This is the first of four articles that address various issues concerning the generation and utilization of electronic signals in the operation of micromachined planar vibratory microgyroscopes and other sensory devices that include electrostatically actuated, capacitively sensed mechanical resonators. The subject of this article is that part of the overall electronic circuitry of a planar vibratory gyroscope that generates a signal proportional to the rate of rotation.

Some background information is prerequisite to a description of this circuitry and to the descriptions of the circuits described in the following three articles. Various aspects of micromachined planar vibratory microgyroscopes have been described in a number of previous articles in NASA Tech Briefs. The basic principle of operation is as follows: Four planar silicon plates are connected together by silicon springs in a symmetrical pattern resembling a clover leaf. The silicon springs lie at the center of the pattern. When in equilibrium (not vibrating), all plates lie in the same plane.

The Portion of This Circuit That Generates the Rotation-Rate Signal exploits the sum and difference of the outputs of the transconductance amplifiers. The difference signal is either multiplied by, or detected synchronously with respect to, the sum signal.

Together, the plates and springs constitute a mechanical resonator characterized by two orthogonal degenerate modes of vibration. Two of the plates are driven electrostatically to generate oscillations in one of these modes, denoted the driven mode. The oscillatory displacements or velocities of all four plates are measured by use of capacitive sensors.

One seeks to measure rotation about the axis perpendicular to the equilibrium plane of the resonator plates. The Coriolis force associated with this rotation couples energy from the driven mode to the other mode, denoted the sensing mode, in which there is a difference between the velocities of the two plates that are not driven electrostatically (the sensing plates). This difference between velocities gives rise to a corresponding difference between the outputs of the capacitive sensors for the sensing plate. The difference signal, called the "Coriolis signal," is proportional to (1) the amplitude of oscillation of the driven plates; (2) the rate of rotation, Ω ; and (3) the resonance quality factor, Q, which is inversely proportional to the rate of damping of vibrations.

The circuitry in question is designed to generate a signal proportional to the Coriolis signal and thus to Ω. This circuitry is part of the overall circuit shown in the figure. As explained in more detail in the following article, the inputs to the transconductance amplifiers are the raw velocity signals from the sensing-plate capacitors. Thus, the difference between the outputs of the two transconductance amplifiers contains the desired information.

Because of common-mode rejection, the sum of transconductance-amplifier outputs, which is proportional to the driven-mode velocity signal, contains no information on Ω. If the magnitude of oscillation is held constant as described in the following article, then the sum signal has a constant magnitude. In any event, the sum signal is used as a reference for phase-sensitive detection of the difference signal. In one version of this circuitry, the difference signal is multiplied by a 90°-phase-shifted replica of the sum signal. In another version, the difference signal is synchronously detected, using the phase-shifted sum signal as the timing reference. In either version, the time-averaged output signal is proportional to ΩQ.

This work was done by Christopher Stell, Vatché Vorperian, Roman Gutierrez, and Tony Tang of Caltech for NASA's Jet Propulsion Laboratory.


This Brief includes a Technical Support Package (TSP).
Circuit Generates Rotation Signal From a Vibratory Gyroscope

(reference NPO20087) is currently available for download from the TSP library.

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