Tunable filter
A tunable filter that is capable of magnifying a pass band width or increasing a frequency variable amount includes a resonator circuit portion provided in at least one of a series arm connecting an input terminal and an output terminal to each other and a parallel arm connecting the series arm and a ground potential to each other, a first variable capacitor is connected in series to the resonator circuit portion and a second variable capacitor is connected in parallel to the resonator circuit portion. The resonator circuit portion includes a piezoelectric substrate including LiNbO 3 or LiTaO 3 , an elastic wave resonator including an electrode located on the piezoelectric substrate, and a bandwidth extending inductance Lx, Lx connected to the elastic wave resonator.
1. A tunable filter of a ladder circuit configuration, comprising:
a series arm resonator provided in a series arm;
a parallel arm resonator provided in a parallel arm; and
a variable capacitor connected to at least one of the series arm resonator and the parallel arm resonator; wherein
when a resonant frequency and an anti-resonant frequency of the series arm resonator are FrS and FaS and a resonant frequency and an anti-resonant frequency of the parallel arm resonator are FrP and FaP, FrS≦{(n−1) FrP+FaP}/n and FaP≦{(n−1) FaS+FrS}/n are satisfied where n is an integer number greater than or equal to 2 and less than or equal to 30.
2. The tunable filter according to claim 1 , wherein
FrS≦(FrP +FaP)/2, FaP>FrS, and FaP<FaS are satisfied.
3. The tunable filter according to claim 1 , wherein
FrS≦(2 FrP +FaP)/3, FaP>FrS, and FaP<FaS are satisfied.
4. The tunable filter according to claim 1 , wherein
when a value obtained by normalizing a frequency variable width of the tunable filter by (FaP +FrS)/2 is t and a value obtained by normalizing an absolute value of a difference between a resonant frequency and an anti-resonant frequency of each of the series arm resonator and the parallel arm resonator by the resonant frequency of each thereof is y, a value, obtained by normalizing Δfr/FrP, a ratio of Δfr=FrS−FrP to FrP,by the fractional band width y, is less than or equal to a value indicated by the following Expression:
{(2− t/ 0.9)×(1+ y )−(2+ t/ 0.9)}/{(2+ t/ 0.9)× y}× 100(%).
5. The tunable filter according to claim 1 , wherein
a maximum value of a ratio of a difference between the resonant frequency FrS of the series arm resonator and the resonant frequency FrP of the parallel arm resonator to a bandwidth of the series arm resonator is caused to be within a range illustrated in the following Table:
Fractional Band Width of Resonator (%)
Greater
Greater
Greater
Greater
Greater
than 20
than 25
than 30
than 40
than 50
and
and
and
and
and
Less
Less
Less
Less
Less
than or
than or
than or
than or
than or
Equal
Equal
Equal
Equal
Equal
12
13
14
15
16
17
18
19
20
to 25
to 30
to 40
to 50
to 60
{(FrS − FrP)/
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Bandwidth of
than or
than or
than or
than or
than or
than or
than or
than or
than or
than or
than or
than or
than or
than or
Resonator} (%)
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
to 33
to 37
to 41
to 44.5
to 47.5
to 50
to 52.6
to 54.7
to 56.6
to 63.9
to 68.3
to 74.4
to 78.0
to 80.5.
6. The tunable filter according to claim 5 , wherein
a minimum 3 dB band width is either the smaller of (FrS-FrP) ×0.9 or (FaS-FaP)×0.9, and a maximum frequency variable width is caused to be within a range of 140×(FaP-FrS) /(FaP+FrS)(%) to 180×(FaP-FrS)/(FaP+FrS)(%).
