Abstract: The invention relates to design of micromechanical resonators and, more precisely, to the design of microelectromechanical systems (MEMS) resonators. The invention provides an improved design structure for a microelectromechanical systems (MEMS) resonator in which the width of the spring elements (3), (23-24), (27-30) is greater than the width of the electrode fingers (5-9), (25-26), (31-34), said widths specifically dimensioned so that the sensitivity of the resonant frequency change with respect to dimensional manufacturing variations d(??0/?0)/d? approaches zero. The improved structure is frequency robust to manufacturing variations and enables reliable frequency referencing with good performance, particularly in small size solutions.

Abstract: A dual in-situ mixing approach for extended tuning range of resonators. In one embodiment, a dual in-situ mixing device tunes an input radio-frequency (RF) signal using a first mixer, a resonator body, and a second mixer. In one embodiment, the first mixer is coupled to receive the input RF signal and a local oscillator signal. The resonator body receives the output of the first mixer, and the second mixer is coupled to receive the output of the resonator body and the local oscillator signal to provide a tuned output RF signal as a function of the frequency of local oscillator signal.

Abstract: An array of micromechanical oscillators have different resonant frequencies based on their geometries. In one embodiment, a micromechanical oscillator has a resonant frequency defined by an effective spring constant that is modified by application of heat. In one embodiment, the oscillator is disc of material supported by a pillar of much smaller diameter than the disc. The periphery of the disc is heated to modify the resonant frequency (or equivalently the spring constant or stiffness) of the disc. Continuous control of the output phase and frequency may be achieved when the oscillator becomes synchronized with an imposed sinusoidal force of close frequency. The oscillator frequency can be detuned to produce an easily controlled phase differential between the injected signal and the oscillator feedback. A phased array radar may be produced using independent phase controllable oscillators.

Abstract: An apparatus including a resonator electrode and a second electrode separated from the resonator electrode by a gap having a size that facilitates electron transfer across the gap, wherein the resonator electrode is a resonator electrode mounted for oscillatory motion relative to the second electrode that results in a size of the gap between the resonator electrode and the second electrode being time variable; a feedback circuit configured to convey an electron transfer signal dependent upon electron transfer across the gap as a feedback signal; and a drive electrode adjacent the resonator electrode configured to receive a feedback signal from a feedback circuit configured to provide a time-varying feedback signal dependent upon electron transfer across a gap.

Abstract: A residual stress gradient in a structural layer is employed to form a resonator deflected out of plane when at rest and the resulting strain gradient is utilized in out-of-plane transduction. Use of the strain gradient enables out-of-plane (e.g., vertical) transduction without yield and reliability problems due to stiction (e.g., the sticking of the resonator to the substrate) when the resonator is driven by an electrode to dynamically deflect out-of-plane. In particular embodiments, out-of-plane transduction is utilized to achieve better transduction efficiency as compared to lateral resonator designs of similar linear dimensions (i.e. footprint) results in a lower motional resistance.

Abstract: A micromechanical resonator operable in a bulk acoustic mode includes a resonator apparatus suspended over a substrate by a plurality of pairs of anchors. The resonator apparatus includes a conductive metal layer, a piezoelectric layer on the conductive metal layer and a plurality of interdigitated electrodes on the piezoelectric layer. The interdigitated electrodes are configured so that a total number of electrode fingers in the plurality of interdigitated electrodes is greater than a total number of the plurality of pairs of anchors.

Abstract: A tunable nanoscale resonator has potential applications in precise mass, force, position, and frequency measurement. One embodiment of this device consists of a specially prepared multiwalled carbon nanotube (MWNT) suspended between a metal electrode and a mobile, piezoelectrically controlled contact. By harnessing a unique telescoping ability of MWNTs, one may controllably slide an inner nanotube core from its outer nanotube casing, effectively changing its length and thereby changing the tuning of its resonance frequency. Resonant energy transfer may be used with a nanoresonator to detect molecules at a specific target oscillation frequency, without the use of a chemical label, to provide label-free chemical species detection.

