Electronics for Resonant Sensors

Resonant force or displacement sensing based on observing the change in resonant frequency is attractive because of its relative insensitivity to 1/f noise, high resolution and bandwidth, and “quasi-digital” output. Applications include inertial and strain sensors, biosensors based on mass-loading, and atomic force microscopy. The main contributions of this dissertation are
  • Design of low-noise high fidelity MEMS resonators for sensing,
  • Electronic oscillator circuits for these resonators, and
  • Electronic demodulation of the frequency modulated output and conversion to a digital representation.

The proposed solutions are verified in a resonant MEMS strain sensor. 

In resonant sensors, the purity of the oscillation signal determines the achievable resolution. This requires minimizing noise, which is usually attempted by maximizing the Q (quality factor) of the MEMS resonator. It is shown, however, that there exists a tradeoff between noise that is close to the carrier and noise far from the carrier. While the former decreases with Q as expected, far from carrier noise worsens when Q is increased. Especially in applications demanding relatively high bandwidth the optimal Q can be well below 100.

Because of the relatively weak interaction between the mechanical and electrical domains of MEMS resonators with electrostatic interfaces, these devices exhibit large series resistance, often in the mega-Ohm range. Low Q designs exacerbate this problem. In many setups the resulting small motional current is completely swamped by capacitive feedthrough, preventing oscillation with typical oscillator circuits. The proposed time variant square wave drive oscillator (SWO) overcomes the problem by separating motional and feedthrough current in the time domain. Reliable oscillation has been demonstrated for resonators with motional resistance in excess of 100MΩ and orders of magnitude larger feedthrough than acceptable with traditional oscillator circuits.

The output from a resonant sensor is a frequency modulated sine-wave that must be converted to a digital representation. Owing to the typically small modulation index and moderate to high bandwidth requirements, simple solutions such as frequency counting and conventional PLLs cannot easily be used for this purpose. A new type of sigma-delta PLL (Σ∆PLL) addresses these challenges and combines both demodulation and digitization into a single step. 

A prototype resonant strain sensor measurement system with a SWO oscillator and a Σ∆PLL was implemented with surface mount components on a PC board. With the SWO oscillator, we obtained a phase noise floor of –120 dBc/Hz. This is the best noise performance obtained to date for resonant sensors in this resonant frequency range. This confirms the conclusions from the model that predicted an improved phase noise floor as the Q is brought closer to its optimum value. The Σ∆PLL achieved a 1Hz frequency resolution (21 ps period resolution) in a 10kHz bandwidth and the overall strain sensor measurement system achieved a 33 nε resolution in 10kHz.

Publication date: 
December 31, 2005
Publication type: 
Ph.D. Dissertation
Wojciechowski, K. E. (2005). Electronics for Resonant Sensors. United States: University of California, Berkeley.

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