AT-CUT QUARTZ RESONATORS WITH INVERTED-MESA ELECTRODES

This paper presents a theoretical analysis of trapped-energy AT-cut qu artz resonators with au inverted-mesa electrode for obtaining a low ca pacitance ratio and inharmonic mode suppression. By decreasing the thi ckness of the electrode at its central region, the displacement distri bution represents a single peak curve, a nat curve or a twin peak curv e. The capacitance ratio has a minimum value in the region where the d isplacement distribution becomes Bat. To suppress the inharmonic mode response, the energy trapping factor is located at the threshold point where the lowest symmetric inharmonic mode S-1 is to be trapped, The calculated result confirms that there is a combination of design param eters which can achieve the minimum capacitance ratio and the inharmon ic mode suppression simultaneously using the inverted-mesa electrode. The capacitance ratio of an AT-cut quartz resonator with the inverted- mesa electrode has a minimum value of 169.