B perpendicular to the direction 91 A. The metallization ratio η and a pitch P 1 are defined on the width W 1 of the finger 101 and the distance D 1 between the fingers 101 in the direction 91 B as follows.

P 1= W 1+ D 1

η= W 1/ P 1

FIG. 20 shows the relation between the Q factor at the anti-resonance frequency and the metallization ratio η of the resonator. In FIG. 20 , the vertical axis represents the Q factor which is normalized on the Q factor at the metallization ratio η of 0.50. As shown in FIG. 20 , the Q factor increases as the metallization ratio η increases. FIGS. 21A and 21B show transmission characteristics and an admittance at η=0.45, respectively. FIGS. 22A and 22B show transmission characteristics and an admittance at η=0.50, respectively. FIGS. 23A and 23B show transmission characteristics and an admittance at η=0.55, respectively. The pitch P 1 is 1.00 μm. Piezoelectric substrate 9 is made of 5° rotated Y-cut lithium niobate. The ratio of the thickness of the comb electrodes 10 A and 10 B ( 12 A and 12 B) to the wavelength of the acoustic wave propagating on the piezoelectric substrate 9 is 8%. The ratio of the dielectric layer 31 to the wavelength of the acoustic wave is 10%. The comb electrodes 10 A and 10 B ( 12 A and 12 B) essentially contains aluminum. The spurious in a frequency region higher than the resonance frequency is caused in the transverse mode, and is suppressed by adjusting the apodized weighting factor. Spurious 501 , 502 , 601 , 602 , 701 , and 702 in the frequency region lower than the resonance frequency increases as the metallization ratio 11 increases. FIG. 24A shows the relationship between the metallization ratio η and the spurious of the transmission characteristics. FIG. 24B shows the relationship between the metallization ratio η and the spurious of the admittance. As shown in FIGS. 24A and 24B , the spurious increases as the metallization ratio η increases. Thus, if the metallization ratio η increases, the Q factor and the level at the attenuation pole are improved, however, the spurious increases. In other words, in that case that the metallization ratio η is small, the bias voltage applied at the forming of the dielectric layer 31 may be reduced, accordingly improving the characteristics.

Then, the characteristics depending on the pitch P 1 of the comb electrodes 10 A and 10 B ( 12 A and 12 B) were evaluated. FIGS. 25A and 25B show transmission characteristics and an admittance of the resonator having the pitch P 1 of 0.95 μm, respectively. FIGS. 26A and 26B show the transmission characteristics and the admittance of the resonator having the pitch P 1 of 1.05 μm, respectively. The metallization ratio η is 0.50. The characteristics of the resonator having the pitch of 1.00 μm correspond to those shown in FIGS. 22A and 22B . In FIGS. 25A , 25 B, 26 A, and 26 B, the spurious in a frequency region higher than the resonance frequency is caused in the transverse mode, and is suppressed by adjusting the apodized weighting factor. Spurious 901 , 902 , 2001 , and 2002 increases as the pitch P 1 increases. FIG. 27A shows the relationship between the pitch P 1 and the transmission characteristics. FIG. 27B shows the relationship between the pitch P 1 and the admittance. As shown in FIGS. 27A and 27B , the spurious increases as the pitch P 1 increases. That is, the spurious increases as the resonance frequency of the resonator increases.

As described in above, three conditions of the surface acoustic wave resonator were confirmed regarding the spurious in the frequency region lower than the resonance frequency. The first condition is that the bias voltage applied to the piezoelectric substrate 9 for forming the dielectric layer 31 is increased to control the shape of the dielectric layer 31 , accordingly suppressing the spurious, however, having characteristics particularly at the anti-resonance frequency of the surface acoustic wave resonator deteriorate. The second condition is that the increasing of the metallization ratio η of the comb electrodes 10 A and 10 B ( 12 A and 12 B) increases the Q factor at the anti-resonance frequency, however, increases the spurious. The third condition is that the decreasing of the pitch P 1 of the comb electrodes 10 A and 10 B ( 12 A and 12 B), i.e., the increasing of the resonance frequency increases the spurious.

In the case that a ladder-type filter includes plural surface acoustic wave resonators, in general, the surface acoustic wave resonators provided at series arms have resonance frequencies different from those of the surface acoustic wave resonators provided at parallel arms. In order to provide a band-pass characteristic, the resonance frequencies of the surface acoustic wave resonators 7 A to 7 C are determined to be higher than the resonance frequencies of the surface acoustic wave resonators 8 A and 8 B. If the bias voltage applied to the piezoelectric substrate 9 is determined such that the spurious in the region lower than the resonance frequencies of the resonators 7 A to 7 B provided at the series arms, the bias voltage becomes excessively high for the resonators 8 A and 8 B provided at the parallel arm, and may have characteristics of the resonators 8 A and 8 B deteriorate. The deteriorating of the characteristics of the resonators 8 A and 8 B provided at the parallel arms can be suppressed based on the above three conditions of the spurious, thereby providing the surface acoustic wave filter 1001 with preferable characteristics. That is, the metallization ratio of the surface acoustic wave resonators 7 A to 7 C having high resonance frequencies are determined to be larger than the metallization ratio of the surface acoustic wave resonators 8 A and 8 B having low resonance frequencies, thereby suppressing the spurious in the Rayleigh mode.

Thus, the apodized weighting factor and the metallization ratio 1 of the surface acoustic wave resonator are determined appropriately to reduce the spurious in both the transverse mode and the Rayleigh mode, thus providing the filter 1001 with preferable characteristics. The apodized weighting factor and the metallization ratio η are also applicable to the boundary acoustic wave filter 1002 shown in FIG. 14 , providing the same effects.

Terms, such as “upper surface” and “directly above”, indicating directions do not indicate absolute directions, such as vertical directions, but indicate relative directions defined by the positions of components, such as piezoelectric substrate 9 .