7. The tunable filter according to claim 1 , wherein
a maximum value of a ratio of a difference between the resonant frequency FrS of the series arm resonator and the resonant frequency FrP of the parallel arm resonator to a bandwidth of the series arm resonator is caused to be within a range illustrated in the following Table:
Fractional Band Width of Resonator (%)
Greater
Greater
Greater
Greater
Greater
than 20
than 25
than 30
than 40
than 50
and
and
and
and
and
Less
Less
Less
Less
Less
than or
than or
than or
than or
than or
Equal
Equal
Equal
Equal
Equal
12
13
14
15
16
17
18
19
20
to 25
to 30
to 40
to 50
to 60
{(FrS − FrP)/
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Less
Bandwidth of
than
than
than
than
than
than
than
than
than
than or
than or
than or
than or
than or
Resonator} (%)
or
or
or
or
or
or
or
or
or
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
Equal
to 52.4
to 58.7
to 66.7
to 71.4
to 74.6.
to 11
to
to
to 27
to 31
to
to
to
to
17.2
22.4
34.4
37.6
40.4
42.9
8. The tunable filter according to claim 1 , wherein each of a fractional band width of the series arm resonator and a fractional band width of the parallel arm resonator is greater than or equal to about 13% and less than or equal to about 60%.
9. The tunable filter according to claim 1 , further comprising a surface acoustic wave resonator having an electrode normalized film thickness within a range illustrated in the following Table when Euler angles of LiNbO 3 are (0°, 70° to 115 °,0°) and a duty ratio is X:
Electrode
Electrode Normalized
Material
Film Thickness H/λ
Al
≧0.18032 − 0.15186X + 0.04954X 2
Mo
≧0.13336 − 0.25984X + 0.1623X 2
Cu
≧0.11452 − 0.16714X + 0.06712X 2
Ni
≧0.14498 − 0.27652X + 0.17081X 2
Ag
≧0.0904 − 0.13393X + 0.0518X 2
Au
≧0.05966 − 0.10753X + 0.05177X 2
W
≧0.08039 − 0.15733X + 0.08902X 2
Ta
≧0.08344 − 0.15413X + 0.0806X 2
Pt
≧0.06404 − 0.12311X + 0.06493X 2
X in the table indicates a duty ratio.
10. The tunable filter according to claim 1 , wherein
the series arm resonator and parallel arm resonator include bulk wave resonators; and
the bulk wave resonator includes:
a substrate including a cavity open in a top surface;
a piezoelectric thin film or a piezoelectric thin plate arranged on the substrate so as to cover the cavity of the substrate;
a first excitation electrode provided in a portion that is a bottom surface of the piezoelectric thin film and faces the cavity; and
a second excitation electrode provided in a top surface of the piezoelectric thin film and disposed so as to face the first excitation electrode through the piezoelectric thin film.
11. The tunable filter according to claim 10 , wherein the bulk wave resonator is a thickness-shear vibration resonator.
12. The tunable filter according to claim 11 , wherein the bulk wave resonator is a thickness-shear vibration resonator utilizing a piezoelectric thin film or a piezoelectric thin plate, which includes LiNbO 3 , and Euler angles thereof are within one of ranges illustrated in the following Table:
Fractional Band Width Is Greater than or Equal to 20%
(0 ± 5°, 63° to 97°, ψ)
(10 ± 5°, 62° to 100°, ψ)
(20 ± 5°, 67° to 103°, ψ)
(30 ± 5°, 72° to 108°, ψ)
(40 ± 5°, 76° to 113°, ψ)
(50 ± 5°, 77° to 115°, ψ)
(60 ± 5°, 78° to 117°, ψ).
13. The tunable filter according to claim 10 , wherein the bulk wave resonator is a thickness-longitudinal vibration resonator.
14. The tunable filter according to claim 13 , wherein
the bulk wave resonator is a thickness-longitudinal vibration resonator utilizing a piezoelectric thin film or a piezoelectric thin plate, which includes LiNbO 3 , and Euler angles thereof are within a range of (0±5°, 107° to 137°, ψ), (10±5°, 112° to 133°, ψ), (50±5°, 47° to 69°, ψ), or (60±5°, 43° to 73°, ψ).