Patent Publication Number: US-2021184324-A1

Title: Filter device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority to Japanese Patent Application No. 2020-110656 filed on Jun. 26, 2020 and Japanese Patent Application No. 2019-223404 filed on Dec. 11, 2019. The entire contents of these applications are hereby incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a filter device. 
     2. Description of the Related Art 
     As a bandpass filter used in a communication apparatus, such as in a mobile information terminal, a filter using surface acoustic wave (SAW) elements is utilized. To support multiple frequency bands with one antenna, a multiplexer including multiple duplexers is used. A multiplexer includes a plurality of bandpass filters, for example. An example of such a multiplexer is disclosed in International Publication No. 2018/003297. 
     To achieve a desired pass band, a bandpass filter using SAW elements includes multiple SAW resonators connected with each other. In a SAW resonator utilizing leaky waves or shear horizontal (SH) waves as the main waves, resonance may be produced due to unwanted waves, such as Rayleigh waves, at a frequency lower than the fundamental resonant frequency of the main waves. This may cause a ripple in the bandpass characteristics in the stopband of the bandpass filter, which may adversely influence the attenuation characteristics in the stopband of the bandpass filter. 
     Additionally, when a plurality of bandpass filters having different pass bands are connected to a single common terminal, a ripple due to unwanted waves produced in one bandpass filter may adversely influence the bandpass characteristics in the pass band of a different bandpass filter if the frequency of the ripple is included in the pass band of this different bandpass filter. 
     SUMMARY OF THE INVENTION 
     Preferred embodiments of the present invention provide filter devices that are each able to reduce ripples caused by unwanted waves. 
     According to a preferred embodiment of the present invention, a filter device includes a common terminal, first and second individual terminals, and first and second filters. The first filter is connected between the common terminal and the first individual terminal. The second filter is connected between the common terminal and the second individual terminal. The pass band of the second filter is in a frequency range lower than the pass band of the first filter. The first filter includes a plurality of surface acoustic wave (SAW) resonators. At least one of the plurality of SAW resonators is includes a plurality of divided resonators connected in parallel with each other. Each of the plurality of divided resonators includes an interdigital transducer (IDT). The plurality of divided resonators include at least two divided resonators. Among the at least two divided resonators, the pitch of the IDT of a divided resonator is different from that of another divided resonator. 
     According to a preferred embodiment of the present invention, a filter device includes a SAW filter including plurality of SAW resonators. At least one of the plurality of SAW resonators includes a plurality of divided resonators connected in parallel with each other. Each of the plurality of divided resonators includes an IDT. Among the plurality of divided resonators, the pitch of the IDT of a divided resonator is different from that of another divided resonator. (Pmax−Pmin)/Pa is about 0.7% or smaller, where Pa is the average of the pitches of the IDTs of the plurality of divided resonators, and Pmax and Pmin are the maximum value and the minimum value, respectively, of the pitches of the IDTs of the plurality of divided resonators. 
     According to a preferred embodiment of the present invention, a filter device includes a substrate and a plurality of SAW resonators. The substrate is made of a piezoelectric material. The plurality of SAW resonators are disposed on the substrate and are connected with each other. At least one of the plurality of SAW resonators includes a plurality of divided resonators connected in parallel with each other. Each of the plurality of divided resonators includes an IDT. Among the plurality of divided resonators, the pitch of the IDT of a divided resonator is different from that of another divided resonator. Among the plurality of divided resonators, the arrangement direction of electrode fingers of the IDT of a divided resonator is parallel or substantially parallel with that of another divided resonator. The IDTs of the plurality of divided resonators are displaced from each other in a direction perpendicular or substantially perpendicular to the arrangement direction of the electrode fingers. 
     With the use of SAW resonators including a plurality of parallel-connected divided resonators, ripples caused by unwanted waves produced in each of the SAW resonators are able to be reduced. 
     The above and other elements, features, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an equivalent circuit diagram of a filter device according to a first preferred embodiment of the present invention. 
         FIG. 2  is an equivalent circuit diagram of a filter device according to a comparative example. 
         FIG. 3A  is a graph schematically illustrating the bandpass characteristics of the filter device of the first preferred embodiment of the present invention shown in  FIG. 1 . 
         FIG. 3B  is a graph schematically illustrating the bandpass characteristics of the filter device of the comparative example shown in  FIG. 2 . 
         FIGS. 4A and 4B  are schematic plan views illustrating examples of the arrangement of interdigital transducers (IDTs) of two parallel-connected divided resonators of the filter device shown in  FIG. 1 . 
         FIG. 5  is an equivalent circuit diagram of a filter device according to a second preferred embodiment of the present invention. 
         FIG. 6  illustrates the arrangement of SAW resonators, longitudinally coupled SAW filters, wires, terminals, and other components included in the filter device of the second preferred embodiment of the present invention as viewed from above. 
         FIG. 7  is an equivalent circuit diagram of a filter device according to a comparative example. 
         FIGS. 8A and 8B  are graphs illustrating the measurement results of the bandpass characteristics in the path from a common terminal to a second individual terminal in the filter device of the second preferred embodiment of the present invention shown in  FIG. 5 . 
         FIGS. 8C and 8D  are graphs illustrating the measurement results of the bandpass characteristics in the path from a common terminal to a second individual terminal in the filter device of the comparative example shown in  FIG. 7 . 
         FIG. 9  is a graph illustrating the measurement results of the bandpass characteristics in the path from the common terminal to a first individual terminal in the filter device of the second preferred embodiment of the present invention shown in  FIG. 5  and those of the filter device of the comparative example shown in  FIG. 7 . 
         FIG. 10A  is an enlarged graph showing a specific frequency range in the graph of  FIG. 9 . 
         FIG. 10B  is an enlarged graph showing a specific frequency range in the graph of  FIG. 10A . 
         FIG. 11  is a graph illustrating the simulation results of the bandpass characteristics obtained while the IDT pitch of one divided resonator of the filter device of the second preferred embodiment of the present invention is fixed and the IDT pitch of the other divided resonator is varied. 
         FIG. 12  is a graph illustrating the relationship between the pass band of a first bandpass filter and that of a second bandpass filter in the filter device of the second preferred embodiment of the present invention on the frequency axis. 
         FIG. 13A  is a circuit diagram of a ladder bandpass filter configured similarly to the first bandpass filter of the filter device of the second preferred embodiment of the present invention. 
         FIG. 13B  is a circuit diagram of a ladder bandpass filter configured differently from that in  FIG. 13A . 
         FIG. 14  is an equivalent circuit diagram of a filter device according to a third preferred embodiment of the present invention. 
         FIGS. 15A and 15B  are graphs illustrating the measurement results of the bandpass characteristics in the path from a common terminal to a second individual terminal in the filter device of the third preferred embodiment of the present invention shown in  FIG. 14 . 
