Abstract: A micro-electrical-mechanical system (MEMS) resonator device includes at least one functionalization material arranged over at least a central portion, but less than an entirety, of a top side electrode. For an active region exhibiting greatest sensitivity at a center point and reduced sensitivity along its periphery, omitting functionalization material over at least one peripheral portion of a resonator active region prevents analyte binding in regions of lowest sensitivity. The at least one functionalization material extends a maximum length in a range of from about 20% to about 95% of an active area length and extends a maximum width in a range of from about 50% to 100% of an active area width. Methods for fabricating MEMS resonator devices are also provided.

Abstract: The present disclosure relates to circuitry for driving a piezoelectric transducer. The circuitry comprises amplifier circuitry configured to receive a drive signal and to output an output signal, based on the drive signal, to the piezoelectric transducer, a variable capacitor configured to be coupled in series with the piezoelectric transducer, and control circuitry. The control circuitry is configured to control a capacitance of the variable capacitor to compensate for hysteresis in the piezoelectric transducer and to control a gain of the amplifier circuitry to compensate for signal attenuation caused by the variable capacitor.

Abstract: A microelectromechanical system (MEMS) resonator includes a resonant semiconductor structure, drive electrode, sense electrode and electrically conductive shielding structure. The first drive electrode generates a time-varying electrostatic force that causes the resonant semiconductor structure to resonate mechanically, and the first sense electrode generates a timing signal in response to the mechanical resonance of the resonant semiconductor structure. The electrically conductive shielding structure is disposed between the first drive electrode and the first sense electrode to shield the first sense electrode from electric field lines emanating from the first drive electrode.

Abstract: Ultraviolet (UV), Terahertz (THZ) and Infrared (IR) radiation detecting and sensing systems using graphene nanoribbons and methods to making the same. In an illustrative embodiment, the detector includes a substrate, single or multiple layers of graphene nanoribbons, and first and second conducting interconnects each in electrical communication with the graphene layers. Graphene layers are tuned to increase the temperature coefficient of resistance to increase sensitivity to IR radiation. Absorption over a wide wavelength range of 200 nm to 1 mm are possible based on the two alternative devices structures described within. These two device types are a microbolometer based graphene film where the TCR of the layer is enhanced with selected functionalization molecules. The second device structure consists of a graphene nanoribbon layers with a source and drain metal interconnect and a deposited metal of SiO2 gate which modulates the current flow across the phototransistor detector.

Abstract: A method for manufacturing a micromechanical layer structure, including: providing a first protective layer patterned to have at least one opening which is filled with sacrificial layer material; depositing a functional-layer layer structure; producing a first opening in the functional-layer layer structure to at least one opening of the first protective layer, so that in at least one of the layers of the functional-layer layer structure; depositing a second protective layer so that the first opening is filled with material of the second protective layer; patterning the second protective layer and the filled first opening to have a second opening to the first protective layer, the second opening having the same or a lesser width than the first opening; removing sacrificial layer material at least in the opening of the first protective layer; and removing protective layer material at least in the second opening.

Abstract: 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.

Abstract: A ring gyroscope which comprises a substantially circular and flexible ring which defines a ring plane, one or more primary piezoelectric split transducers configured to drive the ring into resonance oscillation, four or more mass elements which form a symmetrical mass distribution in relation to both a first and a second transversal symmetry axis and to a first and a second diagonal symmetry axis. The ring gyroscope also comprises a suspension structure configured to support the weight of the ring and the mass elements, wherein the suspension structure comprises N outer suspenders, where N is an integer greater than or equal to two, and each outer suspender extends along a ring tangent from a suspension attachment point on the outer edge of the ring to an anchor point.

Abstract: An aspect of the present disclosure concerns an oscillator circuit including a driver circuit that includes a first amplifier and a current detector where the first amplifier produces an oscillation voltage signal, where the current detector detects an oscillation current signal and produces a drive voltage signal, and where the oscillation current signal corresponds to difference in voltage between the oscillation voltage signal and the drive voltage signal; a feedback circuit that includes a second amplifier receiving the oscillation voltage signal and the drive voltage signal, to produce a feedback voltage signal to the driver circuit; and an oscillator that oscillates at a frequency determined in accordance with the drive voltage signal.

