Abstract: A method for approximating the behavior of a periodic parameter of a time-domain device in response to a perturbation, the method comprising the following steps: collecting data points at discreet times, wherein each data point represents a measurement of the parameter; dividing the time domain into intervals, each given interval containing at least one data point sampled during the given interval; fitting a polynomial function to the data points of each interval such that each interval has a corresponding polynomial function that is time-centered on the interval's center point and that accurately describes the parameter behavior over that interval; and stitching together the polynomial functions piece-wise to create an analytic approximation of the behavior of the system parameter over the entire time domain.

Abstract: An oscillatory apparatus and methods of utilizing the same. In one embodiment, the apparatus comprises a force sensor having a proof mass, with one or more sensing electron tunneling electrodes disposed thereon, and a frame comprising one or more reference electron tunneling electrodes. Conductive plates disposed on the sensor base and capping wafers induce oscillations of the proof mass. The sensing and the reference electrode pairs are disposed in a face-to-face configuration, thus forming a digital switch characterized by one or more closed states. In the closed state, the switch generates triggering events, thereby enabling the sensing apparatus to generate a digital output indicative of the mass position. The time period between consecutive trigger events is used to obtain mass deflection due to external forcing. Time separation between the triggering events is based on the physical dimensions established during fabrication, thus not requiring ongoing sensor calibration.

Abstract: A photoelectric cell comprising: a cathode layer configured to eject electrons in response to receiving photons from a light source; a substantially-photon-transparent anode configured to receive the ejected electrons; first and second, substantially-photon-transparent, dielectric layers, wherein the first dielectric layer is disposed between the cathode layer and the anode layer and wherein the anode layer is disposed between the first and second dielectric layers such that the cathode layer, the first dielectric layer, the anode layer, and the second dielectric layer form a layered stack; and wherein at least a first portion of the layered stack overlaps a second portion of the layered stack.

Abstract: Systems and methods for perturbation analysis of harmonic oscillations in the time domain according to several embodiments can include a time domain switching sensor and a resonator for imposing a first oscillation and a second oscillation on the sensor. The first and second oscillations can have the same amplitude A and period P, but can have a known phase shift. The sensor can use a time interval, which can be defined by the time between when the sensor passes a reference point due to motion caused by the first oscillation and when the sensor passes the same reference point, but due to motion caused by the second oscillation. With this configuration an improved accuracy of measurement for the system can be realized.

Abstract: A method for increasing the accuracy of a time-domain apparatus comprising the following steps: initiating a periodic oscillation with the time-domain apparatus; measuring time intervals between trigger events during each oscillation, wherein the trigger events correspond to the oscillation passing known values; detecting a perturbation to the oscillation by monitoring changes in the time intervals between trigger events; and adjusting a parameter of the oscillation based on the perturbation such that measurement error is reduced.

Abstract: A time-domain inertial sensor comprising: a support structure having an electrode plane parallel to an x-y plane of an x-y-z mutually orthogonal coordinate system, wherein the support structure's largest dimension lies within the x-y plane; a proof mass having a first surface parallel to the x-y plane; wherein the proof mass is springedly coupled to the support structure such that the first surface is separated from the electrode plane by a gap; a driver configured to drive the proof mass to oscillate with respect to the support structure in approximately only the x-direction such that, while oscillating, the gap does not vary significantly; and a first, time-domain, proximity switch disposed to switch from an open state to a closed state each time the proof mass is in a first reference position with respect to the support structure.

Abstract: A gyroscope comprising: a frame; a tuning fork comprising a base and first and second prongs, wherein the base has proximal and distal ends, and wherein the proximal end is coupled to the frame and the distal end is coupled to the first and second prongs; first and second drivers configured to drive the first and second prongs respectively to oscillate with respect to the frame in a first direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other; and at least two digital position triggers operatively coupled to the frame and to the tuning fork, wherein each position trigger is configured to experience at least two trigger events during each oscillation of the tuning fork in a second direction, wherein the second direction is orthogonal to the first direction.

Abstract: An in-plane, monolithically-integrated, inertial device comprising: a support structure and first and second spring mass systems springedly coupled to the support structure. The first spring mass system comprises first and second time domain digital triggers configured to measure rotation and displacement respectively of the support structure about a first axis and along an orthogonal second axis respectively. The second spring mass system comprises third and fourth time domain digital triggers configured to measure acceleration and displacement respectively of the support structure about the second axis and along the first axis respectively.

Abstract: Systems and methods for perturbation analysis of harmonic oscillations in the time domain according to several embodiments can include a time domain switching sensor and a resonator for imposing a first oscillation and a second oscillation on the sensor. The first and second oscillations can have the same amplitude A and period P, but can have a known phase shift. The sensor can use a time interval, which can be defined by the time between when the sensor passes a reference point due to motion caused by the first oscillation and when the sensor passes the same reference point, but due to motion caused by the second oscillation. With this configuration an improved accuracy of measurement for the system can be realized.

Abstract: A gyroscope comprising: a multi-layer substrate, comprising drive spring and sense spring layers; a rigid support structure formed from the substrate; a plurality of drive springs formed in each drive spring layer wherein each drive spring is operatively coupled to the support structure; a drive mass formed from at least one layer of the substrate, wherein the drive mass is coupled to the support structure via the drive springs; a drive mass driver operatively coupled to the drive mass and configured to cause movement of the drive mass with respect to the support structure; a plurality of sense springs formed in each sense spring layer, wherein each sense spring is operatively coupled to the drive mass; and a sense mass formed from at least one layer, wherein the sense mass is coupled to the drive mass via the sense springs.

