Lower Bounds on the Frequency Estimation Error in Magnetically Coupled MEMS Resonant Sensors

MEMS inductor-capacitor (LC) resonant pressure sensors have revolutionized the treatment of abdominal aortic aneurysms. In contrast to electrostatically driven MEMS resonators, these magnetically coupled devices are wireless so that they can be permanently implanted in the body and can communicate to an external coil via pressure-induced frequency modulation. Motivated by the importance of these sensors in this and other applications, this paper develops relationships among sensor design variables, system noise levels, and overall system performance. Specifically, new models are developed that express the Cramér-Rao lower bound for the variance of resonator frequency estimates in terms of system variables through a system of coupled algebraic equations, which can be used in design and optimization. Further, models are developed for a novel mechanical resonator in addition to the LC-type resonators.