MEASUREMENT AND ANALYSIS OF CHARGE-DISTRIBUTIONS INDUCED ON RECTANGULAR AT-CUT QUARTZ RESONATORS

For the design of a strip-shaped rectangular AT-cut plate used frequen tly in recent years, an accurate spurious analysis method is required to avoid many spurious vibrations which have phase variations in both the X and Z' directions. At present, Mindlin's approximate analysis me thod based on the plate equations has the highest accuracy, although i ts degree of approximation has not been studied sufficiently. In this paper, the spurious modes excited in a rectangular AT cut are studied. Tn addition, to investigate the applicability of the plate equation f or the analysis of characteristics of these modes, the surface charge distributions of the spurious mode are obtained experimentally and com pared with the computations. From the computed results and the experim ental results obtained with a highly accurate surface charge measureme nt system based on the principle of the electric probe, it is found th at the spurious modes all belong to the thickness-flexure and the face -shear/flexure except for the weak resonances considered to be excited by the nonsymmetry of the plate. It is pointed out that improvement o f the degree of approximation of the plate equations requires adjustme nt of the coupling between the thickness-flexure modes and the face-sh ear/flexure modes.