A double-resonator design has been devised for a cloverleaf-shaped silicon microelectromechanical resonator. The double-resonator design provides for an inner, higher-frequency resonator suspended on an outer, lower-frequency resonator. This design concept affords several advantages, as described below.
The figure schematically depicts mathematical models of the previous single-resonator design and the present double-resonator design. The schematic diagrams reflect the observation that it is more accurate to model the substrate as a finite mass with damping than to assume that the substrate is so rigidly mounted that it represents an infinite mass. In the single-resonator design, resonator mass M1 is coupled, via a spring of stiffness k1, to a damped substrate mass M2. This model yields close agreement between predicted and measured Q factors.
In the double-resonator design, inner resonator mass M1 is suspended on a spring of stiffness k1 that is attached to an intermediate mass M2, which, in turn, is coupled to damped substrate mass M3 via a spring of stiffness k2. M2 is chosen to be much greater than M1; consequently, the frequency and mode shape of the higher-frequency (M1,k1,M2) resonance does not differ greatly from that of the single-resonator design. M3 is also chosen to be much greater than M1; this choice, in combination with the choice of M2, and with the choice of k1 and k2 to be approximately equal, ensures that the damping on M3 exerts little effect on the Q of the higher-frequency resonance.
Because of the isolation provided by k2, very little of any mounting stress that might be imposed on M3 is coupled into k1. In addition, because of the largeness of M2 relative to M1, very little of any vibration imposed on M3 propagates to M1. Another advantage of the double-resonator design is that M2 can be tailored to exert a slight effect on the resonances (in other words, to tune the vibrating system); it is easier to tune in this way that to tailor k1.
In the prototype double resonator, the substrate of a cloverleaf resonator substructure is suspended by four springs that connect it to an outer frame. The lowest resonance frequency of the cloverleaf is designed to be 6 kHz, while the lowest resonance frequency for vibration isolation is designed to be 200 Hz. It has been predicted that the cloverleaf resonance will have a Q > 104, and that because of damping in the outer frame, the substrate resonance will have Q < 100.
This work was done by Roman Gutierrez, Tony K. Tang, and Kirill Shcheglov of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Mechanics category.
In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to
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Refer to NPO-20658, volume and number of this NASA Tech Briefs issue, and the page number.
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Micromachined Double Resonator
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Overview
The document presents a technical support package from NASA's Jet Propulsion Laboratory (JPL) detailing a novel double-resonator design for a cloverleaf-shaped silicon microelectromechanical resonator (MEMS). This innovative design aims to enhance vibration isolation and improve the performance of MEMS devices, which are critical in various applications, including sensors and actuators.
The double-resonator system consists of an inner, higher-frequency resonator suspended on an outer, lower-frequency resonator. This configuration offers several advantages, such as minimizing the coupling of mounting stress and vibration from the outer resonator to the inner one. The design allows for better tuning of the system's resonances, as the larger mass of the outer resonator can be adjusted to exert a slight effect on the inner resonator's frequencies, making it easier to achieve desired performance characteristics.
In the prototype described, the cloverleaf resonator's lowest resonance frequency is set at 6 kHz, while the vibration isolation frequency is designed to be 200 Hz. The quality factor (Q) of the cloverleaf resonance is predicted to exceed 10,000, indicating high efficiency, while the substrate resonance is expected to have a Q value of less than 100 due to damping effects in the outer frame. This disparity in Q values highlights the effectiveness of the design in isolating vibrations.
The work was conducted by a team of researchers, including Roman Gutierrez, Tony K. Tang, and Kirill Shcheglov, at Caltech for NASA. The document emphasizes that the contractor retains title to the invention, and inquiries regarding commercial use should be directed to the Technology Reporting Office at JPL.
The document also includes disclaimers regarding the use of specific trade names and the liability of the United States Government concerning the information provided. It underscores that the research was conducted under a contract with NASA, ensuring that the findings are rooted in rigorous scientific inquiry.
Overall, this technical support package outlines a significant advancement in MEMS technology, showcasing the potential for improved performance in microelectromechanical systems through innovative design strategies. The double-resonator approach represents a promising avenue for future research and application in various fields.
