Abstract: A method for modifying the resonance frequency of a micro-mechanical resonator, and resonators on which the method is practiced. A packaged resonator is trimmed by directing electromagnetic energy to the resonator through a transparent portion of the package. The removal of mass (by the energy) affects the resonance frequency of the resonator in a predictable manner. In some embodiments, the energy is sourced from a femtosecond laser. In some variations of the illustrative embodiment, the amount of mass to be removed is determined as a function of its location on the resonator. A mass-trimming map is developed that identifies a plurality of potential mass-trimming sites on the resonator. A site can be classified as a fine-tuning site or a coarse-tuning site as a function of the degree to which mass removal at those sites affects the resonance frequency. The sites can also be characterized as a function of their position relative to features of the resonator (e.g., nodal lines, etc.).

Abstract: A method for modifying the resonance frequency of a micro-mechanical resonator, and resonators on which the method is practiced. A packaged resonator is trimmed by directing electromagnetic energy to the resonator through a transparent portion of the package. The removal of mass (by the energy) affects the resonance frequency of the resonator in a predictable manner. In some embodiments, the energy is sourced from a femtosecond laser. In some variations of the illustrative embodiment, the amount of mass to be removed is determined as a function of its location on the resonator. A mass-trimming map is developed that identifies a plurality of potential mass-trimming sites on the resonator. A site can be classified as a fine-tuning site or a coarse-tuning site as a function of the degree to which mass removal at those sites affects the resonance frequency. The sites can also be characterized as a function of their position relative to features of the resonator (e.g., nodal lines, etc.).

Abstract: The illustrative embodiment of the present invention is a vertical-mode, free-free beam resonator, and micromechanical circuits that include one or more such resonators. In accordance with the illustrative embodiment, the resonator comprises a movable beam that overlies a drive electrode. The movable beam is supported by a plurality of supports, the length of which is substantially less than one-quarter of a wavelength of the resonant frequency of the resonator.