A SAW resonator with two-dimensional reflectors

It is known that a part of the loss of leaky SAW resonators is due to radiation of acoustic energy in the bus-bars. Many researchers are working on so-called phononic crystals. A 2-D grating of very strong reflectors allows these devices to fully reflect, for a given frequency band, any incoming wave. A new device based on the superposition of a regular SAW resonator and a 2-D periodic grating of reflectors is proposed. Several arrangements and geometries of the reflectors were studied and compared experimentally on 48° rotated Y-cut lithium tantalate. In particular, a very narrow aperture (7.5 ?) resonator was manufactured in the 900 MHz range. Because of its small size, this resonator has a resonance Q of only 575 when using the standard technology, whereas a resonance Q of 1100 was obtained for the new device without degradation of the other characteristics. Because of the narrow aperture, the admittance of the standard resonator showed a very strong parasitic above the resonance frequency, whereas this effect is drastically reduced for the new device. These results demonstrate the feasibility of the new approach.     

Analysis of an optical resonator formed by a pair of specially shaped axicons

We propose a design for an optical resonator suited to using large-bore active media. The resonator consists of a pair of waxicons, so we call it a "wwaxicon optical resonator." The resonator is considered a conventional (solid) resonator surrounded by coaxial annular resonators. A numerical simulation of the resonator designed for use in a commercial CO2 laser is performed. It is found that parasitic oscillation modes can be suppressed by the use of an spatial-frequency filter. The resonator exhibits oscillation in the TEM*01 transverse mode and produces twice as much output power as a sevenfold multipass stable optical resonator.     

1.52-GHz micromechanical extensional wine-glass mode ring resonators

Vibrating polysilicon micromechanical ring resonators, using a unique extensional wine-glass-mode shape to achieve lower impedance than previous UHF resonators, have been demonstrated at frequencies as high as 1.2 GHz with a Q of 3,700, and 1.52 GHz with a Q of 2,800. The 1.2-GHz resonator exhibits a measured motional resistance of 1 MOmega with a dc-bias voltage of 20 V, which is 2.2 times lower than the resistance measured on radial contourmode disk counterparts at the same frequency. The use of larger rings offers a path toward even lower impedance, provided the spurious modes that become more troublesome as ring size increases can be properly suppressed using methods described herein. With spurious modes suppressed, the high-Q and low-impedance advantages, together with the multiple frequency on-chip integration advantages afforded by capacitively transduced micromechanical resonators, make this device an attractive candidate for use in the front-end RF filtering and frequency generation functions needed by wireless communication devices.     

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. A resonator with a high Q may not have a similarly high Q when mounted on a base. Hence, the base is an energy sink and the Q will be affected by the shape and size of this base. A lower bound Q will be obtained if the base is a semi-infinite base since it will absorb all acoustical energies radiated from the resonator. A scaled boundary finite element method is employed to model a semi-infinite base. The frequency spectra of the quartz resonator with and without the base are presented. In addition to the loss of energy via the base, there are other factors which affect the resonator Q, such as, for example, material dissipation, and damping at the interfaces of quartz and electrodes. The energy dissipation due to material damping increases with the resonant frequency and the reduction of resonator size; hence material damping becomes important in the current and future miniaturized resonators operating at very high frequencies. An energy sink model along with material dissipation would provide realistic Q, motional capacitance, motional resistance, and other figures of merit useful for designing resonators. The model could be used for evaluating resonator and mountings designs of microelectromechanical systems and miniaturized devices. The effect of the mountings, and plate and electrode geometries on the resonator Q and other electrical parameters are presented for AT-cut quartz resonators. Model results from the energy sink method were compared with experimental results and were found to be good.     

Experimental study on the characteristic of the NS-GT cut quartz crystal resonator oscillating in the sub-resonant frequency

We previously reported that the dynamic photo-elastic method was a very effective measuring technique for the stress distribution of vibrating quartz crystal resonators. The existence of a twisted asymmetrical vibration mode has been verified experimentally when the NS-GT cut quartz crystal resonator was vibrating in the main resonant frequency (MRF). A MRF and a sub-resonant frequency (SRF) of the NS-GT cut quartz resonator were defined as follows. If a mechanical standing wave was in the x' or y' direction of the resonator, the former was MRF vibration and the latter was SRF vibration, respectively. In this paper, stress distributions of two samples of the NS-GT cut quartz crystal resonator, one of which had a thickness of 80 mum and the other 150 mum, were measured by the dynamic photo-elastic method when the resonators were vibrating in each SRF. Thereafter, vibration modes of those resonators were estimated by the experimental data of stress distributions. We find that the vibration mode of the 80-mum resonator had a simple mechanical standing wave on the y' direction and the vibration mode of the 150-mum resonator was combined with a shearing mode in the SRF vibration. From the experiment, we decided that vibration modes of the NS-GT cut quartz crystal resonator were composed of the longitudinal stress T(3)' belonging to the z' direction of the plate and of the shearing stress T(5)' when the plate thickness was thickened and the resonator was oscillating in the SRF.     

Temperature-stable double SAW resonators

The temperature stability of SAW resonators on quartz can be enhanced by means of double resonators. The turnover temperatures of the double resonators' components, called single resonators, are positioned above and below room temperature. As a consequence, the temperature coefficients of frequency of the 1st order (TCF1) have opposite signs at room temperature, leading to the vanishing TCF1 of the double resonators. Frequently, different turnover temperatures are adjusted by different propagation directions on an ST cut of quartz. An overview of known and new methods for compensating the temperature coefficient of frequency of the 2nd order (TCF2) of two-port and one-port SAW double resonators is given. A concept by means of which temperature-stable circuits of single resonators are found is described. Two types of temperature-stable double resonators found by applying that concept are treated in detail: 1) a two-port resonator composed of two cascaded two-port resonators and a coupling inductance, and 2) a one-port resonator comprising a series connection of one-port resonators with an inductance in parallel with each single resonator. The substrates are 35.5 degrees rotY cuts of quartz. In both cases, the shift of resonance frequency within the temperature range from -30 degrees C to 70 degrees C is smaller than 20 ppm.     

