Lamb-wave resonator and oscillator
A Lamb-wave resonator includes: a piezoelectric substrate; an interdigital transducer electrode formed on a main surface of the piezoelectric substrate, the interdigital transducer electrode including a plurality of electrode finger elements being interdigitated, and a bus bar electrode coupling the plurality of electrode finger elements; and a pair of reflectors disposed on opposite sides of the interdigital transducer electrode in a propagation direction of a Lamb wave. A thickness t of the piezoelectric substrate is in a range expressed by 0<t/λ≦3 where a wavelength of the Lamb wave to be excited is represented as λ. If a width of the bus bar electrode is Wb, a distance from the electrode finger elements to the bus bar electrode is Wg, in an orthogonal coordinate with an x axis indicating the distance Wg and a y axis indicating the width Wb, both the distance Wg and the width Wb are in one of a first range and a second range. The first range is surrounded by a circular arc expressed by an equation of a circle (x−10) 2 +(y+12.7) 2 =19 2 , and Wg≧1λ and Wb≧1λ, and the second range is surrounded by a straight line connecting coordinates of (1.0, 7.0), (1.0, 20.0), (2.0, 21.0), (4.5, 22.5), (7.5, 25.0), (12.0, 23.0), (15.5, 20.8), (18.0, 14.0), (20.0, 7.0), (16.0, 10.0), (15.0, 9.0), (12.5, 8.0), (10.0, 8.0), (8.0, 9.0), (7.0, 8.0), (5.0, 8.0), (3.5, 10.0), (2.0, 10.0), (1.0, 7.0) in this order if the coordinates are represented as (Wg, Wb).
1. A Lamb-wave resonator, comprising:
a piezoelectric substrate being a quartz substrate;
an interdigital transducer electrode formed on a main surface of the piezoelectric substrate, the interdigital transducer electrode being formed of aluminum and including:
a plurality of electrode finger elements being interdigitated; and
a bus bar electrode coupling the plurality of electrode finger elements; and
a pair of reflectors disposed on opposite sides of the interdigital transducer electrode in a propagation direction of a Lamb wave, wherein a thickness t of the piezoelectric substrate is in a range expressed by 0<t/λ≦3 where a wavelength of the Lamb wave to be excited is represented as λ, a width of the piezoelectric substrate is greater than a cross width of the plurality of electrode finger elements that are interdigitated, the cross width of the plurality of electrode finger elements that are interdigitated is greater than or equal to 20λ and less than or equal to 50λ, and if a width of the bus bar electrode is Wb, a distance from the electrode finger elements to the bus bar electrode is Wg, in an orthogonal coordinate with an x axis indicating the distance Wg and a y axis indicating the width Wb, both the distance Wg and the width Wb are in one of a first range and a second range, wherein the first range is surrounded by a circular arc expressed by an equation of a circle (x−10) 2 +(y+12.7) 2 =19 2 , and Wg≧1λ and Wb≧1λ, and the second range is surrounded by a straight line connecting coordinates of (1.0, 7.0), (1.0, 20.0), (2.0, 21.0), (4.5, 22.5), (7.5, 25.0), (12.0, 23.0), (15.5, 20.8), (18.0, 14.0), (20.0, 7.0), (16.0, 10.0), (15.0, 9.0), (12.5, 8.0), (10.0, 8.0), (8.0, 9.0), (7.0, 8.0), (5.0, 8.0), (3.5, 10.0), (2.0, 10.0), (1.0, 7.0) in this order if the coordinates are represented as (Wg, Wb), wherein a unit of measure for Wg and Wb is λ.
2. The Lamb-wave resonator according to claim 1 , wherein the piezoelectric substrate has an Euler angle (φ, θ, ψ) satisfying φ=0 degrees, 35 degrees≦θ≦47.2 degrees, and −5 degrees<ψ<+5 degrees, and a relation between the thickness t and the wavelength λ of the Lamb wave satisfies 0.176≦t/λ≦1.925.
3. An oscillator, comprising:
1. b-wave resonator according to claim 1 ; and
an oscillation circuit for exciting the Lamb-wave resonator.