Influences of the feedthrough capacitance on the frequency synchronization of the weakly coupled resonators

Influences of the feedthrough capacitance on weakly coupled micromechanical resonators are theoretically analyzed and experimentally observed using current vector analysis and the Nyquist plots method for the first time. By analyzing the equivalent electric model of the weakly coupled resonators with feedthrough capacitance, it is found that the existence of the feedthrough capacitance will lead to frequency asynchronization and measurement error of the amplitude ratio of the mode localization based sensors. The variations of the transmission responses of the weakly coupled resonators with the influence of the feedthrough capacitance are experimentally demonstrated. The frequency asynchronization became less than 2.3 ppm, down from the previous 55.6 ppm, and the measurement error of the amplitude ratio was reduced from 25.9% to approximately 0 after compensating the feedthrough capacitance using the method presented in the paper. This enhancement lays the foundation for the accurate measurement of the eigenstate and the amplitude ratio of the mode localization based sensors.