Abstract: A contour mode micromechanical piezoelectric resonator. The resonator has a bottom electrode; a top electrode; and a piezoelectric layer disposed between the bottom electrode and the top electrode. The piezoelectric resonator has a planar surface with a cantilevered periphery, dimensioned to undergo in-plane lateral displacement at the periphery. The resonator also includes means for applying an alternating electric field across the thickness of the piezoelectric resonator. The electric field is configured to cause the resonator to have a contour mode in-plane lateral displacement that is substantially in the plane of the planar surface of the resonator, wherein the fundamental frequency for the displacement of the piezoelectric resonator is set in part lithographically by the planar dimension of the bottom electrode, the top electrode or the piezoelectric layer.

Abstract: A MEMS array structure including a plurality of bulk mode resonators may include at least one resonator coupling section disposed between the plurality of bulk mode resonators. The plurality of resonators may oscillate by expansion and/or contraction in at least one direction/dimension. The MEMS array structure may include a plurality of sense electrodes and drive electrodes spaced apart from the plurality of bulk mode resonators by a gap. The MEMS array structure may further include at least one anchor coupling section disposed between the at least one resonator coupling section and a substrate anchor.

Abstract: An electromechanical resonator includes a resonator portion which includes a fixed electrode and an oscillator formed separately from the fixed electrode with a gap. The gap has a first gap region and a second gap region which are arranged in a thickness direction of the fixed electrode. The first gap region is different in width from the second gap region.

Abstract: A resonator and a filter that can be miniaturized and highly integrated are provided. In the invention, a resonator wherein parts of resonators, support sections, and joint sections are mutually shared is formed. The mutual configuration is selectively switched as required and a large number of frequencies can be selected in the same filter unit. The resonators, the support sections, and the joint sections different in size and shape are used in combination, whereby a filter unit having a large number of selective frequencies is provided.

Abstract: A high frequency device including an electrostatic type vibrator, a pad, and a circuit. The electrostatic type vibrator is operable via a DC bias voltage. The pad is configured to supply the DC bias voltage. The circuit is positioned electrically between the pad and the vibrator. The circuit is configured to stabilize the DC bias voltage. The circuit and the high frequency signal device are on a common substrate.

Abstract: An electronic device for generating an electric oscillating signal is described based on a micro-electromechanical system (MEMS). The electronic device typically comprises a substrate a moveable element which is moveable with respect to the substrate and an actuating means and a sensor. The actuating means is used to induce vibration of the moveable element and comprises two inductive elements, a first one provided fixed to the substrate and a second one provided fixed to the moveable element. The induced vibration of the moveable element is sensed using the sensor and converted into an electric oscillating signal.

Abstract: Novel configurations for a miniature vibrating beam mechanical resonator provide low energy transfer to a supporting structure and low sensitivity to mounting misalignment. A symmetric suspended portion includes two vibrating beams that vibrate normal to a quiescent plane of the resonator, 180 degrees out of phase relative to one another. The vibrating beams are attached, at least at one end, to a torsional coupling element that is joined to a mounting pad along a non-translating suspension boundary. Counterbalances are attached to the vibrating beams, and the resonator is configured such that dynamic forces and moments coupled to each torsional coupling element from the vibrating beams are balanced along each nominal non-translating suspension boundary proximate to the symmetry axis and along the symmetry axis proximate to each nominal non-translating suspension boundary. Each non-translating suspension boundary is a torsional axis for a twisting deformation of the first torsional coupling element.

Abstract: A tangentially poled piezoelectric single crystal ring resonator is disclosed. A single crystal material is machined into elements and formed into a ring structure. The single crystal elements have a <110> poled tangential axis. The elements may also have a <211>, <511> or <322> orientation range in the radial direction. The elements may have a generally wedge shape.

