Abstract: In one embodiment, an apparatus includes a resonant structure having a plate, a drive electrode and a sense electrode. The resonant structure defines an axis substantially orthogonal to a plane defined by the plate when the resonant structure is not excited. The plate is formed from a piezoelectric material. The drive electrode is configured to excite the resonant structure, and the sense electrode is configured to sense a signal in response to rotation of the resonant structure about the axis.

Abstract: Methods and apparatus for anchoring resonators, such as microelectromechanical systems (MEMS) resonators. A resonator may include a substrate, a mechanical resonating structure, and at least one anchor. The mechanical resonating structure may be configured to resonate in a resonance mode of vibration at a frequency. The anchor may couple the mechanical resonating structure to the substrate. The anchor may be configured to exhibit an acoustic bandgap at the frequency of the resonance mode of vibration of the mechanical resonating structure. The anchor may be oriented in a direction substantially parallel to a direction of propagation of the resonance mode of vibration of the mechanical resonating structure.

Abstract: Methods are described for constructing a mechanical resonating structure by applying an active layer on a surface of a compensating structure. The compensating structure comprises one or more materials having an adaptive resistance to deform that reduces a variance in a resonating frequency of the mechanical resonating structure, wherein at least the active layer and the compensating structure form a mechanical resonating structure having a plurality of layers of materials A thickness of each of the plurality of layers of materials results in a plurality of thickness ratios therebetween.

Abstract: In one embodiment, an apparatus comprises a micromechanical gyroscope and a circuit. The micromechanical gyroscope is configured to be excited in a first mode by a drive signal, and configured to be excited in a second mode by a gyroscopic effect. The circuit is coupled to the micromechanical gyroscope and configured to detect the gyroscopic effect when the micromechanical gyroscope is in the second mode.

Abstract: Suppression of spurious modes of vibration for resonators and related apparatus and methods. A device may include a MEMS resonating structure, a substrate, and anchors between the MEMS resonating structure and the substrate. The MEMS resonating structure may have at least one main eigenmode of vibration and at least one spurious eigenmode of vibration. The anchors may be configured to suppress the response of the at least one spurious mode of vibration.

Abstract: Mechanical resonating structures are described, as well as related devices and methods. The mechanical resonating structures may have a compensating structure for compensating temperature variations.

Abstract: Apparatus and methods for control of the second order temperature dependence of the frequency of a mechanical resonating structure are described. The second order temperature dependence of frequency of the mechanical resonating structure may be non-linear. Control may be provided by doping of a semiconductor layer of the mechanical resonating structure.

Abstract: Microelectromechanical systems (MEMS) resonators and related methods and apparatus are provided. A MEMS resonator may include a first portion and a second portion. The first portion may be configured to resonate, and the second portion may be configured to operate based on an energy trapping principle to prevent energy from traveling therethrough from the first portion. The MEMS resonator may be a Lamb wave resonator. The MEMS resonator may be anchorless. The MEMS resonator may have a side contacted by the anchor, wherein the anchor contacts greater than approximately 50% of the side.

Abstract: Micromechanical resonators having stub anchors are described. The micromechanical resonators may be suspended, being connected to a substrate or support by one or more anchors. The anchor(s) may include one or more stubs which can impact the acoustic impedance of the anchor(s). The stub(s) may have various shapes and sizes. In some instances, multiple resonators may be coupled together by a connector having one or more stubs.

Abstract: In one embodiment, an apparatus includes a resonant structure having a plate, a drive electrode and a sense electrode. The resonant structure defines an axis substantially orthogonal to a plane defined by the plate when the resonant structure is not excited. The plate is formed from a piezoelectric material. The drive electrode is configured to excite the resonant structure, and the sense electrode is configured to sense a signal in response to rotation of the resonant structure about the axis.

Abstract: A device or system that incorporates teachings of the present disclosure may include, for example, a resonant structure having a plate, a mass and a set of electrodes. The plate can have an extensional mode at a frequency when excited. The set of electrodes can be used to measure an acceleration of the mass when the acceleration of the mass changes the frequency of the plate. Other embodiments are disclosed.

Abstract: Devices having piezoelectric material structures integrated with substrates are described. Fabrication techniques for forming such devices are also described. The fabrication may include bonding a piezoelectric material wafer to a substrate of a differing material. A structure, such as a resonator, may then be formed from the piezoelectric material wafer.

Abstract: Devices having piezoelectric material structures integrated with substrates are described. Fabrication techniques for forming such devices are also described. The fabrication may include bonding a piezoelectric material wafer to a substrate of a differing material. A structure, such as a resonator, may then be formed from the piezoelectric material wafer.

Abstract: Apparatus and methods for control of charge in a semiconductor material of a mechanical resonating structure are described. Controlling the charge of the material may control the material properties of the semiconductor, such as the stiffness. Such control may result in changes in the behavior of the mechanical resonating structure, allowing for control and tuning of the behavior of the mechanical resonating structure.

Abstract: Systems and methods for operating with oscillators configured to produce an oscillating signal having an arbitrary frequency are described. The frequency of the oscillating signal may be shifted to remove its arbitrary nature by application of multiple tuning signals or values to the oscillator. Alternatively, the arbitrary frequency may be accommodated by adjusting operation one or more components of a circuit receiving the oscillating signal.

Abstract: Mechanical resonating structures are described, as well as related devices and methods. The mechanical resonating structures may have a compensating structure for compensating temperature variations.

Abstract: Mechanical resonating structures are described, as well as related devices and methods. The mechanical resonating structures may have a compensating structure for compensating temperature variations. The compensating structure may have multiple layers, one of which may have a stiffness that increases with increasing temperature and one of which may have a stiffness that decreases with increases in temperature.

Abstract: Integrated circuits having electrically conductive traces are described. The electrically conductive traces may be formed of multiple electrically conductive layers. One or more of the multiple electrically conductive layers may have a cut formed therein to form a gap in that electrically conductive layer. One or more electrical conductive layers of the electrical conductive traces may bridge the gap.

Abstract: Resonator structures and electrodes are described, as well as methods for manufacturing the same. Resonator electrodes may be formed using two or more photolithographic steps and masks, with different masks being used to define different features of the electrodes. The masks may create self-aligned electrodes, which can be aligned with one or more anchors of the resonator.

Abstract: Systems and methods for operating with oscillators configured to produce an oscillating signal having an arbitrary frequency are described. The frequency of the oscillating signal may be shifted to remove its arbitrary nature by application of multiple tuning signals or values to the oscillator. Alternatively, the arbitrary frequency may be accommodated by adjusting operation one or more components of a circuit receiving the oscillating signal.