         FIGS. 15C and 15D  are graphs illustrating the measurement results of the bandpass characteristics in the path from the common terminal to the second individual terminal in the filter device of the comparative example shown in  FIG. 7 . 
         FIG. 16  is a block diagram of a communication apparatus according to a fourth preferred embodiment of the present invention. 
         FIG. 17A  is an equivalent circuit diagram of a filter device according to a fifth preferred embodiment of the present invention. 
         FIG. 17B  is an equivalent circuit diagram of a filter device according to a modified example of the fifth preferred embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will be described in detail below with reference to the drawings. 
     First Preferred Embodiment 
     A filter device according to a first preferred embodiment will be described below with reference to  FIGS. 1 through 4B . 
       FIG. 1  is an equivalent circuit diagram of a filter device  20  according to the first preferred embodiment. The filter device  20  is a ladder filter device including a plurality of surface acoustic wave (SAW) resonators  21 . Parallel arms branch off from branch nodes  27  of a series arm connecting a first terminal  25  and a second terminal  26 . Each of the parallel arms is grounded on the other side opposite the corresponding branch node of the series arm. A ladder filter device refers to a filter device using series elements and parallel elements of a ladder circuit as resonators. A ladder circuit includes one input terminal, one output terminal, and a ground terminal to which an input/output ground potential is supplied. The series elements are elements connected between the input terminal and the output terminal of the ladder circuit. The parallel elements are elements connected between the corresponding series elements and the ground potential. 
     At least one SAW resonator  21  is interposed between two adjacent branch nodes  27  of the series arm and also on each of multiple parallel arms. The SAW resonators  21  disposed on the series arm may also be called series arm resonators, while the SAW resonators  21  disposed on the parallel arms may also be called parallel arm resonators. The SAW resonator  21 , which is the series arm resonator disposed between the first and second branch nodes as seen from the first terminal  25 , includes two divided resonators  22  connected in parallel with each other. Each of the divided resonators  22  includes an interdigital transducer (IDT) including a pair of interlocking comb-shaped electrodes. The pitch of multiple electrode fingers of the IDT (hereinafter simply called the IDT pitch) of one divided resonator  22  is different from that of the other divided resonator  22 . The SAW resonators  21  are designed to utilize, for example, leaky waves or shear horizontal (SH) waves as the main waves. 
     In a broad sense, each of the divided resonators  22  can be regarded as one SAW resonator. In this specification, however, a SAW resonator including a plurality of parallel-connected divided resonators is distinguished from a SAW resonator which is a resonator divided from this SAW resonator. Due to the manufacturing variations, the IDT pitch may be varied within an allowance. In this case, the IDT pitch P is defined as P=L/(N−1) where L is the center-to-center distance between the electrode fingers of an IDT positioned at both ends and N is the number of electrode fingers. 
     Advantages of the first preferred embodiment will be explained below in comparison with a comparative example. 
       FIG. 2  is an equivalent circuit diagram of a filter device  20  according to a comparative example. The circuit configuration of the filter device  20  according to the comparative example is the same or substantially the same as that of the first preferred embodiment shown in  FIG. 1 , except for the following point. As opposed to the SAW resonator  21  including the two divided resonators  22  in the first preferred embodiment, the corresponding SAW resonator  21  in the comparative example is not divided into multiple resonators, but includes the single SAW resonator. The other SAW resonators  21  in the comparative example have the same or substantially the same characteristics as those of the first preferred embodiment. 
       FIG. 3A  is a graph schematically illustrating the bandpass characteristics of the filter device  20  according to the first preferred embodiment ( FIG. 1 ).  FIG. 3B  is a graph schematically illustrating the bandpass characteristics of the filter device  20  according to the comparative example ( FIG. 2 ). In  FIGS. 3A and 3B , only distinctive portions are shown in detail, while the other portions are shown in a simplified manner. In the graphs, the horizontal axis indicates the frequency, while the vertical axis indicates the insertion loss. The insertion loss increases downward on the vertical axis. 
     Both of the filter device  20  of the first preferred embodiment and that of the comparative example are bandpass filters having a lower cutoff frequency at fL and a higher cutoff frequency at fH. In the filter device  20  of the first preferred embodiment ( FIG. 1 ), two ripples  80  occur in the frequency range lower than the pass band. The pass band of a bandpass filter is the frequency band between the lower cutoff frequency and the higher cutoff frequency. As the lower cutoff frequency and the higher cutoff frequency, the frequencies at which the highest level of power in the pass band drops by about 3 dB, in other words, the frequencies at which the smallest insertion loss increases by about 3 dB, are used. The ripples  80  occur due to unwanted waves produced in the respective two divided resonators  22 , and more specifically, due to Rayleigh waves. Ripples caused by Rayleigh waves may also be called a Rayleigh response. Since the IDT pitch of one divided resonator  22  is different from that of the other divided resonator  22 , the resonant frequencies of the two divided resonators  22  corresponding to the unwanted waves slightly differ from each other. This is why the two ripples  80  occur in response to the two divided resonators  22 . 
     In contrast, in the filter device  20  of the comparative example ( FIG. 2 ), the SAW resonator  21  corresponding to the SAW resonator  21  including the two divided resonators  22  in the first preferred embodiment includes only a single SAW resonator. As a ripple caused by unwanted waves produced in this SAW resonator  21 , only one ripple  81  is observed, as shown in  FIG. 3B . The insertion loss at the frequency at which the ripple  81  is observed is smaller than that in the other portions of the stopband, thus failing to obtain desired filter characteristics. It is thus preferable to regulate a drop in the insertion loss caused by the ripple  81  so that the insertion loss at the frequency of the ripple  81  becomes as large as that in the other portions of the stopband. 
     In the first preferred embodiment, the two ripples  80  occur in response to the unwanted waves. Accordingly, a drop in the insertion loss caused by each of the two ripples  80  becomes smaller than that by the single ripple  81  in the comparative example. In the first preferred embodiment, therefore, the attenuation characteristics in the frequency bands other than the pass band are not decreased as much as those of the comparative example. 
     The difference in the IDT pitch between the two divided resonators  22  is small, and the total capacitance of the two divided resonators  22  is equal or substantially equal to the capacitance of the corresponding single SAW resonator  21  of the filter device  20  of the comparative example. Thus, even if the single SAW resonator  21  is replaced by the two divided resonators  22  after a filter is designed with the circuit configuration of the comparative example ( FIG. 2 ), the filter characteristics of the pass band and its adjacent bands remain almost unchanged. It is thus not necessary to design a new filter in the configuration in which the single SAW resonator  21  is replaced by the two divided resonators  22 . Accordingly, it does not become more difficult to design the filter device  20  of the first preferred embodiment than to design the comparative example. 
