Accelerometer apparatuses and systems for noise rejection

A differential sensor system comprising:

• a resonator;
• a transducer configured to detect a first position of the resonator;
• a second transducer configured to detect a second position of the resonator;
• a damping resistor configured to electrostatically actuate the transducer and convert a thermomechanical noise of the resonator to an electromechanical noise;
• a second damping resistor configured to electrostatically actuate the second transducer and convert the thermomechanical noise of the resonator to a second electromechanical noise;
• a first switch configured to receive a first signal from the transducer;
• a filter stage configured to receive the first signal and adjust a phase and a gain of the first signal and output a filtered first signal;
• a second switch configured to receive a second signal from the transducer;
• a third switch configured to receive a third signal from the second transducer;
• a second filter stage configured to receive the third signal and adjust a phase and a gain of the third signal and output a filtered third signal;
• a fourth switch configured to receive a fourth signal from the second transducer;
• a noise rejection stage configured to receive the filtered first signal, the second signal, the filtered third signal, and the fourth signal, and reduce a first differential value between the filtered first signal and the filtered third signal from a second differential value between the second signal and the fourth signal;
• a first integrating capacitor coupled to the noise rejection stage;
• a fifth switch configured to reset a charge on the first integrating capacitor;
• a second integrating capacitor coupled to the noise rejection stage;
• and
• a sixth switch configured to reset a charge on the second integrating capacitor,
• wherein the first and third switches are controlled by a first phase signal,
• wherein the second and fourth switches are controlled by a second phase signal,
• wherein the fifth and sixth switches are controlled by a third phase signal, and
• wherein the differential sensor system is time-multiplexed.