Abstract: An array of micromechanical oscillators have different resonant frequencies based on their geometries. In one embodiment, a micromechanical oscillator has a resonant frequency defined by an effective spring constant that is modified by application of heat. In one embodiment, the oscillator is disc of material supported by a pillar of much smaller diameter than the disc. The periphery of the disc is heated to modify the resonant frequency (or equivalently the spring constant or stiffness) of the disc. Continuous control of the output phase and frequency may be achieved when the oscillator becomes synchronized with an imposed sinusoidal force of close frequency. The oscillator frequency can be detuned to produce an easily controlled phase differential between the injected signal and the oscillator feedback. A phased array radar may be produced using independent phase controllable oscillators.

Abstract: Disclosed are micromechanical resonator apparatus having features that permit multiple resonators on the same substrate to operate at different operating frequencies. Exemplary micromechanical resonator apparatus includes a support substrate and suspended micromechanical resonator apparatus having a resonance frequency. In one embodiment, the suspended micromechanical resonator apparatus comprises a device substrate that is suspended from and attached to the support substrate, a piezoelectric layer formed on the suspended device substrate, and a plurality of interdigitated upper electrodes formed on the piezoelectric layer. In another embodiment, the suspended micromechanical resonator apparatus comprises a device substrate that is suspended from and attached to the support substrate, a lower electrode formed on the suspended device substrate, a piezoelectric layer formed on the lower electrode, and a plurality of interdigitated upper electrodes formed on the piezoelectric layer.

Abstract: A method for fabrication of single crystal silicon micromechanical resonators using a two-wafer process, including either a Silicon-on-insulator (SOI) or insulating base and resonator wafers, wherein resonator anchors, a capacitive air gap, isolation trenches, and alignment marks are micromachined in an active layer of the base wafer; the active layer of the resonator wafer is bonded directly to the active layer of the base wafer; the handle and dielectric layers of the resonator wafer are removed; viewing windows are opened in the active layer of the resonator wafer; masking the single crystal silicon semiconductor material active layer of the resonator wafer with photoresist material; a single crystal silicon resonator is machined in the active layer of the resonator wafer using silicon dry etch micromachining technology; and the photoresist material is subsequently dry stripped.

Abstract: The coupled resonator comprises a first low frequency resonator, such as a balance spring (1) and a second higher frequency resonator, such as a tuning fork (2), the two resonators (1 and 2) including permanent mechanical coupling means. Application to the regulating system of a timepiece.

Abstract: Disclosed herein are devices and methods for generating a modulated signal with a MEMS resonator, or microresonator. A bias, or polarization, voltage for activating the MEMS resonator is determined by a control signal, or input voltage, indicative of information to be carried by the modulated signal. In some cases, the MEMS resonator may be driven by an oscillator circuit to facilitate operation of the MEMS resonator. The control signal may include an amplitude modulated voltage or a digital data stream such that output signals of the MEMS resonator or oscillator circuit may carry information via frequency modulation, such as frequency shift keying modulation.

Abstract: One embodiment of the present invention sets forth a MEMS resonator system that reduces interference signals arising from undesired capacitive coupling between different system elements. The system includes a MEMS resonator, two or more resonator electrodes, and at least one resonator electrode shield. 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 flexural vibration piece includes: a flexural vibrator that has a first region on which a compressive stress or a tensile stress acts due to vibration and a second region having a relationship in which a tensile stress acts thereon when a compressive stress acts on the first region and a compressive stress acts thereon when a tensile stress acts on the first region, and performs flexural vibration in a first plane; and a heat conduction path, between the first region and the second region, that is formed of a material having a thermal conductivity higher than that of the flexural vibrator and thermally connects between the first region and the second region, wherein when m is the number of heat conduction paths, ?th is the thermal resistivity of the heat conduction path, ?v is the thermal resistivity of the flexural vibrator, tv is the thickness of the flexural vibrator in, a direction orthogonal to the first plane, and tth is the thickness of the heat conduction path, a relationship of tth?(1/m)×tv×(?th/?v