     If the difference in the IDT pitch between the two divided resonators  22  is too small, the two ripples  80  occurring in response to unwanted waves do not sufficiently separate from each other. This fails to fully achieve the advantageous effect of regulating a drop in the insertion loss caused by the ripples  80 . If the difference in the IDT pitch between the two divided resonators  22  is too large, the filter characteristics of the pass band and its adjacent bands significantly vary. It is thus preferable to set the difference in the IDT pitch between the two divided resonators  22  so that the ripples  80  can be clearly separated from each other and the filter characteristics of the pass band and its adjacent bands are not significantly influenced. As an example, Pd/Pa is preferably set to be about 0.02% to about 0.7%, where Pd is the difference in the IDT pitch between the two divided resonators  22  and Pa is the average of the IDT pitches of the two divided resonators  22 . The basis for the upper limit and the lower limit in this preferable range of the difference in the IDT pitch will be discussed later with reference to  FIG. 11 . 
     The arrangement of the IDTs of the two divided resonators  22  ( FIG. 1 ) will be discussed below with reference to  FIGS. 4A and 4B . 
       FIG. 4A  is a schematic plan view illustrating an example of the arrangement of the IDTs of the two divided resonators  22  ( FIG. 1 ). Electrode fingers of the IDTs shown in  FIG. 4A  are fewer than those of the actual IDTs. A pair of interlocking comb-shaped electrodes  221  define an IDT  222 . The pitch of the IDT  222  of one divided resonator  22  is indicated by P 1 , while that of the other divided resonator  22  is indicated by P 2 . The multiple electrode fingers of the IDTs  222  of the two divided resonators  22  are aligned. Reflectors  223  are disposed at both sides of each of the two IDTs  222 . The reflectors  223  reflect SAWs having the resonance wavelength of the corresponding IDT  222 . 
       FIG. 4B  is a schematic plan view illustrating another example of the arrangement of the IDTs of the two divided resonators  22  ( FIG. 1 ). In the example in  FIG. 4B , the arrangement direction of the plurality of electrode fingers of the IDT  222  of one divided resonator  22  is parallel or substantially parallel with that of the other divided resonator  22 . The two IDTs  222  are displaced from each other in the direction perpendicular or substantially perpendicular to the arrangement direction of the electrode fingers. The reflector  223  disposed at one side of one IDT  222  partially overlaps the other IDT  222  or the reflector  223  disposed at one side of the other IDT  222  in the arrangement direction of the electrode fingers. 
     It is possible to make the total dimensions of the two divided resonators  22  shown in  FIG. 4A  smaller than those in  FIG. 4B  in the direction perpendicular or substantially perpendicular to the arrangement direction of the electrode fingers. It is possible to make the total dimensions of the two divided resonators  22  shown in  FIG. 4B  smaller than those in  FIG. 4A  in the direction parallel or substantially parallel with the arrangement direction of the electrode fingers. A preferable one of the two arrangements shown in  FIGS. 4A and 4B  may be selected in terms of the relationship with the other SAW resonators  21  ( FIG. 1 ). 
     Various modified examples of the first preferred embodiment will be described below. 
     In the first preferred embodiment ( FIG. 1 ), the SAW resonator  21  interposed between the first and second branch nodes  27  of the series arm as seen from the first terminal  25  includes two divided resonators  22 . Another SAW resonator  21  may include two divided resonators  22 . For example, the SAW resonator  21  disposed between branch nodes  27  of the series arm positioned closer to the second terminal  26  with respect to the second branch node  27  seen from the first terminal  25  may include two divided resonators  22 . A SAW resonator  21  disposed on a parallel arm may include two divided resonators  22 . 
     In the first preferred embodiment ( FIG. 1 ), one SAW resonator  21  includes two divided resonators  22 , for example. Alternatively, each of multiple SAW resonators  21  may include two parallel-connected divided resonators  22 . Additionally, one or multiple SAW resonators  21  may each include three or more parallel-connected divided resonators  22 , for example. In this case, it is preferable that (Pmax−Pmin)/Pa is about 0.02% to about 0.7%, where Pmax and Pmin are the maximum value and the minimum value, respectively, of the IDT pitches of the multiple divided resonators  22 , and Pa is the average of the IDT pitches of the multiple divided resonators  22 . 
     In the first preferred embodiment ( FIG. 1 ), both of the series arm resonator and the parallel arm resonator are connected to the first terminal  25 , while only the series arm resonator is connected to the second terminal  26 . Alternatively, both of the series arm resonator and the parallel arm resonator may be connected to each of the first and second terminals  25  and  26 . Conversely, parallel arm resonators may be connected to neither of the first terminal  25  nor the second terminal  26 . 
     In the first preferred embodiment ( FIG. 1 ), the ladder filter includes a plurality of series arm resonators and a plurality of parallel arm resonators, for example. However, the ladder filter may include one series arm resonator and a plurality of parallel arm resonators, or a plurality of series arm resonators and one parallel arm resonator, or one series arm resonator and one parallel arm resonator. In such a ladder filter, at least one SAW resonator may include multiple parallel-connected divided resonators. For example, a T-type filter, a  7 L-type filter, and an L-type filter are examples of such a ladder filter. A filter device including a plurality of SAW resonators provided in a circuit configuration other than that of the ladder filter of the first preferred embodiment ( FIG. 1 ), may be used. In such a filter device, one of the SAW resonators may include multiple parallel-connected divided resonators. 
     In the first preferred embodiment ( FIG. 1 ), leaky waves or SH waves, for example, are preferably utilized as the main waves. Although the ripples  80  occur due to Rayleigh waves, which are unwanted waves, in a stopband of the bandpass characteristics, a drop in the insertion loss caused by the ripples  80  can be regulated. Alternatively, another type of acoustic waves may be utilized as the main waves. In this case, although ripples  80  occur due to unwanted waves in the frequency range lower than the resonant frequency of the main waves, a drop in the insertion loss caused by the ripples  80  can be regulated by the application of the configuration of the first preferred embodiment. 
     In the first preferred embodiment, the IDT pitch of the same divided resonator  22  is preferably constant or substantially constant. However, the IDT pitch may be changed, for example, progressively or in a stepwise manner in the same divided resonator  22 . The IDT pitch of a SAW resonator  21  other than the SAW resonator  21  including the divided resonators  22  may also be changed. Changing the IDT pitch in the same SAW resonator  21  can reduce ripples in the pass band. 
     If the IDT pitch is varied in each of the two divided resonators  22 , the average of the IDT pitches of one divided resonator  22  is set to be different from that of the other divided resonator  22 . As an example, when the average IDT pitch of one divided resonator  22  is Pa 1  and that of the other divided resonator  22  is Pa 2 , the difference between the average IDT pitches Pa 1  and Pa 2  is used as the difference Pd in the IDT pitch between the two divided resonators  22 , and the average of the average pitches Pa 1  and Pa 2  is used as the average Pa of the IDT pitches of the two divided resonators  22 . As in the first preferred embodiment, Pd/Pa is preferably set to be about 0.02% to about 0.7%, for example. 
