Quadrature FM gyroscope

Abstract

A dual mass vibratory gyroscope sensor demonstrates the quadrature frequency modulated (QFM) operating mode, where the frequency of the circular orbit of a proof mass is measured to detect angular rate. In comparison to the mode-matched open loop rate mode, the QFM mode receives the same benefit of improved SNR but without the penalties of unreliable scale factor and decreased bandwidth. A matched pair of gyroscopes, integrated onto the same die, is used for temperature compensation, resulting in 6 ppb relative frequency tracking error, or an Allan deviation of 370 deg/hr with a 70 kHz resonant frequency. The integrated CMOS electronics achieve a capacitance resolution of 0.1 zF/rt-Hz with nominal 6 fF sense electrodes.

The First Frequency-Modulated (FM) Pitch Gyroscope

“…Being the two natural frequencies different by design in this LFM pitch gyroscope (see Table 1), the proof mass precesses in the yz-plane following the so-called Lissajous trajectory. When an angular rate Ω acts along the x-direction, the Coriolis' force couples the two modes (y-and z-) inducing an apparent resonance frequency variation on each axis [1]:…”

“…Note that in Equations (1) and (2) cross-stiffness and cross-damping terms are neglected for the sake of simplicity, however the full expression can be easily obtained from the dynamic equations of motion as done in [1] for a yaw FM gyroscope.…”

“…FM gyroscopes, firstly studied in [1] for yaw measurement, are here proposed as a possible solution, thanks to their ultra-stable, ratiometric scale factor. In FM microgyroscopes the external angular rate modulates the resonance frequency of the micromachined structure, rather than the amplitude of the motion along the sense axis.…”

“…While amplitude-modulated (AM) operation relies on controlling the displacement of the drive axis and measuring the displacement variation along the sense axis due to the Coriolis' force, FM operation controls the two axes velocities (both in amplitude and phase) and measures the frequency variation due to the Coriolis' force. Depending on the phase difference ∆Φ imposed between the driving velocities of the two axes of the gyroscope, there are two different FM schemes (see [1] for more details): Quadrature frequency modulation (QFM: ∆Φ = ±90°) and Lissajous frequency modulation (LFM: ∆Φ = ∆ω·t where ∆ω is the frequency mismatch between the two axes).…”

A high-Q birdbath resonator gyroscope (BRG)

“…Therefore RIGs require an axisymmetric geometry with a very long τ. An alternative method for a rate gyro to achieve both large dynamic range and bandwidth based on the measurement of change in the oscillation frequency caused by the Coriolis force is suggested in [1][2]. However, this method similarly requires a gyro with a long τ and well-matched f for accurate phase detection, which makes it equally challenging to develop such a sensor.…”