Abstract: A contour mode micromechanical piezoelectric resonator. The resonator has a bottom electrode; a top electrode; and a piezoelectric layer disposed between the bottom electrode and the top electrode. The piezoelectric resonator has a planar surface with a cantilevered periphery, dimensioned to undergo in-plane lateral displacement at the periphery. The resonator also includes means for applying an alternating electric field across the thickness of the piezoelectric resonator. The electric field is configured to cause the resonator to have a contour mode in-plane lateral displacement that is substantially in the plane of the planar surface of the resonator, wherein the fundamental frequency for the displacement of the piezoelectric resonator is set in part lithographically by the planar dimension of the bottom electrode, the top electrode or the piezoelectric layer.

Abstract: A system, device, method, and apparatus provide the ability to wire a voltage sensitive device to a nanoelectromechanical system (NEMS) resonator. A voltage sensitive device is configured to detect one or more voltage signals and output one or more electrical potentials in real-time. An array of piezoelectric NEMS resonators (with each resonator tuned to a unique frequency) is used to receive the output electrical potentials and convert each output electrical potential to a corresponding resonance frequency varying signal. The output signal from each resonator varies in linear proportion to the resonator's corresponding frequency variation arising from the applied elecrical potential. The frequency varying signals are multiplexed together into a single readout signal path that is monitored to determine variations in vibrational amplitude. A demodulation device deconvolves the multiplexed frequency varying signals to recover and uniquely identify the output electrical 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: Provided is a micro-electromechanical device capable of processing an electric signal in the high frequency region by a simple device structure. The micro-electromechanical device is formed, including an oscillator element having a plurality of electrodes disposed on a substrate and a beam facing the electrodes to oscillate by electrostatic drive. An input/output of a high frequency signal is applied to one of the combinations of the electrodes and the beam.

Abstract: This array (10) of coupled resonators (16i) comprises means (12) for supplying an input electrical signal (Ve) and means (14) for electrically exciting N coupled resonators (16i) of the array using this input electrical signal. The electrical excitation means (14) comprise, for each of these N coupled resonators (16i), actuation means (18,) connected to the means (12) for supplying the input electrical signal for an actuation of this coupled resonator according to the input electrical signal, and variable gain input amplification means (20i) for the actuation of this coupled resonator specific to this coupled resonator (16i). Furthermore, they comprise means (22) for controlling a specific setting of the variable gain of each of the input amplification means (20i).

Abstract: A resonator and a filter that can be miniaturized and highly integrated are provided. In the invention, a resonator wherein parts of resonators, support sections, and joint sections are mutually shared is formed. The mutual configuration is selectively switched as required and a large number of frequencies can be selected in the same filter unit. The resonators, the support sections, and the joint sections different in size and shape are used in combination, whereby a filter unit having a large number of selective frequencies is provided.

Abstract: An object of the invention is to provide a coupling element of an MEMS filter with design flexibility and minimization of mass loading effects. The invention provides a structure wherein the mass loading effects are not reflected on the MEMS filter characteristic by using a nanosize coupling element with a very small mass compared to a microsize MEMS resonator, such as a carbon nanotube (CNT), as a coupling element part.

Abstract: An acoustic wave filter device having a greatly reduced size includes a balance-unbalance conversion function and an input/output impedance ratio of about 1. The acoustic wave filter device includes a second IDT of a first acoustic wave filter portion that is connected to an unbalanced terminal. The second IDT includes first and second divided IDT portions which are divided in an overlap width direction and connected in series with each other between the unbalanced terminal and a ground potential. A fifth IDT of a second acoustic wave filter portion connected to the first acoustic wave filter portion includes first and second divided IDT portions which are divided in an acoustic wave propagating direction. The first and second divided IDT portions of the fifth IDT are connected to first and second balanced terminals, respectively.

