Design of spurious mode-free elliptical ring resonators

Abstract

Spurious modes suppression to retain the purity of the main resonance in lateral-extensional contour modes is one of the most important requirements for commercializing vibrating RF MEMS resonators. This issue becomes much more critical for ring-shaped micromechanical resonators that are normally susceptible to both out-of-plane flexural modes and in-plane torsional modes at frequencies adjacent to that of the desired lateral-extensional mode. However, this kind of lateral-extensional mode resonators hold unique ability to achieve GHz frequencies without excessive scaling of its key dimensions, such as inner and outer radius, to facilitate strong electromechanical coupling coefficient by either capacitive or piezoelectric transducers while exhibiting high Q’s on the orders of a few thousands. This paper presents a new type of ring resonators based on a hollow ellipsoid structure operating in the extensional wine-glass mode. Due to the mode shape matching to the resonator body shape, vibration amplitude at this strategically-designed mode becomes much larger than those for other modes. Moreover, a harmonic analysis to verify the basic design principles and further discussions towards design optimization have been presented.