Phase noise reduction in an oscillator through coupling to an internal resonance

In this paper, we describe an oscillator, operating at room temperature that can be operated in a condition of internal resonance, where a driven, in-plane mode of the MEMS frequency selective resonator interacts with a torsional mode, resulting in 70 dB decrease in phase noise at a 1 Hz offset as compared to the oscillator operating in driven mode alone. The resonator element is a clamped-clamped beam where the primary mode of oscillation is an in-plane flexural mode, which can be driven at a frequency where vibrational energy is coupled to a higher frequency torsional mode. The coupling to the torsional mode stabilizes the vibrational frequency of the primary mode, resulting in a measured phase noise of-90 dBc at 1 Hz offset and an Allan deviation of 4 x 10^-9. These oscillators show similar behavior to quartz crystals and could be explored for use in timing applications where, currently, single mode resonator micro-and nano-mechanical oscillators are being used in applications such as clocks and frequency standards. We present a theoretical model that qualitatively explains the behavior and demonstrates that phase noise can be greatly reduced at the internal resonance condition.