An offset-canceling low-noise lock-in architecture for capacitive sensing

We describe an offset-canceling low-noise lock-in architecture for capacitive sensing. We take advantage of the properties of modulation and demodulation to separate the signal from the DC offset and use nonlinear multiplicative feedback to cancel the offset. The feedback also attenuates out-of-band noise and further enhances the power of a lock-in technique. Experimentally, in a 1.5-μm BiCMOS chip, a fabrication DC offset of 2 mV and an intentional offset of 100 mV were attenuated to 9 μV. Our offset-canceling technique could also be useful for practical multipliers that need tolerance to fabrication errors. We present a detailed theoretical noise analysis of our architecture that is confirmed by experiment. As an example application, we demonstrate the use of our architecture in a simple capacitive surface-microelectromechanical-system vibration sensor where the performance is limited by mechanical Brownian noise. However, we show that our electronics limits us to 30 μg/√Hz, which is at least six times lower than the noise floor of commercial state-of-the-art surface-micromachined inertial sensors. Our architecture could, thus, be useful in high-performance inertial sensors with low mechanical noise. In a 1-100-Hz bandwidth, our electronic detection threshold corresponds to a one-part-per-eight-million change in capacitance.