     Second Preferred Embodiment 
     A filter device according to a second preferred embodiment of the present invention will be described below with reference to  FIGS. 5 through 13B . An explanation of the elements configured similarly to those of the filter device  20  of the first preferred embodiment ( FIG. 1 ) will be omitted. 
       FIG. 5  is an equivalent circuit diagram of a filter device  20  according to the second preferred embodiment. The filter device  20  of the second preferred embodiment includes a first bandpass filter  30 , a second bandpass filter  40 , a third bandpass filter  50 , a common terminal  60 , a first individual terminal  31 , a second individual terminal  41 , and a third individual terminal  51 . The first bandpass filter  30  is connected between the common terminal  60  and the first individual terminal  31 . The second bandpass filter  40  is connected between the common terminal  60  and the second individual terminal  41 . The third bandpass filter  50  is connected between the common terminal  60  and the third individual terminal  51 . 
     The common terminal  60  is connected to an antenna  68 . An impedance matching inductor  61  is connected between the common terminal  60  and a ground. The first, second, and third individual terminals  31 ,  41 , and  51  are connected to a low-noise amplifier  63  via a switch  62 . Impedance matching inductors  65 ,  66 , and  67  are respectively connected between the first, second, and third individual terminals  31 ,  41 , and  51  and a ground. 
     The filter device  20  of the second preferred embodiment is a receiver triplexer that separates radio-frequency (RF) signals received by the antenna  68  into RF signals in three frequency bands. For example, the pass bands of the first, second, and third bandpass filters  30 ,  40 , and  50  preferably correspond to those standardized by the third generation partnership project (3GPP). More specifically, for example, the pass band of the first bandpass filter  30  is equal or substantially equal to Band  41  downlink frequency band (about 2496 MHz to about 2690 MHz), the pass band of the second bandpass filter  40  is equal or substantially equal to Band  66  downlink frequency band (about 2110 MHz to about 2200 MHz), and the pass band of the third bandpass filter  50  is equal or substantially equal to Band  3  downlink frequency band (about 1805 MHz to about 1880 MHz). That is, the pass band of the second bandpass filter  40  is lower than that of the first bandpass filter  30 , and the pass band of the third bandpass filter  50  is lower than that of the second bandpass filter  40 . 
     Each of the first, second, and third bandpass filters  30 ,  40 , and  50  is preferably a ladder SAW filter, for example. 
     The first bandpass filter  30  includes SAW resonators  32 A,  32 B,  32 C, and  32 D and one longitudinally coupled SAW filter  33 . The SAW resonator  32 B is disposed between the first and second branch nodes of the series arm as seen from the common terminal  60 . As in the SAW resonator  21  disposed between the first and second branch nodes  27  of the series arm as seen from the first terminal  25  in the filter device  20  of the first preferred embodiment ( FIG. 1 ), the SAW resonator  32 B includes two parallel-connected divided resonators  34 . The longitudinally coupled SAW filter  33  is inserted between the SAW resonator  32 B and the second branch node. 
     No SAW resonator is interposed between the common terminal  60  and the first branch node as seen from the common terminal  60 . The SAW resonator  32 D is connected between the second branch node and the first individual terminal  31 . As seen from the common terminal  60 , the SAW resonator  32 A is disposed on the parallel arm which branches off from the first branch node of the series arm, while the SAW resonator  32 C is disposed on the parallel arm which branches off from the second branch node of the series arm. Each of the SAW resonators  32 A,  32 C, and  32 D may include a plurality of divided resonators connected in series with each other. 
     The second bandpass filter  40  includes five SAW resonators  42 A,  42 B,  42 C,  42 D, and  42 E and one longitudinally coupled SAW filter  43 . The SAW resonator  42 A is connected between the common terminal  60  and the first branch node as seen from the common terminal  60 . The SAW resonator  42 C and the longitudinally coupled SAW filter  43  are connected in series with each other between the first and second branch nodes. The SAW resonator  42 E is connected between the second branch node and the second individual terminal  41 . The SAW resonator  42 B is disposed on the parallel arm which branches off from the first branch node of the series arm, while the SAW resonator  42 D is disposed on the parallel arm which branches off from the second branch node of the series arm. Each of the SAW resonators  42 A through  42 E may include a plurality of series-connected divided resonators. 
     The third bandpass filter  50  includes four SAW resonators  52 A,  52 B,  52 C, and  52 D and one longitudinally coupled SAW filter  53 . The SAW resonator  52 A is connected between the common terminal  60  and the first branch node as seen from the common terminal  60 . The SAW resonator  52 C and the longitudinally coupled SAW filter  53  are connected in series with each other between the first and second branch nodes. The SAW resonator  52 B is disposed on the parallel arm which branches off from the first branch node of the series arm, while the SAW resonator  52 D is disposed on the parallel arm which branches off from the second branch node of the series arm. Each of the SAW resonators  52 A through  52 D may include a plurality of series-connected divided resonators. 
       FIG. 6  illustrates the arrangement of the SAW resonators, the longitudinally coupled SAW filters, wires, terminals, and other components included in the filter device  20  of the second preferred embodiment as viewed from above. On the surface of a substrate  28  made of a piezoelectric material, the common terminal  60 , the first through third individual terminals  31 ,  41 , and  51 , multiple ground terminals, multiple SAW resonators, multiple longitudinally coupled SAW filters, wires and other components are disposed. As the substrate  28 , a single crystal substrate made of a piezoelectric material, such as LiTaO 3  or LiNbO 3 , for example, may preferably be used. 
     In  FIG. 6 , ground wires are indicated by the sparse hatched portion, while series arm wires are indicated by the dense hatched portion. An insulating film is disposed where two wires cross each other so as to provide electrical insulation therebetween. The SAW resonators, the longitudinally coupled SAW filters, and terminals are designated by the same reference numerals provided to those in the equivalent circuit diagram shown in  FIG. 5 . The IDTs of two divided resonators  34  of the SAW resonator  32 B are arranged in the configuration shown in  FIG. 4B . 
     The filter device  20  of the second preferred embodiment preferably has a length of about 1.8 mm, a width of about 1.4 mm, and a height of about 0.6 mm, for example. The filter device  20  is mounted on a package substrate with its top side facing downward. 
     Advantages of the second preferred embodiment will be explained below with reference to  FIGS. 8A through 10B  in comparison with a filter device  20  of a comparative example shown in  FIG. 7 . 
       FIG. 7  is an equivalent circuit diagram of the filter device  20  according to the comparative example. In the comparative example, the SAW resonator  32 B of the filter device  20  of the second preferred embodiment is replaced by a single SAW resonator  32 B. The other elements of the comparative example are the same or substantially the same as those of the second preferred embodiment. The filter device  20  of the second preferred embodiment ( FIG. 5 ) and the filter device  20  of the comparative example ( FIG. 7 ) were prepared and the bandpass characteristics of the two filter devices  20  were measured. 