Abstract: A processing unit processes an input signal from an external apparatus and includes a first terminal to which a reference voltage is input from the external apparatus, a second terminal to which a first pulse signal having a first frequency is input from the external apparatus, and a control portion to process the input signal. A memory stores data to be transmitted to the external apparatus, and a clock generating unit generates a clock signal having a higher frequency than the first frequency of the first pulse signal. To transmit a data signal to the external apparatus from the processing unit, the control portion switches a load between the first terminal and the second terminal based on the data stored in the memory during a period in which a second pulse signal having a second frequency lower than the first frequency is input from the external apparatus.

Abstract: Provided is an oscillator including: a resonator; a first circuit device electrically coupled to the resonator; and a second circuit device. The first circuit device generates a first clock signal by causing the resonator to oscillate, and performs first temperature compensation processing for temperature compensating a frequency of the first clock signal. The second circuit device receives the first clock signal from the first circuit device, generates a second clock signal based on the first clock signal, and performs second temperature compensation processing for temperature compensating a frequency of the second clock signal.

Abstract: A microelectromechanical system (MEMS) resonator includes a resonant semiconductor structure, drive electrode, sense electrode and electrically conductive shielding structure. The first drive electrode generates a time-varying electrostatic force that causes the resonant semiconductor structure to resonate mechanically, and the first sense electrode generates a timing signal in response to the mechanical resonance of the resonant semiconductor structure. The electrically conductive shielding structure is disposed between the first drive electrode and the first sense electrode to shield the first sense electrode from electric field lines emanating from the first drive electrode.

Abstract: Methods and apparatus generate an oscillating output signal having a voltage swing greater than a voltage swing across nodes of active devices. An example oscillator includes a tank to generate an oscillating output signal in response receiving an edge of an enable signal; a feedback generator including a first gain stage forming a first feedback loop with the tank, the first feedback loop providing a first charge to maintain the oscillating output signal and a second gain stage forming a second feedback loop with the tank, the second feedback loop providing a second charge to maintain the oscillating output signal, the first and second charges combining with the oscillating output signal to generate a high voltage swing; and an attenuator connected between the tank and the feedback generator to isolate the tank from active components of the feedback generator.

Abstract: A passive wireless sensor system is disclosed that includes components fabricated from carbon nanotube (CNT) structures. In some situations, the passive wireless sensor system includes a CNT structure sensor and an antenna that communicates wirelessly by altering an impedance of the antenna. The passive wireless sensor system includes a non-battery-powered energy storage device that harvests energy from carrier signals received at the antenna. The antenna and the energy storage device can be formed from CNT structures.

Abstract: A physical quantity detection apparatus includes a vibrator which outputs a detection signal in accordance with a physical quantity and a drive circuit which drives the vibrator to oscillate, wherein the drive circuit includes: an oscillation detecting unit which detects an oscillating state or a non-oscillating state of the vibrator based on a drive signal of the vibrator; a start-up oscillation unit which assists an oscillating operation of the vibrator when a detection result of the oscillation detecting unit represents the non-oscillating state; and a switching count monitoring unit which detects that the number of times switching is performed between the oscillating state and the non-oscillating state in the oscillation detecting unit has exceeded a set upper limit number of times.

Abstract: Electro-mechanical designs for MEMS scanning mirrors are described. In various embodiments, a driving coil may be situated on a reflective portion of a MEMS mirror. In some embodiments, a sensing coil may be situated partially or entirely on an outer frame portion of the MEMS mirror. Other embodiments are described and claimed.

Abstract: Ultraviolet (UV), Terahertz (THZ) and Infrared (IR) radiation detecting and sensing systems using graphene nanoribbons and methods to making the same. In an illustrative embodiment, the detector includes a substrate, single or multiple layers of graphene nanoribbons, and first and second conducting interconnects each in electrical communication with the graphene layers. Graphene layers are tuned to increase the temperature coefficient of resistance to increase sensitivity to IR radiation. Absorption over a wide wavelength range of 200 nm to 1 mm are possible based on the two alternative devices structures described within. These two device types are a microbolometer based graphene film where the TCR of the layer is enhanced with selected functionalization molecules. The second device structure consists of a graphene nanoribbon layers with a source and drain metal interconnect and a deposited metal of SiO2 gate which modulates the current flow across the phototransistor detector.

