Provided are micromechanical resonators and resonator systems including the micromechanical resonators. The micromechanical resonators may each include a supporting beam including a fixed end fixed on a supporting member and a loose end configured to vibrate, and a lumped mass arranged on the loose end, wherein the loose end has a width greater than a width of the fixed end, and a width of the lumped mass is greater than that the width of the fixed end.

A micro-mechanical resonator die includes: micro-mechanical resonator die layers; a cavity formed in at least one of the micro-mechanical resonator die layers; and a micro-mechanical resonator suspended in the cavity. The micro-mechanical resonator includes: a base; a first resonator portion extending from the base along a first plane; and a second resonator portion extending from the base along a second plane. The first resonator portion is configured to operate in an out-of-plane flexural mode that displaces at least part of the first resonator portion out of the first plane. The second resonator portion is configured to operate in an out-of-plane flexural mode that displaces at least part of the second resonator portion out of the second plane and out-of-phase relative to the first resonator portion.

A method for designing a narrowband acoustic wave microwave filter including: generating a modeled filter circuit design having circuit elements including an acoustic resonant element defined by an electrical circuit model that includes a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss; and generating a final circuit design. Generating the final circuit design includes optimizing the modeled filter circuit design to generate an optimized filter circuit design; comparing a frequency response of the optimized filter circuit design to requirements; selecting the optimized filter circuit design for construction into the actual acoustic microwave filter based on the comparison; and transforming the optimized filter circuit design to a design description file for input to a construction process.

A microelectromechanical system (MEMS) resonator includes a substrate having a substantially planar surface and a resonant member having sidewalls disposed in a nominally perpendicular orientation with respect to the planar surface. Impurity dopant is introduced via the sidewalls of the resonant member such that a non-uniform dopant concentration profile is established along axis extending between the sidewalls parallel to the substrate surface and exhibits a relative minimum concentration in a middle region of the axis.

A microelectromechanical system (MEMS) resonator includes a substrate having a substantially planar surface and a resonant member having sidewalls disposed in a nominally perpendicular orientation with respect to the planar surface. Impurity dopant is introduced via the sidewalls of the resonant member such that a non-uniform dopant concentration profile is established along axis extending between the sidewalls parallel to the substrate surface and exhibits a relative minimum concentration in a middle region of the axis.

A continuous or distributed resonator geometry is defined such that the fabrication process used to form a spring mechanism also forms an effective mass of the resonator structure. Proportional design of the spring mechanism and/or mass element geometries in relation to the fabrication process allows for compensation of process-tolerance-induced fabrication variances. As a result, a resonator having increased frequency accuracy is achieved.

A method for designing a narrowband acoustic wave microwave filter including: generating a modeled filter circuit design having circuit elements including an acoustic resonant element defined by an electrical circuit model that includes a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss; and generating a final circuit design. Generating the final circuit design includes optimizing the modeled filter circuit design to generate an optimized filter circuit design; comparing a frequency response of the optimized filter circuit design to requirements; selecting the optimized filter circuit design for construction into the actual acoustic microwave filter based on the comparison; and transforming the optimized filter circuit design to a design description file for input to a construction process.

The present invention relates to a method and a device for stabilization of amplitude of a mechanical vibration of a mechanical resonator in a microelectromechanical sensor device. The method comprises exciting the mechanical resonator with an oscillating excitation force by an input transducer. The input transducer is driven with an input AC voltage having essentially constant amplitude at a frequency that deviates from the resonant frequency of the mechanical resonator by a first frequency difference. The first frequency difference is configured to stabilize the amplitude of the mechanical vibration.

Multiple degenerately-doped silicon layers are implemented within resonant structures to control multiple orders of temperature coefficients of frequency.

Embodiments of multi-frequency excitation are described. In various embodiments, a natural frequency of a device may be determined. In turn, a first voltage amplitude and first fixed frequency of a first source of excitation can be selected for the device based on the natural frequency. Additionally, a second voltage amplitude of a second source of excitation can be selected for the device, and the first and second sources of excitation can be applied to the device. After applying the first and second sources of excitation, a frequency of the second source of excitation can be swept. Using the methods of multi-frequency excitation described herein, new operating frequencies, operating frequency ranges, resonance frequencies, resonance frequency ranges, and/or resonance responses can be achieved for devices and systems.