     The characteristics of the SAW resonators and the longitudinally coupled SAW filters of the filter device  20  of the comparative example were determined so that the pass bands of the first, second, and third bandpass filters  30 ,  40 , and  50  of the comparative example would match or substantially match Band  41 , Band  66 , and Band  3  downlink frequency bands, respectively. The IDT pitch of the SAW resonator  32 B ( FIG. 7 ) of the comparative example was first determined. Then, based on the IDT pitch of the SAW resonator  32 B of the comparative example, the IDT pitches of the two divided resonators  34  of the SAW resonator  32 B ( FIG. 5 ) of the second preferred embodiment were determined. More specifically, the IDT pitch of one divided resonator  34  was set to be the same or substantially the same as that of the SAW resonator  32 B of the comparative example. The IDT pitch of the other divided resonator  34  was set to be slightly smaller than that in the comparative example. The difference in the IDT pitch between the two divided resonators  34  was set to be about 0.06% of the average of the IDT pitches of the two divided resonators  34 . 
       FIGS. 8A and 8B  are graphs illustrating the measurement results of the bandpass characteristics in the path from the common terminal  60  to the second individual terminal  41  in the filter device  20  of the second preferred embodiment ( FIG. 5 ).  FIGS. 8C and 8D  are graphs illustrating the measurement results of the bandpass characteristics in the path from the common terminal  60  to the second individual terminal  41  in the filter device  20  of the comparative example ( FIG. 7 ). In the graphs, the horizontal axis indicates the frequency (MHz), while the vertical axis indicates the insertion loss (dB). In  FIGS. 8A and 8C , the scale factor of the vertical axis on the right side is ten times as large as that on the left side. The insertion loss increases downward on the vertical axis. A network analyzer is usually used for measuring the bandpass characteristics. 
       FIG. 8B  is an enlarged graph showing a specific frequency range in the graph of  FIG. 8A .  FIG. 8D  is an enlarged graph showing a specific frequency range in the graph of  FIG. 8C . Markers M 1  and M 2  in the graphs correspond to the frequencies at about 2110 MHz and about 2200 MHz, respectively. The frequency band between the markers M 1  and M 2  is equal or substantially equal to Band  66  downlink frequency band used for the second bandpass filter  40 . 
     As shown in  FIGS. 8C and 8D , in the filter device  20  of the comparative example ( FIG. 7 ), a single large ripple  83  is observed at the frequency of about 2145 MHz. In contrast, in the filter device  20  of the second preferred embodiment ( FIG. 5 ), two ripples  82  are observed at the frequencies of about 2145 MHz and about 2146.2 MHz. An increase in the insertion loss of each of the two ripples  82  is smaller than that of the ripple  83  in the bandpass characteristics ( FIGS. 8C and 8D ) of the filter device  20  of the comparative example. 
       FIGS. 9, 10A, and 10B  are graphs illustrating the measurement results of the bandpass characteristics in the path from the common terminal  60  to the first individual terminal  31  in the filter device  20  of the second preferred embodiment ( FIG. 5 ) and those of the filter device  20  of the comparative example ( FIG. 7 ). In the graphs, the horizontal axis indicates the frequency (MHz), while the vertical axis indicates the insertion loss (dB). The insertion loss increases downward on the vertical axis. In the graphs, the solid line indicates the bandpass characteristics of the filter device  20  of the second preferred embodiment ( FIG. 5 ), while the broken line indicates the bandpass characteristics of the filter device  20  of the comparative example ( FIG. 7 ). 
       FIG. 10A  is an enlarged graph showing a specific frequency range in the graph of  FIG. 9 . In  FIG. 10A , the scale factor of the vertical axis on the right side is ten times as large as that on the left side.  FIG. 10B  is an enlarged graph showing a specific frequency range in the graph of  FIG. 10A . 
     As shown in  FIGS. 9 and 10A , almost no difference is observed between the insertion loss in the pass band of the first bandpass filter  30  of the second preferred embodiment and that of the comparative example.  FIG. 10B  shows that, in the second preferred embodiment, two ripples  84  occur at the frequencies of about 2145 MHz and about 2146.2 MHz, while, in the comparative example, a single large ripple  85  occurs at the frequency of about 2145 MHz. The two ripples  84  in the second preferred embodiment are due to the unwanted waves produced in the two divided resonators  34  ( FIG. 5 ). The large ripple  85  in the comparative example is due to the unwanted waves produced in the SAW resonator  32 B ( FIG. 7 ). 
     The ripples  82  ( FIGS. 8A and 8B ) observed in the pass band of the second bandpass filter  40  of the second preferred embodiment are caused by the ripples  84  ( FIGS. 10A and 10B ) outside the pass band of the first bandpass filter  30 . The ripple  83  ( FIGS. 8C and 8D ) observed in the pass band of the second bandpass filter  40  of the comparative example is caused by the ripple  85  ( FIGS. 10A and 10B ) outside the pass band of the first bandpass filter  30 . Focusing only on the first bandpass filter  30 , the ripple  85  outside the pass band of the first bandpass filter  30  of the comparative example does not significantly influence the bandpass characteristics of the first bandpass filter  30 . Nevertheless, if the frequency of the ripple  85  is included in the pass band of the second bandpass filter  40 , the ripple  85  significantly influences the bandpass characteristics of the second bandpass filter  40 , as shown in  FIG. 8D . 
     In the second preferred embodiment, a drop in the insertion loss caused by the ripples  84  ( FIG. 10B ) outside the pass band of the first bandpass filter  30  is small. This contributes to regulating an increase in the insertion loss caused by the ripples  82  ( FIG. 8B ) in the pass band of the second bandpass filter  40 . It is thus possible to lessen the influence of the ripples  84  on the bandpass characteristics of the second bandpass filter  40 . 
     As shown in  FIGS. 9 and 10A , even when the SAW resonator  32 B includes the two divided resonators  34  ( FIG. 5 ), the resulting bandpass characteristics are the same or almost the same as those obtained when the single SAW resonator  32 B ( FIG. 7 ) is used as in the comparative example. The result of designing the filter device  20  of the comparative example ( FIG. 7 ) can thus be utilized to design the filter device  20  of the second preferred embodiment ( FIG. 5 ). 
     The preferable range of the difference in the IDT pitch between the two divided resonators  34  ( FIG. 5 ) used in the filter device  20  of the second preferred embodiment will be discussed below with reference to  FIG. 11 . The IDT pitch of one divided resonator  34  was fixed to be the same or substantially the same IDT pitch of the SAW resonator  32 B in the comparative example, while the IDT pitch of the other divided resonator  34  was varied. Then, the bandpass characteristics were determined by simulations. 