Abstract: An integrated circuit includes first and second coils, a first pad connected to the first coil and to a resonator, a second pad connected to the second coil and to the resonator, and first and second output terminals. The first pad is arranged to provide signals between the resonator and the first coil. The second pad is arranged to provide signals between the resonator and the second coil. A distance between the first pad and the first coil is less than a distance between the first coil and the first output terminal and a distance between the first coil and the second output terminal. A distance between the second pad and the second coil is less than a distance between the second coil and the first output terminal and a distance between the second coil and the second output terminal.

Abstract: A microelectromechanical system (MEMS) resonator includes a resonant semiconductor structure, drive electrode, sense electrode and electrically conductive shielding structure. The first drive electrode generates a time-varying electrostatic force that causes the resonant semiconductor structure to resonate mechanically, and the first sense electrode generates a timing signal in response to the mechanical resonance of the resonant semiconductor structure. The electrically conductive shielding structure is disposed between the first drive electrode and the first sense electrode to shield the first sense electrode from electric field lines emanating from the first drive electrode.

Abstract: A micro-electrical-mechanical system (MEMS) resonator device includes a top side electrode overlaid with an interface layer including a material having a surface (e.g., gold or other noble metal, or a hydroxylated oxide) that may be functionalized with a functionalization (e.g., specific binding or non-specific binding) material. The interface layer and/or an overlying blocking material layer are precisely patterned to control locations of the interface layer available to receive a self-assembled monolayer (SAM), thereby addressing issues of misalignment and oversizing of a functionalization zone that would arise by relying solely on microarray spotting. Atomic layer deposition may be used for deposition of the interface layer and/or an optional hermeticity layer. Sensors and microfluidic devices incorporating MEMS resonator devices are also provided.

Abstract: The present disclosure relates to a microelectromechanical systems (MEMS) package having two MEMS devices with different pressures, and an associated method of formation. In some embodiments, the (MEMS) package includes a device substrate and a cap substrate bonded together. The device substrate includes a first trench and a second trench. A first MEMS device is disposed over the first trench and a second MEMS device is disposed over the second trench. A first stopper is raised from a first trench bottom surface of the first trench but below a top surface of the device substrate and a second stopper is raised from a second trench bottom surface of the second trench but below the top surface of the device substrate. A first depth of the first trench is greater than a second depth of the second trench.

Abstract: The present disclosure is directed to a method of manufacturing an oscillator. The oscillator includes a resonator element, an oscillation circuit which outputs an oscillation signal by oscillating the resonator element, and a temperature compensation circuit which compensates for temperature characteristics of a frequency of the oscillation signal in a desired temperature range. The method includes a first temperature compensation adjustment step in which the frequency is measured at multiple temperatures, and first temperature compensation data is calculated based on a relationship between temperature and the frequency.

Abstract: An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.

Abstract: An apparatus for determining a position between a wireless power transmitter and a wireless power receiver is provided. The apparatus comprises a first ferrite block having respective portions configured to be disposed in physical contact with each of adjacent second and third ferrite blocks separated by a first gap and with each of adjacent fourth and fifth ferrite blocks separated by a second gap. The apparatus further comprises a plurality of detection loops wrapped around the first ferrite block such that none of the plurality of detection loops physically contact the second, third, fourth or fifth ferrite blocks when the respective portions of the first ferrite block are in physical contact with the second, third, fourth or fifth ferrite blocks. Each of the plurality of detection loops are wrapped around the first ferrite block in mutually perpendicular planes from one another.

Abstract: A bolometer. In one embodiment a graphene sheet is configured to absorb electromagnetic waves. The graphene sheet has two contacts connected to an amplifier, and a power detector connected to the amplifier. Electromagnetic power in the evanescent electromagnetic waves is absorbed in the graphene sheet, heating the graphene sheet. The power of Johnson noise generated at the contacts is proportional to the temperature of the graphene sheet. The Johnson noise is amplified and the power in the Johnson noise is used as a measure of the temperature of the graphene sheet, and of the amount of electromagnetic wave power absorbed by the graphene sheet.

Abstract: An optical second-harmonic generator (or spontaneous parametric down-converter) includes a microresonator formed of a nonlinear optical medium. The microresonator supports at least two modes that can be phase matched at different frequencies so that light can be converted between them: A first resonant mode having substantially radial polarization and a second resonant mode having substantially vertical polarization. The first and second modes have the same radial order. The thickness of the nonlinear medium is less than one-half the pump wavelength within the medium.

