Serial and Parallel Connections of Micromechanical Resonators for Sensing: Theories and Applications

The mass-spring-damper resonator is the basic mechanical component of current microelectromechanical systems (MEMS) sensors. It is typically implemented in various forms of micromechanical cantilevers, beams, diaphragms, rings, etc. In the classical sensing paradigm, the amplitude, frequency, or phase change of a single degree-of-freedom (1-DoF) resonator is used to perform sensing applications. This paper presents the basic theories and applications for serial and parallel connections of 1-DoF micromechanical resonators for sensing. In the serial connection, the amplitude ratio of the two outer resonators is typically selected as the output metric and the mode-localization phenomenon is especially used to mechanically amplify the signal and suppress common-mode noises. Then the signal-to-noise ratio (SNR) of sensors can be improved. In the parallel connection, resonators are combined by an optimal filter to suppress random noises and the SNR can be further improved. Unknown disturbances can also be suppressed by differential sensing in the parallel connection. In a short summary, the serial and parallel connection provide calculation of summation, subtraction, and division, thus enabling further sensing performance improvement. And full compatibility to current MEMS processes provides a new sensing paradigm to improve the performance of MEMS sensors.