Abstract: A method is disclosed for the robust fabrication of a microelectromechanical (MEM) resonator. In this method, a pattern of holes is formed in the resonator mass with the position, size and number of holes in the pattern being optimized to minimize an uncertainty ?f in the resonant frequency f0 of the MEM resonator due to manufacturing process variations (e.g. edge bias). A number of different types of MEM resonators are disclosed which can be formed using this method, including capacitively transduced Lamé, wineglass and extensional resonators, and piezoelectric length-extensional resonators.

Abstract: MEMS resonators containing a first material and a second material to tailor the resonator's temperature coefficient of frequency (TCF). The first material has a different Young's modulus temperature coefficient than the second material. In one embodiment, the first material has a negative Young's modulus temperature coefficient and the second material has a positive Young's modulus temperature coefficient. In one such embodiment, the first material is a semiconductor and the second material is a dielectric. In a further embodiment, the quantity and location of the second material in the resonator is tailored to meet the resonator TCF specifications for a particular application. In an embodiment, the second material is isolated to a region of the resonator proximate to a point of maximum stress within the resonator. In a particular embodiment, the resonator includes a first material with a trench containing the second material.

Abstract: Disclosed are micromechanical resonator apparatus having features that permit multiple resonators on the same substrate to operate at different operating frequencies. Exemplary micromechanical resonator apparatus includes a support substrate and suspended micromechanical resonator apparatus having a resonance frequency. In one embodiment, the suspended micromechanical resonator apparatus comprises a device substrate that is suspended from and attached to the support substrate, a piezoelectric layer formed on the suspended device substrate, and a plurality of interdigitated upper electrodes formed on the piezoelectric layer. In another embodiment, the suspended micromechanical resonator apparatus comprises a device substrate that is suspended from and attached to the support substrate, a lower electrode formed on the suspended device substrate, a piezoelectric layer formed on the lower electrode, and a plurality of interdigitated upper electrodes formed on the piezoelectric layer.

Abstract: A MEMS array structure includes MEMS resonators that form an array. Each MEMS resonator includes beam sections. At least one of the beam sections of a first one of the MEMS resonators is a shared beam section that is also included in another of the MEMS resonators adjacent to the first MEMS resonator.

Abstract: The electromechanical transducer (1) has a resonator element (20) and an actuator (30) for inducing an elastic deformation of the resonator element (20) dependent on the electrical input signal. For temperature stabilization, the electromechanical transducer (1) has a sensing element (40) for providing an electrical sensing signal has a function of a temperature of the resonator element (20), and a heating element (50) for heating the resonator element to reduce the temperature dependent frequency deviation to keep the resonance frequency equal to the nominal frequency at operating temperature. The heating element (50) is controlled by an electrical heating signal based on the electrical sensing signal. The resonator element may have the hating element or the sensing element; it may be part of a wheatstone bridge; it may consist of two longitudinally extendable parts (201, 202) extending in opposite directions, being attached in a support area (204) in a deformation free part (203).

Abstract: To provide an electromechanical signal selection device which can be miniaturized and highly integrated and which can selectively output only a signal of a predetermined frequency without providing any sensitive vibration sensing mechanism, and electric equipment using the electromechanical signal selection device. A micro-vibrator serving as a resonator is provided. The micro-vibrator can be excited by an external force to excite vibration of the micro-vibrator. A material whose physical property is changed in accordance with a structural change is used as the micro-vibrator. Thus, a sensitive electromechanical signal selection device is obtained.

Abstract: One embodiment of the present invention sets forth a serrated tooth actuator for driving MEMS resonator structures. The actuator includes a fixed drive electrode having a serrated tooth surface opposing a MEMS resonator arm also having a serrated tooth surface, where the MEMS resonator arm is configured to rotate towards the drive electrode when an AC signal is applied to the drive electrode. Such a configuration permits higher amplitude signals to be applied to the drive electrode without the performance of the actuator being compromised by nonlinear effects. In addition, the serrated tooth configuration enables a sufficiently high actuating force to be maintained even though the distance traversed by the MEMS resonator arm during operation is quite small. Further, the serrated configuration allows a MEMS resonator system to withstand larger fluctuations in voltage and larger substrate stresses without experiencing a substantial shift in resonant frequency.

