Achieving the desired resonant frequency of resonators has been an important issue, since it determines their performance. This paper presents the design and analysis of two concepts for the resonant frequency tuning of resonators. The proposed methods are based on the stiffness alteration of the springs by geometrical modification (shaft-widening) or by mechanical restriction (shaft-holding) using micromachined frequency tuning units. Our designs have advantages in (1) reversible and repetitive tuning; (2) decoupled control over the amplitude of the resonator and the tuning ratio; and (3) a wide range of applications including torsional resonators. The ability to tune the frequency by both methods is predicted by finite element analysis (FEA) and experimentally verified on a torsional resonator driven by an electrostatic actuator. The tuning units and resonators are fabricated on a double silicon-on-insulator (DSOI) wafer to electrically insulate the resonator from the tuning units. The shaft-widening type and shaft-holding type exhibit a maximum tuning ratio of 5.29% and 10.7%, respectively.
Keywords: resonant frequency tuning; shaft-holding; shaft-widening; torsional resonator.