Abstract: A microelectromechanical system (MEMS) resonator includes a resonant semiconductor structure, drive electrode, sense electrode and electrically conductive shielding structure. The first drive electrode generates a time-varying electrostatic force that causes the resonant semiconductor structure to resonate mechanically, and the first sense electrode generates a timing signal in response to the mechanical resonance of the resonant semiconductor structure. The electrically conductive shielding structure is disposed between the first drive electrode and the first sense electrode to shield the first sense electrode from electric field lines emanating from the first drive electrode.

Abstract: A radio transmission apparatus includes a radio transmission IC including a vibration element and a fractional N-PLL circuit and a power amplifier generating a radio transmission signal and a control device that controls the radio transmission IC, and a temperature detection element. The control device controls the fractional N-PLL circuit based on temperature information obtained from the temperature detection element such that a frequency of the radio transmission signal is temperature-compensated.

Abstract: A power transmitter is configured to wirelessly transfer power to at least one power receiver. The power transmitter includes at least one excitation circuit configured to generate a time-varying first magnetic field in response to a time-varying electric current flowing through the at least one excitation circuit. The time-varying first magnetic field has an excitation frequency. The power transmitter further includes a plurality of magnetic oscillators. Each magnetic oscillator of the plurality of magnetic oscillators has a mechanical resonant frequency substantially equal to the excitation frequency. The plurality of magnetic oscillators is configured to generate a time-varying second magnetic field in response to the first magnetic field.

Abstract: This temperature sensor includes an HBAR resonator, a unit for determining the difference between two distinct resonance frequencies at a temperature T, measured between two electrodes of a same pair of the HBAR resonator and a unit for determining the temperature of the resonator from the difference in frequencies and from a one-to-one function providing the match between the temperature and the frequency difference. The resonator is formed by a stack of a first electrode, a transducer, a second electrode, and acoustic substrate and the cuts of the transducer and of the substrate are selected so as to obtain high electro-acoustic couplings and a difference in frequency temperature sensitivities between two distinct vibration modes co-existing within the resonator, greater than or equal to 1 ppm·K?1.

Abstract: A radio frequency (RF) receiver including a baseband circuitry. The baseband circuitry can include a graphene nano-electro-mechanical (GNEMS) based system, a receiver, and a front-end mixer. The GNEMS based system can include a source, a drain, a gate and a nano-scale suspended graphene resonator. The graphene resonator can be suspended between the source and the drain. The receiver circuitry can be disposed on the baseband and configured to receive an RF signal. The front-end mixer can be disposed between the GNEMS based system and the receiver circuitry. The baseband circuitry can be configured such that an incoming signal sees frequency selective impedance at the receiver circuitry.

Abstract: A resonator has a main resonator body and a secondary resonator structure. The resonator body has a desired mode of vibration of the resonator alone, and a parasitic mode of vibration, wherein the parasitic mode comprises vibration of the resonator body and the secondary resonator structure as a composite body. In this way, unwanted vibrational modes are quenched by the second suspended body.

Abstract: A MEMS resonator system that reduces interference signals arising from undesired capacitive coupling between different system elements. The system, in one embodiment, includes a MEMS resonator, electrodes, and at least one resonator electrode shield. In certain embodiments, the resonator electrode shield ensures that the resonator electrodes interact with either one or more shunting nodes or the active elements of the MEMS resonator by preventing or reducing, among other things, capacitive coupling between the resonator electrodes and the support and auxiliary elements of the MEMS resonator structure. By reducing the deleterious effects of interfering signals using one or more resonator electrode shields, a simpler, lower interference, and more efficient system relative to prior art approaches is presented.

Abstract: A crystal controlled oscillator includes a crystal package and an IC chip board that includes an IC chip integrating an oscillator circuit. The crystal package includes a first container, a crystal resonator, a lid body, and an external terminal at an outer bottom surface of the first bottom wall layer of the first container. The IC chip integrates an oscillator circuit disposed at an outer bottom surface of the first bottom wall layer of the crystal package. The oscillator circuit connects to the lower side excitation electrode of the crystal resonator from the external terminal to an input side with high impedance. The oscillator circuit connects to the upper side excitation electrode to an output side with low impedance. The upper side excitation electrode is a shielding electrode of the crystal resonator.

