Piezoelectric resonator with electrode radius related to resonator thickness and vibration mode, and filter using the same

A piezoelectric resonator comprising first and second piezoelectric resonator elements using an nth-order mode of a thickness longitudinal vibration or a thickness-shear vibration, each of the first and second piezoelectric resonator elements comprising:

• a vibrating section including a piezoelectric layer;
• a pair of electrodes provided on opposite sides of the piezoelectric layer, respectively, the pair of electrodes partially overlapping with each other via the piezoelectric layer to define an opposite electrode portion;
• and
• a support member arranged to hold the vibrating section such that the vibrating section vibrates according to an
• nth-order mode of the thickness longitudinal vibration or the thickness-shear vibration;
• wherein the opposite electrode portion has one of a substantially circular shape having a radius r and a polygonal shape circumscribing a substantially circular shape having a radius r, and the radius r satisfies the following inequality:
• 20t/n≦r
• where t is a thickness of the vibrating section;
• wherein the first and second piezoelectric resonator elements are electrically connected in one of parallel and series, and have different resonant frequencies from each other.