Abstract: A vibratory sensor with a resonator for measuring angular rotation, such as for example a hemispherical resonator gyroscope (HRG) operating in force rebalance mode, includes circuitry to generate a virtual node and antinode in the resonator standing wave. Shifting a pair of pickoff electrodes from a position directly over an actual node in the HRG standing wave to an offset position where the primary and secondary harmonic contributions at the first pickoff electrode are equal to the primary and secondary harmonic contributions at the second pickoff electrode permits the elimination of secondary harmonics contribution. A virtual node is created by offsetting a pair of pickoff electrodes 22.5 degrees from the actual antinode such that each pickoff electrode includes an equal contribution of the secondary harmonic signal present in the standing wave.

Abstract: A time based digital to analog converter is presented in which known reference voltages are used to create variable period waveforms which, when combined according to a desired computation, can convert digital words into a sinusoidal signal of a precision variable. To illustrate the application of the present invention, a hemispherical resonator gyroscope (HRG) operating in force rebalance is presented wherein a time based digital to analog converter with a variable period output controls the HRG electronics in nulling the standing wave. A rate of the standing wave is calculated, and a software component calculates the fraction of the maximum rate needed to oppose and null the initial rate of the standing wave. The fraction of the maximum rate is converted to digital words corresponding to the number of periods of a clock connected to the circuit.