LAUSR

A fast and accurate averaging method was derived and developed for the analysis and design of quartz phononic frequency combs. The phononic frequency combs were obtained from a pair of coupled nonlinear Duffing equations for quartz resonators by solving the equations in the time domain, and performing a Fast Fourier Transformation (FFT) of the steady state vibrations of the time series. Noise simulations were added to the drive frequency to study noise transfer characteristics between the drive signal and the resonances of phononic frequency combs produced in 100-MHz quartz shear-mode resonators. Our new method averaged out the carrier frequency, thus allowed for a fast and efficient computation at parts per million accuracy of noise close to the carrier (~10 Hz). The goal of our study was to develop methods and resonator requirements for engineering the properties of the phononic frequency combs for low-noise clock applications.