An Averaging Method for Phase Noise Studies of Quartz Phononic Frequency Combs.

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.

Design Considerations for Frequency Shifts in a Laterally Finite FBAR Sensor in Contact With the Newtonian Liquid.

Mode-coupled vibrations in a thickness-shear (TSh) mode and laterally finite film bulk acoustic resonator (FBAR) with one face in contact with Newtonian (linearly viscous and compressional) liquid are investigated. With boundary conditions and interface continuity conditions, exact dispersion curves in FBAR sensors contacting with two kinds of liquids are obtained, and they are compared with the dispersion curves in a bare sensor without liquid contact. Frequency spectra, describing mode couplings between the main TSh modal branch and undesirable modal branches, are calculated by employing weak boundary conditions at lateral free edges constructed based on the variational principle.

Lateral Size-Dependence in UHF Mode-Coupled ZnO FBARs to Suppress Undesirable Eigen-Modes and Weaken Mounting Effect.

Mode-coupled vibrations in an ultra-high frequency (UHF) ZnO thin film bulk acoustic resonator (FBAR) operating at thickness-extensional (TE) mode are studied by employing weak boundary conditions (WBCs), constructed based on Saint-Venant's principle and mixed variational principle in the piezoelectric theory. The frequency spectra, describing the lateral size-dependence of mode couplings between the main mode (TE) and undesirable eigen-modes, for clamped lateral edges are compared with the existing frequency spectra for free lateral edges to illustrate the boundary influence. The displacement and stress variations in FBAR volume are also presented to intuitionally understand and distinguish the difference of frequency spectra between these two different lateral edges, and then we discuss how to select outstanding lateral sizes to weaken the mounting effect.

Simulation of Nonlinear Resonance, Amplitude-Frequency, and Harmonic Generation Effects in SAW and BAW Devices.

Nonlinearly coupled sets of piezoelectric field equations in the frequency domain were derived for the nonlinear propagation of finite-amplitude waves in piezoelectric bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices. To verify their accuracy, we have embedded these sets of equations in the finite-element method (FEM) of COMSOL Multiphysics software and compared the FEM results with both the analytical and experimental results found in the published literature. The nonlinear frequency responses for both plano- and contoured-plate resonators of AT-cut quartz were investigated under various voltage drives, circuit resistances, and quality factors.

A Fully Integrated Quartz MEMS VHF TCXO.

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.

On the acceleration sensitivity and its active reduction by edge electrodes in AT-cut quartz resonators.

Incremental piezoelectric equations for small vibrations superposed on initial deformations are presented. The equations are implemented in COMSOL finite element models (FEA). Equations are validated by comparing the results for the force sensitivity coefficient Kf of a circular quartz plate subjected to a pair of diametrical forces with measured data.

Theory and experimental verifications of the resonator Q and equivalent electrical parameters due to viscoelastic and mounting supports losses.

A novel analytical/numerical method for calculating the resonator Q and its equivalent electrical parameters due to viscoelastic, conductivity, and mounting supports losses is presented. The method presented will be quite useful for designing new resonators and reducing the time and costs of prototyping. There was also a necessity for better and more realistic modeling of the resonators because of miniaturization and the rapid advances in the frequency ranges of telecommunication.

Conceptual design of a high-Q, 3.4-GHz thin film quartz resonator.

Theoretical analyses and designs of high-Q, quartz thin film resonators are presented. The resonators operate at an ultra-high frequency of 3.4 GHz for application to high-frequency timing devices such as cesium chip-scale atomic clocks.

Effects of electromagnetic radiation on the Q of quartz resonators.

The quartz resonator Q with aluminum electrodes was studied with respect to its fundamental thickness shear mode frequency and its viscoelastic, viscopiezoelectric, and viscopiezoelectromagnetic behaviors. The governing equations for viscoelasticity, viscopiezoelectricity, and viscopiezoelectromagnetism were implemented for an AT-cut quartz resonator. To simulate the radiation conditions at infinity for the viscopiezoelectromagnetic model, perfectly matched layers over a surface enclosing the resonator were implemented to absorb all incident electromagnetic radiation.

Love wave propagation in piezoelectric layered structure with dissipation.

We investigate analytically the effect of the viscous dissipation of piezoelectric material on the dispersive and attenuated characteristics of Love wave propagation in a layered structure, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of the viscous coefficient on the phase velocity of Love waves and attenuation are presented and discussed in detail. The analytical method and the results can be useful for the design of the resonators and sensors.

Dedicated finite elements for electrode thin films on quartz resonators.

The accuracy of the finite element analysis for thickness shear quartz resonators is a function of the mesh resolution; the finer the mesh resolution, the more accurate the finite element solution. A certain minimum number of elements are required in each direction for the solution to converge. This places a high demand on memory for computation, and often the available memory is insufficient.

Estimation of quartz resonator Q and other figures of merit by an energy sink method.

An important determinant of the quality factor Q of a quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base substrate. The base substrate affects the frequency spectra of the plate resonator.