Crystal resonator

A crystal resonator that vibrates in a thickness-shear mode, the crystal resonator comprising:

• excitation electrodes, being disposed on a front surface and a back surface of a crystal element, wherein
• the excitation electrodes are disposed on the crystal element to have a positional relationship, where a displacement distribution at an edge of the excitation electrode on the front surface is identical to a displacement distribution at an edge of the excitation electrode on the back surface;
• wherein
• the crystal element has a thickness in a Y′-axis direction of a crystal,
• the crystal element having a principal surface on an X′-Z′-surface of the crystal,
• the excitation electrodes disposed on the front surface and the back surface of the crystal element have an identical planar shape and an identical size, and
• defining the excitation electrode disposed on a positive Y′-surface as a first excitation electrode and the excitation electrode disposed on a negative Y′-surface as a second excitation electrode, the second excitation electrode is disposed at a position meeting following relationships with respect to the first excitation electrode,
• (1) the first excitation electrode is moved along an X′-axis of the crystal by a distance dx given by T● tan α in a positive X′-direction,
• (2) the first excitation electrode is moved along a Z′-axis of the crystal by a distance dy given by T● tan β in a negative Z′-direction,
• (3) the second excitation electrode is disposed at a position where a state moved in (1) and (2) is projected on the negative Y′-surface,
• here, T indicates a thickness of the crystal element,
• α and β are angles predetermined according to a cut type of the crystal element, α is a rotation angle at a positive Z′-surface, β is a rotation angle at a positive X′-surface, and
• the X′-axis and the Z′-axis are axes generated by a rotation with respect to an X and a Y as crystallographic axes of the crystal by cut angles of the crystal element.