Abstract: An oscillation apparatus comprising: a frame; a first proof mass coupled to the frame via a spring; a driving circuit operatively coupled to the first proof mass and the frame, wherein the driving circuit is configured to induce oscillatory motion of the first proof mass relative to the frame at a resonant frequency in a first direction; a first electron-tunneling position switch operatively coupled to the first proof mass such that the first position switch is configured to pass through a closed state during each oscillation of the proof mass, wherein the position switch comprises first and second single-atom-thick tunneling electrodes; and a sensing circuit coupled to the position switch, the sensing circuit configured to output a signal whenever the position switch passes through the closed state.

Abstract: A gyroscope comprising: a frame; a tuning fork comprising a base and first and second prongs, wherein the base has proximal and distal ends, and wherein the proximal end is coupled to the frame and the distal end is coupled to the first and second prongs; first and second drivers configured to drive the first and second prongs respectively to oscillate with respect to the frame in a first direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other; and at least two digital position triggers operatively coupled to the frame and to the tuning fork, wherein each position trigger is configured to experience at least two trigger events during each oscillation of the tuning fork in a second direction, wherein the second direction is orthogonal to the first direction.

Abstract: A method for increasing the accuracy of a time-domain apparatus comprising the following steps: initiating a periodic oscillation with the time-domain apparatus; measuring time intervals between trigger events during each oscillation, wherein the trigger events correspond to the oscillation passing known values; detecting a perturbation to the oscillation by monitoring changes in the time intervals between trigger events; and adjusting a parameter of the oscillation based on the perturbation such that measurement error is reduced.

Abstract: A time-domain inertial sensor comprising: a support structure having an electrode plane parallel to an x-y plane of an x-y-z mutually orthogonal coordinate system, wherein the support structure's largest dimension lies within the x-y plane; a proof mass having a first surface parallel to the x-y plane; wherein the proof mass is springedly coupled to the support structure such that the first surface is separated from the electrode plane by a gap; a driver configured to drive the proof mass to oscillate with respect to the support structure in approximately only the x-direction such that, while oscillating, the gap does not vary significantly; and a first, time-domain, proximity switch disposed to switch from an open state to a closed state each time the proof mass is in a first reference position with respect to the support structure.

Abstract: A gyroscope comprising: a support structure; a drive mass springedly coupled to the support structure such that movement of the drive mass with respect to the support structure is substantially restricted to movement in a first direction; a driver configured to cause the drive mass to oscillate with respect to the support structure in the first direction; a sense mass springedly coupled to the drive mass such that movement of the sense mass with respect to the drive mass is substantially restricted to movement in a second direction, which is orthogonal to the first direction; and a digital trigger comprising a proximity switch coupled between the drive mass and the sense mass, wherein the switch is configured to switch from an open state to a closed state each time the sense mass is in a reference position with respect to the drive mass.

Abstract: A system includes a housing disposed within a fluid having a fluid flow. A first member is located substantially external to the housing and is directly exposed to the fluid flow and lengthwise positioned transverse to the direction of the fluid flow. The first member is configured to vibrate independently of the housing responsive to direct exposure to the fluid flow. A coil is coupled to one end of the first member. The coil is disposed within the housing and shielded from direct fluid flow. A magnet is disposed within the housing separate from and adjacent to the coil. The magnet is shielded from direct fluid flow. Magnetic flux from the magnet induces an electric current through the coil responsive to relative motion between the magnet and the coil caused by vibration of the first member.

Abstract: An in-plane, monolithically-integrated, inertial device comprising: a support structure and first and second spring mass systems springedly coupled to the support structure. The first spring mass system comprises first and second time domain digital triggers configured to measure rotation and displacement respectively of the support structure about a first axis and along an orthogonal second axis respectively. The second spring mass system comprises third and fourth time domain digital triggers configured to measure acceleration and displacement respectively of the support structure about the second axis and along the first axis respectively.

Abstract: A rotational energy harvesting apparatus includes a rotor of magnets and a ring of linear-based kinetic energy harvesters. The rotor of magnets is fixed to a rotational source and is caused to sweep past the linear-based kinetic energy harvesters. The rotating magnets compel kinetic energy to be induced in the linear-based kinetic energy harvesters. The kinetic energy is converted into electrical energy.

Abstract: A method for adjusting the accuracy of a time-domain inertial sensor comprising the following steps: operatively positioning a harmonic oscillator of the time-domain inertial sensor between two capacitive plates; initiating harmonic oscillation of the oscillator in a first plane by creating with the capacitive plates a capacitively forced pulse; monitoring the harmonic oscillation of the oscillator; and electrostatically biasing both of the two capacitive plates such that a spring constant of the oscillator is effectively altered.

Abstract: A gyroscope comprising: a support structure; a drive mass springedly coupled to the support structure such that movement of the drive mass with respect to the support structure is substantially restricted to movement in a first direction; a driver configured to cause the drive mass to oscillate with respect to the support structure in the first direction; a sense mass springedly coupled to the drive mass such that movement of the sense mass with respect to the drive mass is substantially restricted to movement in a second direction, which is orthogonal to the first direction; and a digital trigger comprising a proximity switch coupled between the drive mass and the sense mass, wherein the switch is configured to switch from an open state to a closed state each time the sense mass is in a reference position with respect to the drive mass.