       FIG. 11  is a graph illustrating the simulation results. The value of the fixed IDT pitch of one divided resonator  34  is indicated by Pf, while the value of the varied IDT pitch of the other divided resonator  34  is indicated by Pv. The horizontal axis of  FIG. 11  represents the result of (Pv−Pf)/((Pv+Pf)/2) (%). That is, the horizontal axis of  FIG. 11  represents the ratio of the deviation of the IDT pitch to the average of the IDT pitch. The deviation of the IDT pitch is assumed to be positive when Pv&gt;Pf and to be negative when Pv&lt;Pf. The absolute value of the deviation of the IDT pitch will be called the pitch difference. 
     The vertical axis on the left side in  FIG. 11  represents an increase in the insertion loss (dB) caused by the ripples  82  (may also be called the magnitude of ripples  82 ) observed in the pass band of the second bandpass filter  40  ( FIG. 8B ). The vertical axis on the right side of  FIG. 11  represents the largest value of the insertion loss (dB) in the pass band of the first bandpass filter  30 . The insertion loss increases downward on the vertical axis on the right side. In  FIG. 11 , the triangles indicate the magnitude of the ripples  82  in the pass band of the second bandpass filter  40 , while the circles indicate the largest value of the insertion loss in the pass band of the first bandpass filter  30 . 
     The state of the origin of the horizontal axis in  FIG. 11  corresponds to the configuration of the filter device  20  of the comparative example ( FIG. 7 ). The magnitude of the ripples  82  observed in the bandpass characteristics of the second bandpass filter  40  has the largest value when the ratio of the pitch difference to the average of the IDT pitch is zero. This corresponds to the state in which the single large ripple  83  occurs in the pass band of the second bandpass filter  40  in the comparative example, as shown in  FIG. 8D . 
     As the ratio of the pitch difference to the average of the IDT pitch becomes greater to the value not more than about 0.02%, the magnitude of the ripples  82  gradually becomes smaller. This corresponds to the state in which the two ripples  82  shown in  FIG. 8B  partially overlap each other. When the ratio of the pitch difference to the average of the IDT pitch is about 0.02% or greater, the magnitude of the ripples  82  is constant or substantially constant. This corresponds to the state in which the two ripples  82  shown in  FIG. 8B  are clearly separated from each other. It is thus preferable that the ratio of the pitch difference to the average of the IDT pitch is, for example, about 0.02% or greater in order to sufficiently provide the advantageous effect of decreasing the magnitude of the ripples  82  in the pass band of the second bandpass filter  40 . 
     As the ratio of the pitch difference to the average of the IDT pitch increases from zero, the insertion loss in the pass band of the first bandpass filter  30  becomes greater. Especially when the ratio of the pitch difference to the average of the IDT pitch exceeds about 0.7%, the insertion loss rises sharply. It is thus preferable that the ratio of the pitch difference to the average of the IDT pitch is, for example, about 0.7% or smaller. This can regulate an increase in the insertion loss in the pass band caused by the two divided resonators  34  defining the SAW resonator  32 B ( FIG. 5 ). 
     The relationship between the pass band of the first bandpass filter  30  and that of the second bandpass filter  40  will be discussed below with reference to  FIG. 12 . 
       FIG. 12  is a graph illustrating the relationship between the pass band PB 1  of the first bandpass filter  30  and the pass band PB 2  of the second bandpass filter  40  on the frequency axis. The lower cutoff frequency and the higher cutoff frequency of the pass band PB 1  of the first bandpass filter  30  are indicated by fL 1  and fH 1 , respectively. The lower cutoff frequency and the higher cutoff frequency of the pass band PB 2  of the second bandpass filter  40  are indicated by fL 2  and fH 2 , respectively. The higher cutoff frequency fH 2  of the pass band PB 2  of the second bandpass filter  40  is lower than the lower cutoff frequency fL 1  of the pass band PB 1  of the first bandpass filter  30 . 
     Typically, a Rayleigh response of a SAW resonator occurs in the frequency range which is about 0.7 to about 0.85 times as high as the resonant frequency of the SAW resonator. That is, if the frequency range which is about 0.7 to about 0.85 times as high as the resonant frequency of a SAW resonator of the first bandpass filter  30  overlaps the pass band PB 2  of the second bandpass filter  40 , a Rayleigh response due to the first bandpass filter  30  is likely to occur in the pass band PB 2  of the second bandpass filter  40 . 
     In the example in  FIG. 12 , the pass band PB 2  of the second bandpass filter  40  is included in the frequency range of about 0.7 fL 1  to about 0.85 fH 1 . When the pass band PB 1  of the first bandpass filter  30  and the pass band PB 2  of the second bandpass filter  40  have such a relationship, ripples  82  ( FIG. 8B ) are likely to occur in the pass band PB 2  of the second bandpass filter  40 . 
     In addition to when the pass band PB 2  is included in the frequency range of about 0.7 fL 1  to about 0.85 fH 1 , when the frequency range of about 0.7 fL 1  to about 0.85 fH 1  is included in the pass band PB 2  of the second bandpass filter  40  or when a portion of the frequency range of about 0.7 fL 1  to about 0.85 fH 1  overlaps a portion of the pass band PB 2  of the second bandpass filter  40 , ripples  82  ( FIG. 8B ) are also likely to occur in the pass band PB 2  of the second bandpass filter  40 . 
     When the pass band PB 1  of the first bandpass filter  30  and the pass band PB 2  of the second bandpass filter  40  have one of the above-described relationships, it is particularly preferable that a filter device is configured as in the filter device  20  of the second preferred embodiment. 
     A description will be provided, with reference to  FIGS. 13A and 13B , in which a SAW resonator of the first bandpass filter  30  includes two divided resonators  34  in order to maximize the above-described advantages. 
       FIG. 13A  is a circuit diagram of a ladder bandpass filter configured similarly to the first bandpass filter  30 . The bandpass filter  70  and another bandpass filter  75  are connected to a common terminal  60 . 
     A series arm connects the common terminal  60  and an individual terminal  71  of the bandpass filter  70 . A parallel arm is connected between a ground and each of a plurality of branch nodes  73  of the series arm. No SAW resonator is connected between the common terminal  60  and the first branch node  73  as seen from the common terminal  60 . That is, the SAW resonator  72  on the series arm and the SAW resonator  72  on the parallel arm are both connected directly to the common terminal  60 . 
     If resonance due to unwanted waves is produced in any one of the SAW resonators  72  of the bandpass filter  70 , it influences the other bandpass filter  75  via the common terminal  60 . In this case, even when resonance due to unwanted waves is produced in a SAW resonator  72  separated farther from the common terminal  60 , many other SAW resonators  72  intervene between this SAW resonator  72  and the bandpass filter  75 , thus weakening the resonance as it is transmitted to the bandpass filter  75  via the common terminal  60 . In contrast, if unwanted resonance is produced in a SAW resonator  72  positioned close to the common terminal  60 , it is more easily transmitted to the bandpass filter  75 . From this point of view, it is appropriate that a SAW resonator  72  positioned close to the common terminal  60  includes two divided resonators, thus maximizing the advantageous effect of reducing ripples caused by unwanted resonance. 
