The figure illustrates an improved electronic circuit that excites constant-magnitude vibrations in an electrostatically actuated, capacitively sensed mechanical resonator. The circuit can be adapted, for example, to a planar vibratory microgyroscope like the one described in the preceding article.

Mounted on the moving part of the resonator are two electrodes - the driven and the sensing plates - that face corresponding fixed driven and sensing plates. Each pair of electrodes serves as a capacitor; the driven one for electrostatically exciting vibrations, the sensing one for measuring the vibrational velocity. Through the negative-feedback path of the transconductance amplifier, the fixed sensing plate becomes charged up to the dc bias applied to the "+" terminal of the transconductance amplifier. As the resonator vibrates, the voltage across the sensing capacitor thus remains constant, although its capacitance varies at a rate proportional to the vibrational velocity. By the fundamental relationship among capacitance, voltage, and charge, a current proportional to the vibrational velocity must therefore flow between the sensing plate and the "-" input of the transconductance amplifier. As a result, the transconductance amplifier puts out a voltage proportional to the vibrational velocity.

The Mechanical Resonator Is Part of an Oscillator Circuit and determines the frequency of oscillation. The gain of the VCA is continually adjusted to regulate the magnitude of the capacitively sensed mechanical oscillations.

The output of the transconductance amplifier is fed to the signal-input terminal of the voltage-controlled amplifier (VCA) and to the input terminal of the full-wave peak detector. The integrating amplifier produces an error signal that is the integral of the difference between (1) the peak-detector output (which is proportional to the magnitude of the vibrational velocity) and (2) the reference voltage, which represents a desired magnitude of vibration. The error signal is fed to the control-input terminal of the VCA. The output of the VCA is proportional to the velocity and is fed back to the fixed drive plate. With sufficient gain in the amplifiers, the resonator and feedback loop oscillate together. When the amplitude of oscillation is too high or too low, the error signal adjusts the gain of the VCA to drive the magnitude of vibration toward the desired value represented by the reference voltage.

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


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Vibration-Regulating Circuit for a Mechanical Resonator

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Motion Control Tech Briefs Magazine

This article first appeared in the June, 2000 issue of Motion Control Tech Briefs Magazine.

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