Filter and antenna duplexer

1. A filter comprising:

a first resonator;

a second resonator of which an excitation efficiency is reduced more than the first resonator; and

an inductor connected in parallel with the second resonator, and wherein no inductor is connected in parallel with the first resonator,

wherein:

the first resonator and the second resonator are surface acoustic wave resonators;

the first resonator includes a first IDT including two first electrodes and first electrode fingers;

all of the first electrode fingers have an identical width and an identical pitch and are alternately connected to the two first electrodes; and

the second resonator includes two second IDT including two second electrodes and second electrode fingers.

2. The filter according to claim 1 , wherein the inductor is not connected in parallel with the first resonator.

3. A filter comprising:

a first resonator;

a second resonator of which an excitation efficiency is reduced more than the first resonator; and

an inductor connected in parallel with the second resonator, and wherein no

inductor is connected in parallel with the first resonator,

wherein:

the first resonator and the second resonator are piezoelectric thin film resonators;

the first resonator includes a first lower electrode, a first upper electrode and a first piezoelectric film sandwiched between the first lower electrode and the first upper electrode; and

the second resonator includes a second lower electrode, a second upper electrode and a second piezoelectric film sandwiched between the second lower electrode and the second upper electrode.

4. The filter according to claim 1 wherein:

at least three of adjacent second electrode fingers are connected to one of the two second electrodes; and

remaining second electrode fingers other than the at least three adjacent second electrode fingers are alternately connected to the two second electrodes.

5. The filter according to claim 1 , wherein:

at lease one of the second electrode fingers has a larger width than the other second electrode fingers that are identical in width and pitch; and

all of the second electrode fingers are alternately connected to the two second electrodes.

6. The filter according to claim 1 wherein:

at least three of adjacent second electrode fingers has an identical polarity; and

remaining second electrode fingers other than the at least three adjacent second electrode fingers are alternately connected to the two second electrodes.

7. The filter according to claim 1 , every multiple second electrode fingers are alternately connected to the two second electrodes.

8. The filter according to claim 1 , wherein a propagation direction of a surface acoustic wave of the second resonator is different from that of the first resonator.

9. The filter according to claim 1 , wherein a width of the second electrode fingers is different from that of the first electrode fingers.

10. The filter according to claim 1 , wherein dummy electrode fingers that do not contribute to excitation are provided in the second IDT.

11. The filter according to claim 3 , wherein a thickness ratio of the second piezoelectric film to the second upper electrode and that of the second piezoelectric film to the second lower electrode are smaller than a thickness ratio of the first piezoelectric film to the first upper electrode or that of the first piezoelectric film to the first lower electrode.

12. The filter according to claim 3 , wherein at least one of the second upper electrode and the second lower electrode has a film thickness greater than the first upper electrode or the first lower electrode in.

13. The filter according to claim 3 , wherein the second piezoelectric film has a film thickness smaller than-the first piezoelectric film.

14. The filter according to claim 3 , wherein an area of a second membrane region defined on the second upper electrode, wherein the second piezoelectric film and the second lower electrode overlap, is smaller than that of a first membrane region defined on the first upper electrode, wherein the first piezoelectric film and the first lower electrode overlap.

15. The filter according to claim 3 , wherein a capacitance of the second resonator is smaller than that of the first resonator.

16. The filter according to claim 14 , wherein two or more second resonators are connected in parallel.

17. The filter according to claim 1 , wherein the inductor is provided as a line pattern in or on a package in which the first resonator and the second resonator are mounted.

18. The filter according to claim 1 , wherein the inductor is formed in an identical substrate in which the first resonator and the second resonator are provided.

19. The filter according to claim 1 , wherein the inductor is formed in a substrate different from the substrate in which the first resonator and the second resonator are provided.

20. The filter according to claim 1 , wherein the inductor is a chip inductor inside or outside of a package in which the first resonator and the second resonator are mounted.