A micro-electromechanical apparatus includes a rotary element, at least one restraint and at least two folded springs. The rotary element is capable of rotating with respect to an axis. The folded springs are symmetrically disposed about the axis. Each folded spring has a moving end and a fixed end, the moving end is connected to the rotary element, and the fixed end is connected to the at least one restraint. The moving end is not located on the axis, and the fixed end is not located on the axis. A moving distance is defined as a distance between the moving end and the axis, a fixed distance is defined as a distance between the fixed end and the axis. A spring length is defined as a distance between the moving end and the fixed end. The spring length is varied according to the rotation of the rotary element.

A micro-electromechanical apparatus includes a rotary element, at least one restraint and at least two folded springs. The rotary element is capable of rotating with respect to an axis. The folded springs are symmetrically disposed about the axis. Each folded spring has a moving end and a fixed end, the moving end is connected to the rotary element, and the fixed end is connected to the at least one restraint. The moving end is not located on the axis, and the fixed end is not located on the axis. A moving distance is defined as a distance between the moving end and the axis, a fixed distance is defined as a distance between the fixed end and the axis. A spring length is defined as a distance between the moving end and the fixed end. The spring length is varied according to the rotation of the rotary element.

A microelectromechanical device includes: a body; a movable mass, elastically coupled to the body and oscillatable with respect to the body according to a degree of freedom; a frequency detector, configured to detect a current oscillation frequency of the movable mass; and a forcing stage, capacitively coupled to the movable mass and configured to provide energy to the movable mass through forcing signals having a forcing frequency equal to the current oscillation frequency detected by the frequency detector, at least in a first transient operating condition.

A microelectromechanical device includes: a body; a movable mass, elastically coupled to the body and oscillatable with respect to the body according to a degree of freedom; a frequency detector, configured to detect a current oscillation frequency of the movable mass; and a forcing stage, capacitively coupled to the movable mass and configured to provide energy to the movable mass through forcing signals having a forcing frequency equal to the current oscillation frequency detected by the frequency detector, at least in a first transient operating condition.

A microelectromechanical gyroscope structure for detecting angular motion about an axis of angular motion. A drive element is suspended for one-dimensional motion in a direction of a drive axis, and a sense body carries one or more sense rotor electrodes and is coupled to the drive element with a first directional spring structure that forces the sense body to move with the drive element and has a preferred direction of motion in a direction of a sense axis. The drive element includes an actuation body and a drive frame wherein the first spring structure couples the sense body directionally to the drive frame, and a second directional spring structure that couples the drive frame to the actuation body and has a preferred direction of motion in the direction of the sense axis.

A microelectromechanical gyroscope structure for detecting angular motion about an axis of angular motion. A drive element is suspended for one-dimensional motion in a direction of a drive axis, and a sense body carries one or more sense rotor electrodes and is coupled to the drive element with a first directional spring structure that forces the sense body to move with the drive element and has a preferred direction of motion in a direction of a sense axis. The drive element includes an actuation body and a drive frame wherein the first spring structure couples the sense body directionally to the drive frame, and a second directional spring structure that couples the drive frame to the actuation body and has a preferred direction of motion in the direction of the sense axis.

A system is provided that includes a mechanical resonator, and an analog circuit coupled to the mechanical resonator. The analog circuit is arranged to receive a mechanical resonator measurement signal having a quadrature error from the mechanical resonator, and to extract a quadrature error signal from the mechanical resonator measurement signal using a quadrature clock. A digital quadrature controller is coupled to the analog circuit and is arranged to generate a quadrature error compensation signal from the extracted quadrature error signal and apply the quadrature error compensation signal to the mechanical resonator or the mechanical resonator measurement signal to reduce quadrature error in the mechanical resonator measurement signal error.

A system is provided that includes a mechanical resonator, and an analog circuit coupled to the mechanical resonator. The analog circuit is arranged to receive a mechanical resonator measurement signal having a quadrature error from the mechanical resonator, and to extract a quadrature error signal from the mechanical resonator measurement signal using a quadrature clock. A digital quadrature controller is coupled to the analog circuit and is arranged to generate a quadrature error compensation signal from the extracted quadrature error signal and apply the quadrature error compensation signal to the mechanical resonator or the mechanical resonator measurement signal to reduce quadrature error in the mechanical resonator measurement signal error.

A microelectromechanical system (MEMS) gyroscope includes a driving mass and a driving circuit that operates to drive the driving mass in a mechanical oscillation at a resonant drive frequency. An oscillator generates a system clock that is independent of and asynchronous to the resonant drive frequency. A clock generator circuit outputs a first clock and a second clock that are derived from the system clock. The drive loop of the driving circuit including an analog-to-digital converter (ADC) circuit that is clocked by the first clock and a digital signal processing (DSP) circuit that is clocked by the second clock.

An inertial sensor includes a substantially planar, rotationally symmetric proof mass, a capacitive pick-off circuit connected to the proof mass, an electrical drive circuit connected to the four pairs of electrodes. The drive circuit is arranged to apply first in-phase and anti-phase pulse width modulation (PWM) drive signals with a first frequency to the first and third electrode pairs, such that one electrode in each pair is provided with in-phase PWM drive signals and the other electrode in each pair is provided with anti-phase PWM drive signals and to apply second in-phase and anti-phase PWM drive signals with a second frequency, different to the first frequency, to the second and fourth electrode pairs, such that one electrode in each pair is provided with in-phase PWM drive signals and the other electrode in each pair is provided with anti-phase PWM drive signals.