New cuts for width-extensional mode quartz crystal resonators

Various characteristics for a width-extensional mode quartz crystal resonator are described. A new cut for a width-extensional mode quartz crystal resonator, the KT-cut, is proposed, and its frequency characteristics, frequency temperature behavior, and electrical characteristics are clarified. A frequency equation is derived under the conditions that width X₀ is much larger than thickness Z₀ but much smaller than length Y ₀ by solving partial differential equations for a new shape GT cut quartz crystal resonator with a variational principle. The modified shape for the resonator is referred to as the GT resonator. From this equation, relationships of resonant frequency versus width X₀ and the first- and second-order temperature coefficients α, β versus a cut angle θ are analyzed theoretically. Series resistance R₁ and a quality factor Q are examined in the frequency range of approximately 8.7 to 32 MHz