Abstract: One embodiment of the present invention sets forth a serrated tooth actuator for driving MEMS resonator structures. The actuator includes a fixed drive electrode having a serrated tooth surface opposing a MEMS resonator arm also having a serrated tooth surface, where the MEMS resonator arm is configured to rotate towards the drive electrode when an AC signal is applied to the drive electrode. Such a configuration permits higher amplitude signals to be applied to the drive electrode without the performance of the actuator being compromised by nonlinear effects. In addition, the serrated tooth configuration enables a sufficiently high actuating force to be maintained even though the distance traversed by the MEMS resonator arm during operation is quite small. Further, the serrated configuration allows a MEMS resonator system to withstand larger fluctuations in voltage and larger substrate stresses without experiencing a substantial shift in resonant frequency.

Abstract: One embodiment of the present invention sets forth a serrated tooth actuator for driving MEMS resonator structures. The actuator includes a fixed drive electrode having a serrated tooth surface opposing a MEMS resonator arm also having a serrated tooth surface, where the MEMS resonator arm is configured to rotate towards the drive electrode when an AC signal is applied to the drive electrode. Such a configuration permits higher amplitude signals to be applied to the drive electrode without the performance of the actuator being compromised by nonlinear effects. In addition, the serrated tooth configuration enables a sufficiently high actuating force to be maintained even though the distance traversed by the MEMS resonator arm during operation is quite small. Further, the serrated configuration allows a MEMS resonator system to withstand larger fluctuations in voltage and larger substrate stresses without experiencing a substantial shift in resonant frequency.

Abstract: An electromechanical filter capable of achieving overall miniaturization by employing a micro oscillator such as a carbon nanotube with superior conductivity so as to enable selection of signals of a predetermined frequency. The apparatus includes an inner wall composed of a carbon nanotube that changes physically as a result of an input signal, and an outer wall composed of a carbon nanotube arranged so as to cover the inner wall and spaced by a microscopic gap from the inner wall. The outer wall detects an oscillation of the inner wall when a signal of a predetermined frequency is inputted from a connected signal input side electrode to the inner wall, so that this signal is outputted via a connected signal output side electrode.

Abstract: Three or more piezoelectric resonators having resonance frequencies different from one another are realized on the same substrate. First through third frequency adjustment layers 107a through 107c of first through third piezoelectric resonators 102a through 102c provided on the same substrate 101 are formed by varying, among the frequency adjustment layers, the ratio of area (depressions 109 and 110) to be etched to area not to be etched.

Abstract: An object of the invention is to provide a coupling element of an MEMS filter with design flexibility and minimization of mass loading effects. The invention provides a structure wherein the mass loading effects are not reflected on the MEMS filter characteristic by using a nanosize coupling element with a very small mass compared to a microsize MEMS resonator, such as a carbon nanotube (CNT), as a coupling element part.

Abstract: An object is to provide an electromechanical filter which can define a vibration mode so that a vibrator can be excited only in a desired vibration mode, that is, a filter which can suppress any vibration mode other than a desired vibration mode. The electromechanical filter includes a first member for inputting a signal, a second member disposed at a predetermined distance from the first member so as to surround the first member and to be excited due to an electrostatic force caused by the signal input from the first member, and a third member disposed at a predetermined distance from the second member so as to surround the second member and to detect vibration of the second member. The second member is designed to receive an attractive force from the first member and the third member so as to be bound and regulated as to a vibration direction.

