Abstract: Synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Experimental implimentation allows for unprecedented observation and control of parameters governing the dynamics of synchronization. Close quantitative agreement is found between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchonized state, a significant reduction in the phase noise of the oscillators is demonstrated, which is key for applications such as sensors and clocks. Oscillator networks constructed from nanomechanical resonators form an important laboratory to commercialize and study synchronization—given their high-quality factors, small footprint, and ease of co-integration with modern electronic signal processing technologies. Networks can be made including one-, two-, and three-dimensional networks. Triangular and square lattices can be made.

Abstract: A passive electro-mechanical device that reduces phase noise in oscillators, thereby improving their frequency precision. The noise reduction device can consist of a pair of coupled nonlinear resonators that are driven parametrically—by modulating their natural frequency in time, through the output signal of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators can exhibit oscillation at an inherent frequency. The novel possibility for noise elimination is realized by tuning the system to operating points for which this periodic signal is immune to frequency noise in the drive signal, providing a way to clean the phase noise of the driving oscillator.

Abstract: A passive electro-mechanical device that reduces phase noise in oscillators, thereby improving their frequency precision. The noise reduction device can consist of a pair of coupled nonlinear resonators that are driven parametrically—by modulating their natural frequency in time, through the output signal of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators can exhibit oscillation at an inherent frequency. The novel possibility for noise elimination is realized by tuning the system to operating points for which this periodic signal is immune to frequency noise in the drive signal, providing a way to clean the phase noise of the driving oscillator.

Abstract: Synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Experimental implimentation allows for unprecedented observation and control of parameters governing the dynamics of synchronization. Close quantitative agreement is found between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchonized state, a significant reduction in the phase noise of the oscillators is demonstrated, which is key for applications such as sensors and clocks. Oscillator networks constructed from nanomechanical resonators form an important laboratory to commercialize and study synchronization—given their high-quality factors, small footprint, and ease of co-integration with modern electronic signal processing technologies. Networks can be made including one-, two-, and three-dimensional networks. Triangular and square lattices can be made.

Abstract: A parametric feedback oscillator includes a resonator which has at least one transduction element and at least one electromechanical resonating element. The resonator is configured to accept as input a parametric excitation signal at a frequency 2?0 and to provide a resonating output signal at a frequency ?0. A cascaded feedback path in any electrically coupled cascade order includes at least one non-linear element, at least one phase shifter electrically, and at least one amplifier. The cascade feedback path is configured to receive as input the resonating output signal at a frequency ?0 and configured to provide as output a feedback path signal as the parametric excitation signal at a frequency 2?0 to the resonator. A parametric feedback oscillator output terminal is configured to provide the resonating output signal at the frequency ?0 as an output signal. A method of causing a parametric feedback oscillation is also described.

Abstract: A parametric feedback oscillator includes a resonator which has at least one transduction element and at least one electromechanical resonating element. The resonator is configured to accept as input a parametric excitation signal at a frequency 2?0 and to provide a resonating output signal at a frequency ?0. A cascaded feedback path in any electrically coupled cascade order includes at least one non-linear element, at least one phase shifter electrically, and at least one amplifier. The cascade feedback path is configured to receive as input the resonating output signal at a frequency ?0 and configured to provide as output a feedback path signal as the parametric excitation signal at a frequency 2?0 to the resonator. A parametric feedback oscillator output terminal is configured to provide the resonating output signal at the frequency ?0 as an output signal. A method of causing a parametric feedback oscillation is also described.