Analysis of Trapped Energy Resonators with Tabs

A simple theoretical model is presented for analyzing the effects of tab electrodes on trapped energy resonators with rectangular electrodes. A tab of a strip type extending along the 2' axis on an AT- cut rectangular plate is treated. The model is based on the mode- matching method so that it can accurately describe two-dimensional displacement fields. Equations that determine the resonant frequen- cies, mode shapes, and mode strength are derived. The calculated re- sults of resonant frequencies and inductances for AT-cut third overtone resonators are compared with measured results. It is shown from the comparison between experiment and theory that the model predicts well the strong acoustical effects of tabs on anharmonic trapped modes having phase reversals in the tab direction and little effect on the main and other anharmonic spurious modes. This paper presents a simple theoretical model for ana- lyzing the effects of tab electrodes on trapped energy res- onators with rectangular electrodes. A tab of strip type extending along the Z' axis on an AT-cut rectangular plate is treated. The model, which is an extension of the pre- vious one (3), is based on the mode-matching method and so can be applied to trapped modes decaying exponen- tially and also untrapped modes with a sinusoidal varia- tion along the tab. Experimental measurements of reso- nant frequencies and mode strength for anharmonic modes on third overtone AT-cut quartz resonators are provided to substantiate the theory's validity. Calculated and mea- sured results show that the tabs have a strong acoustical effect on anharmonic spurious modes with phase reversals in the tab direction and little effect on the main and other spurious modes.