Ladder filter

1. A ladder filter comprising:

a series arm resonator including an elastic wave resonator; and

a plurality of parallel arm resonators each including an elastic wave resonator; wherein

the plurality of parallel arm resonators include a first parallel arm resonator defining a pass band together with the series arm resonator, and a second parallel arm resonator;

each of the elastic wave resonators includes first and second busbars, and a plurality of first electrode fingers and a plurality of second electrode fingers connected at ends thereof to the first and second busbars, respectively, and when a portion in which the plurality of first electrode fingers and the plurality of second electrode fingers overlap each other when viewed in an elastic wave propagation direction is defined as an overlap width region, and a region between the overlap width region and each of the first and second busbars is defined as a gap region, a dimension, in an overlap width direction, of the gap region in the second parallel arm resonator is larger than a dimension, in the overlap width direction, of the gap region in the first parallel arm resonator; and

a resonant frequency of the second parallel arm resonator is in a frequency range of not lower than a resonant frequency of the series arm resonator.

2. The ladder filter according to claim 1 , wherein the resonant frequency of the second parallel arm resonator is in a frequency range of not lower than an anti-resonant frequency of the series arm resonator.

3. The ladder filter according to claim 1 , wherein L 1 <7×λ is satisfied when a wavelength determined based on an electrode finger pitch of the second parallel arm resonator is denoted by λ and a dimension of the overlap width region along the overlap width direction is denoted by L 1 .

4. The ladder filter according to claim 3 , wherein L 1 <4×λ is satisfied when the wavelength determined based on the electrode finger pitch of the second parallel arm resonator is denoted by λ and the dimension of the overlap width region along the overlap width direction is denoted by L 1 .

5. The ladder filter according to claim 1 , wherein the plurality of parallel arm resonators connect the series arm resonator and a ground.

6. The ladder filter according to claim 1 , wherein the series arm resonator includes a plurality of series arm resonators.

7. The ladder filter according to claim 6 , wherein the elastic wave resonators are surface acoustic wave resonators.

8. The ladder filter according to claim 6 , wherein the resonant frequency of the second parallel arm resonator is higher than resonant frequencies of the series arm resonators.

9. The ladder filter according to claim 1 , further comprising reflectors located at outer ends of the elastic wave resonators.

10. The ladder filter according to claim 1 , wherein the overlap width region is rectangular or substantially rectangular.

11. The ladder filter according to claim 1 , wherein an arithmetic mean of lengths of portions where the first and second electrode fingers overlap defines a dimension in the overlap width direction.

12. The ladder filter according to claim 1 , wherein a transverse mode ripple is not located in the pass band.

13. The ladder filter according to claim 1 , wherein a transverse mode ripple is spaced away from the resonant frequency of the second parallel arm resonator.

14. The ladder filter according to claim 1 , wherein the second parallel arm resonator includes a plurality of second parallel arm resonators.

15. A duplexer comprising:

the ladder filter according to claim 1 ; wherein

the ladder filter defines a transmission filter.