Abstract: A MEMS filter has an input layer for receiving a signal input, and an output layer for providing a signal output. The MEMS filter also has a first resonator and a second resonator coupled to the first resonator such that movement transduced in the first resonator by the signal input causes movement of the second resonator which transduces the signal output. A method of manufacturing a MEMS filter is also disclosed. A dielectric layer is formed on a base. A patterned electrode layer is formed at least in part on the dielectric layer. The base is etched to define a resonator structure. A method of adjusting a desired input impedance and an output impedance of a dielectrically transduced MEMS filter having transduction electrodes coupled to a dielectric film is further disclosed. The method includes adjusting a DC bias voltage on the transduction electrodes.

Abstract: There are many inventions described and illustrated herein. In one aspect, the present invention is directed to a temperature compensated microelectromechanical resonator as well as fabricating, manufacturing, providing and/or controlling microelectromechanical resonators having mechanical structures that include integrated heating and/or temperature sensing elements. In another aspect, the present invention is directed to fabricate, manufacture, provide and/or control microelectromechanical resonators having mechanical structures that are encapsulated using thin film or wafer level encapsulation techniques in a chamber, and including heating and/or temperature sensing elements disposed in the chamber, on the chamber and/or integrated within the mechanical structures. Other aspects of the inventions will be apparent from the detailed description and claims herein.

Abstract: A micro-resonator of a single structure which outputs signals of two resonance frequencies of mutually opposite phases and in which different resonance frequencies are adjusted independently is provided. The micro-resonator includes: an oscillation portion 6 sustained with a gap by support portions 8 [8A, 8B] and an input electrode 3 and an output electrode 4 that become lower electrodes facing the oscillation portion 6 across the gap, in which the input electrode 3 and the output electrode 4 are disposed to face each other along a line intersecting the oscillation portion 6, the oscillation portion 6 generates torsional oscillation and flexural oscillation, and output signals of two resonance frequencies close to each other based on different resonance modes have mutually different phases by 180°.

Abstract: Disclosed are micromechanical resonators having features that compensate for process variations and provide improved inherent temperature stability. Exemplary resonators may comprise comb drive resonators or parallel-plate drive resonators. The resonators comprise a (silicon-on-insulator) substrate with resonator apparatus formed therein. The resonator apparatus has one or more anchors connected to the substrate, at least one excitation/sense port that is electrically insulated from the substrate, and a resonator. The resonator comprises one or more flexural members connected to the one or more anchors that are separated from the substrate and separated from the excitation/sense port by gaps. A mass is coupled to flexural members, is separated from the substrate, and comprises a grid. Process compensation is achieved using a resonator mass in the form of a grid of lines that form holes or lines through the mass, wherein widths of lines of the grid are approximately ? the width of the flexural members.

Abstract: A method for fabrication of single crystal silicon micromechanical resonators using a two-wafer process, including either a Silicon-on-insulator (SOI) or insulating base and resonator wafers, wherein resonator anchors, a capacitive air gap, isolation trenches, and alignment marks are micromachined in an active layer of the base wafer; the active layer of the resonator wafer is bonded directly to the active layer of the base wafer; the handle and dielectric layers of the resonator wafer are removed; viewing windows are opened in the active layer of the resonator wafer; masking the single crystal silicon semiconductor material active layer of the resonator wafer with photoresist material; a single crystal silicon resonator is machined in the active layer of the resonator wafer using silicon dry etch micromachining technology; and the photoresist material is subsequently dry stripped.

Abstract: A superconducting filter device includes a dielectric base, a resonator pattern formed of a superconducting material on the dielectric base, an anisotropic dielectric or magnetic body positioned over the resonator pattern, and an angle adjusting mechanism for changing a horizontal angle of the anisotropic dielectric or magnetic body with respect to an input signal.

Abstract: Thermally induced frequency variations in a micromechanical resonator are actively or passively mitigated by application of a compensating stiffness, or a compressive/tensile strain. Various composition materials may be selected according to their thermal expansion coefficient and used to form resonator components on a substrate. When exposed to temperature variations, the relative expansion of these composition materials creates a compensating stiffness, or a compressive/tensile strain.