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Similar to phase-locked loops, frequency-locked loops (FLLs) are useful in many applications involving waveform synchronization or synthesis. Simple logic circuit-based relaxation oscillators convert capacitance to frequency, which is a characteristic inverse relationship between output frequency and input capacitance. The oscillator's logic level square-wave output can be fed into an all-digital FLL that will frequency lock to the input signal and produce a digital output word N , where N is inversely proportional to the input frequency. The result is that N is linearly proportional to the unknown capacitance in the oscillator. This novel approach allows a simple FFL implementation for capacitance measurement and is demonstrated in hardware using a capacitive sensor that measures the mass of small quantities of water with an output capacitance range of 75-185 pF.Index Terms-Capacitance measurement, frequency-locked loop (FLL), sensor interface circuit.

Unlike traditional rotational gyroscopes, microelectromechanical systems (MEMS) gyroscopes use a vibrating proof mass rather than a rotational mass to sense changes in angular rate. They are also smaller and less expensive than traditional gyroscopes. MEMS gyroscopes are known to be susceptible to the effects of acoustic noise, in particular high frequency and high power acoustic noise. Most notably, this has been proven true in aerospace applications where the noise can reach levels in excess of 120 dB and the noise frequency can exceed 20 kHz. The typical resonant frequency for the proof mass of a MEMS gyroscope is between 3 and 20 kHz. High power, high frequency acoustic noise can disrupt the output signal of the gyroscope to the point that the output becomes unreliable. In recent years, considerable research has focused on the fascinating properties found in metamaterials. A metamaterial is an artificially fabricated device or structure that is engineered to produce desired material responses that can either mimic known behaviors or produce responses that do not occur naturally in materials found in nature. Acoustic metamaterials, in particular, have shown great promise in the field of sound attenuation. This paper proposes a method to mitigate the performance degradation of the MEMS gyroscope in the presence of high power, high frequency acoustic noise by using a new acoustic metamaterial in the form of a two-dimensional array of micromachined Helmholtz resonators. The Helmholtz resonators are fabricated in a silicon wafer using standard MEMS manufacturing techniques and are designed to attenuate sound at the resonant frequency of the gyroscope proof mass. The resonator arrays were diced from the silicon wafer in one inch squares and assembled into a box open on one end in a manner to attenuate sound on all sides of the gyroscope, and to seal the gyroscope inside the box. The resulting acoustic metamaterial device was evaluated in an acoustic chamber and was found to successfully attenuate sound as much as 18 dB. This attenuation is in the form of a notch filter at and around 14.5 kHz, which was the target frequency of attenuation. The notch filter attenuation occurred over a 700 Hz frequency band with 18 dB being the largest attenuation in the band.

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