Inharmonic overtones in partially plated AT-cut quartz crystal plates

Spurious modes caused by inharmonic overtones are one of the most familiar problems of AT-cut quartz resonators. Mindlin and Lee had explained this phenomenon theoretically in detail in the 1960's [1]. Their calculation results were also shown to be in good agreement with the experimental data from Curran and Koneval, which are based on quartz plates with relatively large length, width and thickness. Today, the dimensions of quartz plates have decreased enormously due to continuous miniaturization. Whether the calculations of Mindlin and Lee's theory still have great agreement with the measurement data of the miniaturization AT-cut quartz plate is the problem we have to solve. In this paper, the frequency spectrum of quartz plates with partial electrodes at different dimensions was calculated and compared with the experimental data of miniaturized plates. The influence of the length and width of quartz crystal plates and electrodes, and size of mounting area are also studied. It shows the theory still can estimate frequency of inharmonic overtone quite well and the dimensions of plates have little influence on inharmonic overtones. Such results are useful in the design improvement process of quartz crystal resonators.