Phase Noise and Fundamental Sensitivity of Oscillator-Based Reactance Sensors

This paper investigates the fundamental sensitivity of oscillator-based reactance sensors, which are widely used in numerous types of biomedical sensing applications. We first show that the intrinsic sensitivity is limited by the 1/f³ phase noise of the sensing oscillators. To achieve sensor detection sensitivity below this limit, a correlated double counting (CDC) noise suppression scheme is proposed to cancel the correlated 1/f³ phase noise in differential frequency detections. The suppression effect of the CDC scheme is thoroughly modeled. Moreover, the CDC scheme is extended to a high-order configuration, called the Interleaving-N CDC, to further improve the frequency resolution. In addition, we show that the weighting sequence on the Interleaving-N CDC data can be optimized as a digital noise filter to maximize the noise suppression. Given a sensing oscillator with any phase-noise profile, a general weighting optimization method is proposed based on the minimum variance distortion less response. As an example, an oscillator-based inductive magnetic sensor array in a 45-nm CMOS silicon-on-insulator process is implemented with the proposed CDC scheme. It achieves a noise suppression of 10.4 dB with basic CDC sheme and a frequency resolution of 0.128 parts per million for Interleaving-N CDC scheme, both with negligible power overhead. This enables inductance-change detection sensitivity of 0.41 fH for a low-Q on-chip 1.6-nH inductor with a quality factor of only 4.95.