MEMS resonator with wide frequency tuning range and linear response to control voltages for use in voltage control oscillators

• Published in: Journal of micromechanics and microengineering Vol. 29; no. 12; pp. 125007 - 125020
• Main Authors: Kawakami, Kouki, Kaneuchi, Shunya, Tanigawa, Hiroshi, Suzuki, Kenichiro
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.12.2019
• Subjects: MEMS; resonator; temperature compensation; tuning electrodes; voltage control oscillator
• ISSN: 0960-1317; 1361-6439
• DOI: 10.1088/1361-6439/ab4830

In this paper, we evaluated the influence of the tuning electrodes (TEs), which are added to a resonator besides a driving electrode, on the vibration of the resonator and made use of it for the frequency compensation for temperature dependence. We first presented an analytical form for a resonator with TEs and then confirmed the results well by comparing with experimental data: the application of DC voltages to the TEs suppresses the ratio of the frequency change (RFC) over temperature owing to the negative stiffness effect. This tuning method differs from the conventional method at a point that the former can provide much wider frequency tuning range than the latter due to little change in displacement amplitude. Moreover, setting a large bias voltage is helpful for making the response to applied voltages nearly linear, resulting in decreasing the adverse influence of nonlinear relation with voltages on RFC. Such linear response greatly helps for making the design of voltage control oscillators (VCOs) in a very simple form. We demonstrated the theory by applying DC voltages of 10.3-13.1 V linearly to the TEs, through a linear amplifier with a constant gain of  −5.8, depending on the temperature of 25 °C-70 °C. The resulting RFC was successfully decreased to be less than 30 ppm over the temperature. This is approximately 1/31 of the RFC for a silicon resonator itself. This effective tuning control method is suitable for VCOs in various instruments suited for small and portable applications, for example, mobile applications etc.