Abstract
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.
Highlights
Micromachined resonators have a broad range of applications owing to their various advantages such as fast response, high sensitivity, small size, low power consumption, and low fabrication cost [1,2,3]
The resonant frequency tuning of a torsional resonator has been demonstrated by two concepts: shaft-widening and shaft-holding
Based on the finite element analysis (FEA) results, we verified the validity of our tuning methods, and derived the estimated change of torsional stiffness and tuning range
Summary
Micromachined resonators have a broad range of applications owing to their various advantages such as fast response, high sensitivity, small size, low power consumption, and low fabrication cost [1,2,3]. The resonant frequencies of the micromachined resonators often deviate from the intended value. It is reported that the micromachined resonators generally have a deviation in resonant frequency between ±1%~±5% [7]. The first approach is based on the permanent structural modification of the resonators, which is usually referred to as passive frequency tuning [6,10,11,12]. A few works have been reported regarding the frequency tuning of torsional resonators [14,24,25], such as designing angle limiters near the torsional spring [24] or inducing stress on bending flexures [25]. The proposed methods are based on the micromachined frequency tuning unit, which is integrated together with electrostatic torsional resonator on the same chip. The separation of actuators for the tuning unit and resonator enables independent control over the amplitude and resonant frequency of the resonator, allowing continuous and repetitive tuning
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