     As an example, in the direction from the common terminal  60  to the first individual terminal  71 , at least one of the SAW resonator  72  disposed on a series arm portion  90  between the first and second branch nodes  73 , the SAW resonator  72  disposed on a series arm portion  91  between the second and third branch nodes  73 , the SAW resonator  72  disposed on a parallel arm  92  which branches off from the first branch node  73 , and the SAW resonator  72  disposed on a parallel arm  93  which branches off from the second branch node  73  (these SAW resonators  72  are indicated by the hatched portions in  FIG. 13A ) includes two parallel-connected divided resonators. 
       FIG. 13B  is a circuit diagram of a ladder bandpass filter  70  configured differently from that in  FIG. 13A . A SAW resonator  72  is connected between the common terminal  60  and the first branch node  73  as seen from the common terminal  60 . In this configuration, in the direction from the common terminal  60  to the first individual terminal  71 , at least one of the SAW resonator  72  disposed on a series arm portion  95  between the common terminal  60  and the first branch node  73 , the SAW resonator  72  disposed on a series arm portion  96  between the first and second branch nodes  73 , and the SAW resonator  72  disposed on a parallel arm  97  which branches off from the first branch node  73  (these SAW resonators  72  are indicated by the hatched portions in  FIG. 13B ) includes two parallel-connected divided resonators. 
     A modified example of the second preferred embodiment will be described below. Instead of the second bandpass filter  40  ( FIG. 5 ) of the second preferred embodiment, a low pass filter or a band elimination filter may be used. In this modification, advantages similar to those of the second preferred embodiment can be obtained. That is, although ripples caused by the divided resonators  34  of the first bandpass filter  30  occur in the pass band of the low pass filter or the band elimination filter, an increase in the insertion loss caused by the ripples can be regulated. 
     Third Preferred Embodiment 
     A filter device according to a third preferred embodiment of the present invention will be described below with reference to  FIGS. 14 through 15D . An explanation of the elements configured similarly to those of the filter device  20  ( FIGS. 5 and 6 ) of the second preferred embodiment will be omitted. 
       FIG. 14  is an equivalent circuit diagram of a filter device  20  according to the third preferred embodiment. In the second preferred embodiment, the SAW resonator  32 B of the first bandpass filter  30  includes two divided resonators  34 . In the third preferred embodiment, a SAW resonator  42 C of the second bandpass filter  40  includes two divided resonators  34 . The SAW resonator  32 B of the first bandpass filter  30  includes the single SAW resonator. 
       FIGS. 15A and 15B  are graphs illustrating the measurement results of the bandpass characteristics in the path from the common terminal  60  to the second individual terminal  41  in the filter device  20  of the third preferred embodiment (FIG.  14 ).  FIGS. 15C and 15D  are graphs illustrating the measurement results of the bandpass characteristics in the path from the common terminal  60  to the second individual terminal  41  in the filter device  20  of the comparative example ( FIG. 7 ). The bandpass characteristics of the comparative example shown in  FIGS. 15C and 15D  are the same or substantially the same bandpass characteristics shown in  FIGS. 8C and 8D . However, the frequency ranges on the horizontal axis of the bandpass characteristics in  FIGS. 15C and 15D  are different from those in  FIGS. 8C and 8D . 
     In the graphs in  FIGS. 15A through 15D , the horizontal axis indicates the frequency (MHz), while the vertical axis indicates the insertion loss (dB). In  FIGS. 15A and 15C , the scale factor of the vertical axis on the right side is ten times as large as that on the left side. The insertion loss increases downward on the vertical axis.  FIG. 15B  is an enlarged graph showing a specific frequency range in the graph of  FIG. 15A .  FIG. 15D  is an enlarged graph showing a specific frequency range in the graph of  FIG. 15C . Markers M 1  and M 2  in the graphs correspond to the frequencies at about 2110 MHz and about 2200 MHz, respectively. 
     Two ripples  86  ( FIGS. 15A and 15B ) are observed in the bandpass characteristics of the filter device  20  of the third preferred embodiment. In the comparative example, a single ripple  87  ( FIGS. 15C and 15D ) is observed in the bandpass characteristics of the filter device  20 . The ripples  86  and  87 , which are observed at the frequency of about 1677 MHz, are due to unwanted waves produced in the SAW resonator  42 C of the second bandpass filter  40 . 
     Advantages of the third preferred embodiment will be described below. A drop in the insertion loss caused by a ripple will be measured by the height of the ripple. The heights of the two ripples  86  in the third preferred embodiment are lower than that of the ripple  87  in the comparative example. The reason why the heights of the ripples  86  are lower than that of the ripple  87  is that the SAW resonator  42 C of the second bandpass filter  40  includes two divided resonators  34 . Lower heights of the ripples  86  can lessen the influence of the ripples  86  on the bandpass characteristics in the path from the common terminal  60  to the second individual terminal  41 . 
     A modified example of the third preferred embodiment will be described below. In the third preferred embodiment, the SAW resonator  42 C of the second bandpass filter  40  includes two divided resonators  34 . Alternatively, another SAW resonator of the second bandpass filter  40  may include two divided resonators. At least one SAW resonator of the third bandpass filter  50  may include two divided resonators. 
     Fourth Preferred Embodiment 
     A communication apparatus according to a fourth preferred embodiment of the present invention will be described below with reference to  FIG. 16 . The filter device  20  of the second preferred embodiment is used in the communication apparatus of the fourth preferred embodiment. An explanation of the elements configured similarly to those of the filter device  20  of the second preferred embodiment ( FIGS. 5 and 6 ) will be omitted. 
       FIG. 16  is a block diagram of the communication apparatus according to the fourth preferred embodiment. The communication apparatus includes a radio-frequency (RF) front-end circuit  100 , a radio-frequency (RF) signal processing circuit (radio-frequency integrated circuit (RFIC))  140 , a baseband signal processing circuit (baseband integrated circuit (BBIC)  141 , and an antenna  68 . The RF front-end circuit  100  includes a quadplexer  110 , a transmit switch  101 , a receive switch  102 , a power amplifier  103 , and a low-noise amplifier  104 . The quadplexer  110  includes two duplexers  120  and  130 . The duplexer  120  includes a transmit bandpass filter  121 Tx and a receive bandpass filter  121 Rx. The duplexer  130  includes a transmit bandpass filter  131 Tx and a receive bandpass filter  131 Rx. 