Abstract: A manufacturing method of an oscillator is a manufacturing method of an oscillator which includes a vibrator and a semiconductor circuit device including an oscillation part connected to the vibrator and a control part to switch an operation mode between a normal mode in which the oscillation part performs an oscillation operation and an inspection mode in which characteristics of the vibrator are inspected, and the manufacturing method includes preparing the semiconductor circuit device in which the operation mode is set to the inspection mode, connecting the semiconductor circuit device and the vibrator electrically, and inspecting the characteristics of the vibrator which is in a state electrically connected to the semiconductor circuit device.

Abstract: A lid body includes: a first surface; a second surface having a top-bottom relation with the first surface; an outer peripheral surface connecting the first surface and the second surface; a groove provided in the first surface from the outer peripheral surface toward an interior of the first surface; and first and second marks arranged at positions that do not overlap with an outer peripheral edge of the second surface in a plan view.

Abstract: The invention relates to a method for operating control equipment (1) of a resonance circuit (2), wherein the control equipment (1) comprises at least two circuit elements (8, 9) connected in series, in particular each comprising a recovery diode (13, 14) connected in parallel, between which a connection (6) of the resonance circuit (2) is connected. According to the invention, the circuit elements (8, 9) are actuated as a function of the voltage detected at the connection (6). The invention further relates to control equipment (1) of a resonance circuit (2).

Abstract: A resonator element includes a substrate vibrating in a thickness-shear vibration mode, a first excitation electrode disposed on one principal surface of the substrate, and has a shape obtained by cutting out four corners of a quadrangle, and a second excitation electrode disposed on the other principal surface of the substrate, and a ratio (S2/S1) between the area S1 of the quadrangle and the area S2 of the first excitation electrode fulfills 87.7%?(S2/S1)<95.0%.

Abstract: A resonator element includes a substrate including a first principal surface and a second principal surface respectively forming an obverse surface and a reverse surface of the substrate, and vibrating in a thickness-shear vibration mode, a first excitation electrode disposed on the first principal surface, and a second excitation electrode disposed on the second principal surface, and being larger than the first excitation electrode in a plan view, the first excitation electrode is disposed so as to fit into an outer edge of the second excitation electrode in the plan view, and the energy trap confficient M fulfills 15.5?M?36.7.

Abstract: The present disclosure relates to nanoresonator oscillators or NEMS (nanoelectromechanical system) oscillators. A circuit for measuring the oscillation frequency of a resonator is provided, comprising a first phase-locked feedback loop locking the frequency of a controlled oscillator at the resonant frequency of the resonator, this first loop comprising a first phase comparator. Furthermore, a second feedback loop is provided which searches for and stores the loop phase shift introduced by the resonator and its amplification circuit when they are locked at resonance by the first loop. The first and the second loops operate during a calibration phase. A third self-oscillation loop is set up during an operation phase. It directly links the output of the controllable phase shifter to the input of the resonator. The phase shifter receives the phase-shift control stored by the second loop.

Abstract: Aspects of the disclosure provide a circuit. The circuit includes a signal amplifying circuit coupled with a crystal component of a natural frequency to form a crystal oscillator, and a signal generator circuit configured to generate a signal with an energy distribution about the natural frequency, and to provide the signal to the crystal oscillator to assist the crystal oscillator to begin oscillating.

Abstract: Integrated circuit devices include a packaged MEMS-based oscillator circuit, which is configured to support bidirectional frequency margining of a periodic output signal. This bidirectional frequency margining is achieved using a first signal to synchronize changes in a frequency of the periodic output signal and a second signal to control whether the changes in the frequency of the periodic output signal are incremental or decremental. In particular, the oscillator circuit may be configured so that each change in the frequency of the periodic output signal is synchronized to a corresponding first voltage transition of the first signal and a voltage level of the second signal may be used to control whether the changes in the frequency of the periodic output signal are incremental or decremental.

Abstract: Oscillators including mechanical resonators are described, as are methods of operating the oscillators such that the mechanical resonator exhibits non-linear behavior. The non-linear behavior may include multiple stable states, for instance being bi-stable. The non-linear behavior may exhibit hysteresis. The mechanical resonator may be driven to operate in a desired portion of the non-linear operating regime.

