Quasi–Lamé–Mode Quartz–Crystal Resonators

In this paper, quasi-Lamé-mode quartz-crystal resonators formed by etching processes are examined theoretically and experimentally. First, the frequency equation for a Y-plate quartz-crystal resonator is derived by the energy method. Then, the relationship between the cut angles φ y and θ y to vibrate the quasi-Lamé mode is investigated. There are many combinations of φ y and θ y for which the first-order temperature coefficient α becomes zero. Finally, it is theoretically and experimentally demonstrated that the temperature characteristics of a Y-plate quasi-Lamé-mode quartz-crystal resonator is superior to that of a pure-Lamé-mode resonator.