     The duplexer  120  is a Band  41  transmit/receive duplexer, while the duplexer  130  is a Band  66  transmit/receive duplexer, for example. The transmit bandpass filter  121 Tx is disposed between a common terminal  60  and an individual terminal  122 . The receive bandpass filter  121 Rx is disposed between the common terminal  60  and an individual terminal  123 . The transmit bandpass filter  131 Tx is disposed between the common terminal  60  and an individual terminal  132 . The receive bandpass filter  131 Rx is disposed between the common terminal  60  and an individual terminal  133 . As these bandpass filters, SAW filters are used. The antenna  68  is connected to the common terminal  60 . 
     A transmit RF signal output from the power amplifier  103  is input into one of the individual terminals  122  and  132  via the transmit switch  101 . The transmit RF signal passes through the corresponding one of the transmit bandpass filters  121 Tx and  131 Tx and is sent from the antenna  68 . A received RF signal received by the antenna  68  passes through one of the receive bandpass filters  121 Rx and  131 Rx and is input into the low-noise amplifier  104  via the receive switch  102 . 
     The RF signal processing circuit  140  converts a received RF signal output from the low-noise amplifier  104  into a lower frequency signal and outputs it to the baseband signal processing circuit  141 . The RF signal processing circuit  140  converts a transmit RF signal input from the baseband signal processing circuit  141  into a higher frequency signal and outputs it to the power amplifier  103 . The baseband signal processing circuit  141  performs various signal processing operations on a baseband signal. 
     Advantages of the fourth preferred embodiment will be explained below. 
     The receive bandpass filter  121 Rx corresponds to the first bandpass filter  30  of the filter device  20  of the second preferred embodiment ( FIG. 5 ), while the receive bandpass filter  131 Rx corresponds to the second bandpass filter  40  of the filter device  20  ( FIG. 5 ). The receive bandpass filter  121 Rx is configured as in the first bandpass filter  30 . Thus, the bandpass characteristics of the receive bandpass filter  131 Rx are less likely to be influenced by unwanted resonance produced in the receive bandpass filter  121 Rx. 
     As described above, unwanted resonance produced in a bandpass filter of one duplexer, such as the receive bandpass filter  121 Rx of the duplexer  120 , may influence the bandpass characteristics of a bandpass filter of another duplexer, such as the receive bandpass filter  131 Rx of the duplexer  130 . Unwanted resonance produced in a bandpass filter of a duplexer, such as the receive bandpass filter  121 Rx of the duplexer  120 , may also influence the bandpass characteristics of another bandpass filter of the same duplexer, such as the transmit bandpass filter  121 Tx of the duplexer  120 . In this manner, when multiple bandpass filters are connected to the common terminal  60 , unwanted resonance produced in one bandpass filter may adversely influence the bandpass characteristics of another bandpass filter. Even in this case, the influence of the unwanted resonance can be lessened as a result of defining at least one SAW resonator in the bandpass filter having produced the unwanted resonance by multiple divided resonators. 
     Fifth Preferred Embodiment 
     A filter device according to a fifth preferred embodiment of the present invention will be described below with reference to  FIG. 17A . An explanation of the elements configured similarly to those of the filter device  20  of the first preferred embodiment ( FIG. 1 ) and those of the second preferred embodiment ( FIG. 5 ) will be omitted. While the filter device  20  according to the first preferred embodiment ( FIG. 1 ) is a bandpass filter, a filter device  20  according to the fifth preferred embodiment is a low pass filter. 
       FIG. 17A  is an equivalent circuit diagram of the filter device  20  according to the fifth preferred embodiment. The filter device  20  of the fifth preferred embodiment is preferably, for example, a n-type filter. An inductor  23  is connected in parallel with the SAW resonator  21  which connects the first terminal  25  and the second terminal  26 . A SAW resonator  21  is connected between the first terminal  25  and a ground, while another SAW resonator  21  is connected between the second terminal  26  and a ground. The SAW resonator  21  connected between the first terminal  25  and a ground includes two parallel-connected divided resonators  22 . As in the first preferred embodiment, the IDT pitch of one divided resonator  22  and that of the other divided resonator  22  are different from each other. 
     Advantages of the fifth preferred embodiment will be explained below. As in the first preferred embodiment, a drop in the insertion loss caused by ripples due to unwanted waves is regulated. Instead of the first bandpass filter  30  of the filter device  20  of the second preferred embodiment ( FIG. 5 ), the low pass filter of the fifth preferred embodiment may be used. In this case, it is possible to lessen the influence of ripples caused by the low pass filter on the bandpass characteristics of the second bandpass filter  40  or the third bandpass filter  50 . 
     A modified example of the fifth preferred embodiment will be described below with reference to  FIG. 17B . 
       FIG. 17B  is an equivalent circuit diagram of the filter device  20  according to the modified example of the fifth preferred embodiment. The filter device  20  of the modified example is a high pass filter. 
     The filter device  20  of the modified example is preferably, for example, a T-type filter. Two SAW resonators  21  are disposed in series with each other between the first and second terminals  25  and  26 . An inductor  23  and a SAW resonator  21  are interposed in series with each other between a ground and a node between the above-described two SAW resonators  21 . The SAW resonator  21  connected to the first terminal  25  includes two parallel-connected divided resonators  22 . As in the first preferred embodiment, the IDT pitch of one divided resonator  22  and that of the other divided resonator  22  are different from each other. 
     As in the modified example, a SAW resonator  21  included in a high pass filter may include two divided resonators  22 . In the modified example, as well as in the fifth preferred embodiment, the influence of ripples caused by the high pass filter on the bandpass characteristics of a bandpass filter can be reduced. As in the example shown in  FIG. 3A  in the first preferred embodiment, it is possible to regulate a decrease in the attenuation characteristics caused by ripples occurring in the stopband of the high pass filter. 
     Other modified examples of the fifth preferred embodiment will be discussed below. 
     In the fifth preferred embodiment ( FIG. 17A ), the SAW resonator  21  connected between the first terminal  25  and a ground includes two divided resonators  22 . Another SAW resonator  21  may include two divided resonators  22 . In the above-described modified example ( FIG. 17B ), the SAW resonator  21  connected to the first terminal  25  includes two divided resonators  22 . Another SAW resonator  21  may include two divided resonators  22 . 
     Instead of the first bandpass filter  30  in the second preferred embodiment ( FIG. 5 ), a low pass filter is used in the fifth preferred embodiment ( FIG. 17A ), and a high pass filter is used in the modified example of the fifth preferred embodiment. Instead of the first bandpass filter  30 , a band elimination filter may alternatively be used. In this case, one of multiple SAW resonators included in the band elimination filter includes a plurality of divided resonators. 
     The present invention is not limited to the above-described preferred embodiments. The configurations described in the different preferred embodiments may partially be replaced by or combined with each other. Similar advantages obtained by similar configurations in the plurality of preferred embodiments are not repeated in the individual preferred embodiments. 
     While preferred embodiments of the present invention have been described above, it is to be understood that variations and modifications will be apparent to those skilled in the art without departing from the scope and spirit of the present invention. The scope of the present invention, therefore, is to be determined solely by the following claims.