RESUMO
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 the phononic frequency combs produced in 100-MHz quartz shear-mode resonators. Our new method averaged out the carrier frequency, thus allowing for a fast and efficient computation at parts per million accuracies of noise close to the carrier ( â¼ 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.
RESUMO
We report on a 32-MHz quartz temperature compensated crystal oscillator (TCXO) fully integrated with commercial CMOS electronics and vacuum packaged at wafer level using a low-temperature MEMS-after quartz process. The novel quartz resonator design provides for stress isolation from the CMOS substrate, thereby yielding classical AT-cut f/T profiles and low hysteresis which can be compensated to < ±0.2 parts per million over temperature using on-chip third-order compensation circuitry. The TCXO operates at low power of 2.5 mW and can be thinned to as part of the wafer-level eutectic encapsulation. Full integration with large state-of-the-art CMOS wafers is possible using carrier wafer techniques.
