Theoretical Model of Lateral Electric Field Excited Resonator

The method of calculation of characteristics of acoustic oscillations existing in piezoelectric electric field excited resonator was developed. The resonator represents thin piezoelectric plate with two rectangular electrodes on one its side. The developed method is based on the finite element analysis and allows to find the distribution of the mechanical displacement components in piezoelectric plate and electrical potential in piezoelectric plate and surrounding vacuum for the given value of frequency of excited field. At that this method allows to consider various boundary conditions on different areas of surface plate including the presence of damping layers. This allows to calculate the real and imaginary parts of electrical impedance as function of frequency. The resonator under study represented the plate of $X$ – cut lithium niobate with thickness of 0.5 mm. Two rectangular electrodes with width of 5 mm were deposited on one side of the plate in such a way that excited electric field was oriented along crystallographic axis $Y$. The calculations were carried out for different values of width of the gap between electrodes in a range 1 – 3 mm. It has been shown that the increase in the width of gap leads to insignificant increase in resonant frequency and the use of damping layers on outside parts of electrodes allows significantly increase its $Q$-factor. The obtained results are in a satisfactory agreement with experimental data.