Laterally coupled piezo-resonator ladder-type filter with at least one bending mode piezo-resonator

A ladder-type filter comprising:

• at least one series resonator forming a series arm and at least one parallel resonator forming a parallel arm, said series and parallel resonators being mounted adjacent to each other in a horizontal direction and connected to each other along said horizontal direction;
• wherein
• at least one of said series and parallel resonators is a first piezo-resonator including:
• a plate type piezoelectric vibrator having a pair of opposite rectangular surfaces, and four side surfaces coupling said pair of rectangular surfaces with each other,
• first and second resonance electrodes located on said pair of rectangular surfaces of said piezoelectric vibrator, and
• a support part being coupled to an end of each of said side surfaces of said piezoelectric vibrator that is located along a shorter side of each said rectangular surface, and a holding part being coupled to said support part,
• a ratio b/a being set in a range of +/- 10% from a value satisfying the following equation:
• b/a=n(0.3.sigma.+1.48)
• wherein a and b respectively represent lengths of shorter and longer sides of each said rectangular surface, .sigma. represents the Poisson's ratio of the material forming said piezoelectric vibrator and n represents an integer, said first piezo-resonator being arranged and adapted to excite bending mode vibration having a degree of 2m through a piezoelectric transverse effect, wherein m is an integer.