Abstract: An amplifier and oscillator system includes a MEMS resonator and a two stage amplifier topology. The MEMS resonator is configured to generate a resonator signal. The two-stage amplifier topology is configured to amplify the resonator signal with a selected trans-impedance gain. Additionally, the two stage amplifier topology yields a feedback resistance that provides the selected trans-impedance gain.

Abstract: An oscillator device includes: a structural layer extending over a first side of a semiconductor substrate; a semiconductor cap set on the structural layer; a coupling region extending between and hermetically sealing the structural layer and the cap and forming a cavity within the oscillator device; first and second conductive paths extending between the substrate and the structural layer; first and second conductive pads housed in the cavity and electrically coupled to first terminal portions of the first and second conductive paths by first and second connection regions, respectively, which extend through and are insulated from the structural layer; a piezoelectric resonator having first and second ends electrically coupled, respectively, to the first and second conductive pads, and extending in the cavity; and third and fourth conductive pads positioned outside the cavity and electrically coupled to second terminal portions of the first and second conductive paths.

Abstract: Tunable MEMS resonators having adjustable resonance frequency and capable of handling large signals are described. In one exemplary design, a tunable MEMS resonator includes (i) a first part having a cavity and a post and (ii) a second part mated to the first part and including a movable layer located under the post. Each part may be covered with a metal layer on the surface facing the other part. The movable plate may be mechanically moved by a DC voltage to vary the resonance frequency of the MEMS resonator. The cavity may have a rectangular or circular shape and may be empty or filled with a dielectric material. The post may be positioned in the middle of the cavity. The movable plate may be attached to the second part (i) via an anchor and operated as a cantilever or (ii) via two anchors and operated as a bridge.

Abstract: An oscillator includes a resonator section structured such that a dielectric is interposed between first and second conductors and such that the first and second conductors are electrically connected to a resonant tunneling diode, a capacitor section structured such that the dielectric is interposed between the first and second conductors, a line section configured to electrically connect the resonator section and the capacitor section in parallel to each other, and a resistor section configured to electrically connect the first and second conductors to each other. A first position of the resonator section and a second position of the capacitor section are connected to each other by the line section so that the first position and the second position are substantially electrically equivalent to each other in a wavelength range larger than a wavelength of an electromagnetic wave that resonates in the resonator section.

Abstract: An apparatus includes a microelectromechanical system (MEMS) device configured as part of an oscillator. The MEMS device includes a mass suspended from a substrate of the MEMS, a first electrode configured to provide a first signal based on a displacement of the mass, and a second electrode configured to receive a second signal based on the first signal. The apparatus includes an amplifier coupled to the first electrode and a first node. The amplifier is configured to generate an output signal, the output signal being based on the first signal and a first gain. The apparatus includes an attenuator configured to attenuate the output signal based on a second gain and provide as the second signal an attenuated version of the output signal.

Abstract: One embodiment relates to a method of compensating for crystal frequency variation over temperature. An example method includes obtaining an indication of temperature, computing a temperature compensation value based on the indication of temperature and a piecewise linear temperature compensation approximation, and compensating for a temperature offset in a crystal reference signal by adjusting a division ratio of a fractional divider in a phase-locked loop. The piecewise linear temperature compensation approximation can represent an approximation of frequency error in a crystal reference signal originating from a crystal over temperature. The piecewise linear temperature compensation approximation can be, for example, a linear approximation, a quadratic approximation, or a cubic approximation.

Abstract: A micro electro mechanical system (MEMS) oscillator supplies an oscillator output signal having a first frequency that differs from a predetermined frequency of the output signal. An error determination circuit determines frequency error from the predetermined frequency based on initial frequency offset and/or temperature and provides the error information indicating a difference between the first frequency and the predetermined frequency. The error information is used by a receiving system in frequency translation logic that utilizes the oscillator output signal as a frequency reference.

Abstract: A resonating element includes a resonator element that includes a vibrating portion and an excitation electrode provided on both main surfaces of the vibrating portion, an intermediate substrate in which the resonator element is mounted so as to be spaced from the excitation electrode, and a spiral electrode pattern that is provided on at least one main surface of the intermediate substrate, in which the electrode pattern is electrically connected to the excitation electrode.