Practical Limits to Common Mode Rejection in Mode Localized Weakly Coupled Resonators

The amplitude ratio output metric in mode localized weakly coupled resonators has been established to show superior rejection of first order temperature and pressure variations over frequency shift output metric. This work for the first time documents a holistic study on the temperature dependence of amplitude ratio and frequency shift output metric over various operating points of a mode localized resonator while comparing different modes of operation and different coupling schemes. The results show that both modes of an electrically coupled resonator system exhibit ≈ 10× improvement in rejecting temperature fluctuations over the modes of similar mechanically coupled resonators. Both mechanically coupled and electrically coupled resonators showed an improvement of 2-3 orders of magnitude common mode rejection as compared to the frequency shift output. For the first time, a comparison was made between amplitude ratio and differential frequency measurements and the results showed similar rejection capabilities between the two output metrics. The various mechanisms leading to the temperature dependence of the three output metrics are discussed in detail thus highlighting the advantages of using each of them for sensing and timing applications.