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Bulk piezoelectric micro-gyroscope is a miniaturized inertial sensor thatuses a differential thickness-shear bulk mode of a PZT block as the drive modeof the gyroscope. In the paper, a second differential thickness-extensionalmode is identified for the sense mode and mode-matching is proposed for thefirst time by proper design of the device geomtries. Through finite elementmodal analysis, the frequencies of drive mode and sense mode are obtained whenthe length of the PZT block varies from 4.8mm to 5.6mm and the width of the PZTblock varies from 3.0mm to 4.0mm. Using a fitting method, the empiricalformulae with an excellent fit are induced to predict the influence of thelength and the width of the PZT block on the drive and sense mode frequencies.Based on these empirical formulae, the mode-matching equations are introduced.The analysis results show that for a given thickness of the PZT block, theeffect of the width on the drive mode frequency is prominant. Conversly, theeffect of length on the sense mode frequency is dominant. The resonancefrequencies, kinetic energy ratios, scale factors of gyroscope are compared toevaluate the mode quality. The results show that the kinetic energy in y-axisdirection of the drive mode and the kinetic energy in z-axis direction of thesense mode increase with the thickness of the PZT block, and consequently thescale factor of the gyroscope increases. For a constant thickness of the PZTblock the scale factor will decrease as the length increases. Through designoptimization we present a 20 times improvement in the scale factor of themode-matched gyroscope. Given the thickness of PZT block, the length and thewidth will be determined by the mode-matching equations mentioned. Generally,the analysis suggests that the resolution of the gyroscope improves byincreasing the thickness PZT block.

Design optimization of mode-matched bulk-mode piezoelectric micro-gyroscopes through modal analysis