Filter and duplexer

1. A filter comprising:

a single substrate;

one or more series resonators that are connected in series between an input terminal and an output terminal;

one or more parallel resonators that are connected in parallel between the input terminal and the output terminal; and

a laterally coupled resonator that is connected in parallel with at least one of the one or more series resonators,

wherein:

the laterally coupled resonator has a first piezoelectric film portion, a first lower electrode and a plurality of upper electrodes, the first lower electrode and the plurality of upper electrodes sandwiching the first piezoelectric film portion;

each of the one or more series resonators and the one or more parallel resonators is a piezoelectric thin film resonator that has a second piezoelectric film portion, a second lower electrode and a second upper electrode, the second lower electrode and the second upper electrode sandwiching the second piezoelectric film portion;

a material of the first piezoelectric film portion is the same as a material of the second piezoelectric film portion;

a thickness of the first piezoelectric film portion is substantially the same as a thickness of the second piezoelectric film portion; and

the one or more series resonators, the one or more parallel resonators and the laterally coupled resonator are formed on the single substrate.

2. The filter as claimed in claim 1 , wherein the plurality of upper electrodes are comb electrodes that face each other.

3. The filter as claimed in claim 1 further comprising a capacitor that is connected to the at least one of the series resonators in parallel and is connected to the laterally coupled resonator in series.

4. The filter as claimed in claim 1 , further comprising:

a first capacitor that is connected between the input terminal and the laterally coupled resonator in series with the laterally coupled resonator; and

a second capacitor that is connected between the laterally coupled resonator and the output terminal in series with the laterally coupled resonator.

5. The filter as claimed in claim 1 , wherein:

an amplitude of a first signal that passes through the at least one of the series resonators is substantially consistent with an amplitude of a second signal that passes through the laterally coupled resonator; and

a phase of the first signal is substantially reverse to a phase of the second signal.

6. The filter as claimed in claim 1 ,

wherein:

a material of the first lower electrode is the same as a material of the second lower electrode;

a thickness of the first lower electrode is substantially the same as a thickness of the second lower electrode;

a material of the plurality of first upper electrodes is the same as a material of the second upper electrode;

a thickness of the plurality of first upper electrodes is substantially the same as a thickness of the second upper electrode.

7. The filter as claimed in claim 1 , wherein the first piezoelectric film portion and the second piezoelectric film portion form a single piezoelectric film.

8. A duplexer comprising:

a transmit filter that is connected between a common terminal and a transmit terminal; and

a receive filter that is connected between the common terminal and a receive terminal,

wherein at least one of the transmit filter and the receive filter is a filter that comprises:

a single substrate;

one or more series resonators that are connected in series between the common terminal and at least one of the transmit terminal and the receive terminal;

one or more parallel resonators that are connected in parallel between the common terminal and the at least one of the transmit terminal and the receive terminal; and

a laterally connected resonator that is connected in parallel with at least one of the one or more series resonators,

wherein:

the laterally coupled resonator has a first piezoelectric film portion, a first lower electrode and a plurality of upper electrodes, the first lower electrode and the plurality of upper electrodes sandwiching the first piezoelectric film portion;

each of the one or more series resonators and the one or more parallel resonators is a piezoelectric thin film resonator that has a second piezoelectric film portion, a second lower electrode and a second upper electrode, the second lower electrode and the second upper electrode sandwiching the second piezoelectric film portion;

a material of the first piezoelectric film portion is the same as a material of the second piezoelectric film portion;

a thickness of the first piezoelectric film portion is substantially the same as a thickness of the second piezoelectric film portion; and

the one or more series resonators, the one or more parallel resonators and the laterally coupled resonator are formed on the single substrate.

9. The duplexer as claimed in claim 8 , wherein a resonant frequency of the laterally coupled resonator is a frequency such that a phase of a pass band of an opposing filter of the laterally coupled resonator is inductive, the opposing filter being one of the transmit filter and the receive filter.

10. The duplexer as claimed in claim 8 ,

wherein:

a material of the first lower electrode is the same as a material of the second lower electrode;

a thickness of the first lower electrode is substantially the same as a thickness of the second lower electrode;

a material of the plurality of first upper electrodes is the same as a material of the second upper electrode;

a thickness of the plurality of first upper electrodes is substantially the same as a thickness of the second upper electrode.

11. The duplexer as claimed in claim 8 , wherein the first piezoelectric film portion and the second piezoelectric film portion form a single piezoelectric film.

12. A duplexer comprising:

a transmit filter that is connected between a common terminal and a transmit terminal;

a receive filter that is connected between the common terminal and a receive terminal; and

a laterally coupled resonator that is connected between the transmit terminal and the receive terminal in parallel with the transmit filter and the receive filter,

wherein at least one of the transmit filter and the receive filter is a filter that comprises:

a single substrate;

one or more series resonators that are connected in series between the common terminal and at least one of the transmit terminal and the receive terminal; and

one or more parallel resonators that are connected in parallel between the common terminal and the at least one of the transmit terminal and the receive terminal,

wherein:

the laterally coupled resonator has a first piezoelectric film portion, a first lower electrode and a plurality of upper electrodes, the first lower electrode and the plurality of upper electrodes sandwiching the first piezoelectric film portion;

each of the one or more series resonators and the one or more parallel resonators is a piezoelectric thin film resonator that has a second piezoelectric film portion, a second lower electrode and a second upper electrode, the second lower electrode and the second upper electrode sandwiching the second piezoelectric film portion;

a material of the first piezoelectric film portion is the same as a material of the second piezoelectric film portion;

a thickness of the first piezoelectric film portion is substantially the same as a thickness of the second piezoelectric film portion; and

the one or more series resonators, the one or more parallel resonators and the laterally coupled resonator are formed on the single substrate.

13. The duplexer as claimed in claim 12 ,

wherein:

a material of the first lower electrode is the same as a material of the second lower electrode;

a thickness of the first lower electrode is substantially the same as a thickness of the second lower electrode;

a material of the plurality of first upper electrodes is the same as a material of the second upper electrode;

a thickness of the plurality of first upper electrodes is substantially the same as a thickness of the second upper electrode.

14. The duplexer as claimed in claim 12 , wherein the first piezoelectric film portion and the second piezoelectric film portion form a single piezoelectric film.