Non-Linear Stiffness Extraction and Modeling of Wineglass Disk Resonators

Over the past three to four decades the popularity of MEMS has continually grown with the development of different technologies ranging from thin film bulk acoustic resonators (FBAR), to capacitive gap transducers, and surface acoustic wave (SAW) resonators, just to name a few. Each of which has their own benefits and drawbacks when considering different applications, say sensors or radio frequency (RF) front end components. For example, the prevalent use of FBAR in consumer electronics for RF wideband filters is largely due to the technology’s ability to suppress spurious modes, temperature stability, and high coupling coefficient (kt2). However, for the implementation of channel select filters, low phase noise and low power oscillators, and RF switches (or Resoswitches), capacitive gap transducers are desirable because of their low loss, high quality factor characteristics. Where the quality factor of a typical FBAR device at 2GHz sits at around 2,000, that of a capacitive gap transducer operating at 2.97 GHz sits at about 42,900. However, devices with very high quality factors approach their non-linear mode of operation at much lower input powers (drive voltages) in comparison to their low-quality factor counter parts. Thus, in this report, we employ the harmonic balance method to present a robust non-linear analytical model to study device behavior at high input powers.