Doubly rotated contoured quartz resonators

Doubly rotated contoured quartz resonators are used in the design of temperature-compensated stable clocks and dual-mode sensors for simultaneous measurements of pressure and temperature. The design of these devices is facilitated by models that can predict frequency spectra associated with the three thickness modes and temperature and stress-induced frequency changes as a function of crystalline orientation. The Stevens-Tiersten technique for the analysis of the C-mode of a doubly rotated contoured quartz resonator is extended to include the other two thickness modes. Computational results for harmonic and anharmonic overtones of all three thickness modes of such resonators help in optimizing the radius of curvature of the contour and electrode shape for suppression of unwanted modes and prevention of activity dips. The temperature and stress-induced changes in thickness-mode resonator frequencies are calculated from a perturbation technique for small dynamic fields superposed on a static bias. The static bias refers to either a temperature or stress-induced static deformation of the resonator plate. Phenomenological models are also used for calculating the temperature and stress-induced changes in resonant frequencies as a function of crystalline orientation. Results for the SBTC-cut quartz plate with a spherical convex contour of 260 mm indicate that normal trapping occurs for the third (n=3) and fifth (n=5) harmonic of the A-mode, the fundamental (n=1) and third (n=3) harmonic of the B-mode, and the fundamental (n=1) and fifth (n=5) harmonic of the C-mode     

Measuring Shell Resonances of Spherical Acoustic Resonators

Coupling between the gas and shell is a concern in the experiment used at LNE-CNAM to determine the Boltzmann constant k _B by an acoustic method. As the walls of real resonators are not perfectly rigid, some perturbations occur in the frequency range of the acoustic resonances measured within helium gas contained in the cavity. As a contribution for a better understanding of this phenomenon, an experiment to measure the shell modes of the spherical resonators is in use in this laboratory. A work in progress to assess these modes using a hammer blow method together with modal analysis is reported here. The study is carried out with an air-filled, copper-walled, half-liter quasi-spherical resonator in the frequency range from 1 Hz to 20 kHz. Results show that the shell modes expand into multiple resonances of similar modal shape, including the ??breathing?? mode. The observations reported in other studies of shell perturbations at other frequencies than the breathing frequency are confirmed.     

Electroelastic effect of thickness mode langasite resonators

Langasite is a very promising material for resonators due to its good temperature behavior and high piezoelectric coupling, low acoustic loss, and high Q factor. The biasing effect for langasite resonators is crucial for resonator design. In this article, the resonant frequency shift of a thickness-mode langasite resonator is analyzed with respect to a direct current (DC) electric field applied in the thickness direction. The vibration modes of a thin langasite plate fully coated with an electrode are analyzed. The analysis is based on the theory for small fields superposed on a bias in electroelastic bodies and the first-order perturbation integral theory. The electroelastic effect of the resonator is analyzed by both analytical and finite-element methods. The complete set of nonlinear elastic, piezoelectric, dielectric permeability, and electrostrictive constants of langasite is used in the theoretical and numerical analysis. The sensitivity of electroelastic effect to nonlinear material constants is analyzed.     

An Investigation on Efficient Acoustic Energy Reflection of Flexible Film Bulk Acoustic Resonators

This paper investigates the issues on acoustic energy reflection of flexible film bulk acoustic resonators(FBARs). The flexible FBAR was fabricated with an air cavity in the polymer substrate, which endowed the resonator with efficient acoustic reflection and high electrical performance. The acoustic wave propagation and reflection in FBAR were first analyzed by Mason model, and then flexible FBARs of 2.66 GHz series resonance in different configurations were fabricated. To validate efficient acoustic reflection of flexible resonators, FBARs were transferred onto different polymer substrates without air cavities. Experimental results indicate that efficient acoustic reflection can be efficiently predicted by Mason model. Flexible FBARs with air cavities exhibit a higher figure of merit(FOM). Our demonstration provides a feasible solution to flexible MEMS devices with highly efficient acoustic reflection(i.e. energy preserving) and free-moving cavities, achieving both high flexibility and high electrical performance.     

Acceleration sensitivity of crystal resonators affected by the mass and location of electrodes

Predominant thickness-shear frequencies and modes of a crystal plate with electrodes of arbitrary shape and mass distribution are obtained by a finite-element method, based on Mindlin's first-order equations with platings. These frequencies and modes are used in a perturbation method for computing the acceleration sensitivity of crystal resonators with electrodes. Computations are made for a square AT-cut quartz plate that is supported by a four-point mount and coated with identical square and uniform electrodes on the upper and lower faces of the plate. To study the effect of uneven distribution of electrode mass, acceleration sensitivities are calculated when a small mass is added at various locations near the edges of the square electrodes. It is found that the percent increase of the acceleration sensitivity of the resonator with a small added mass to that of the resonator without added mass ranges from 3.8% to 541.7%, depending on the location of the small mass placed at the edges of the electrodes.     

Coupled resonator filter with single-layer acoustic coupler

We discuss the operation of novel coupled-resonator filters with single-layer acoustic couplers. Our analysis employs the physical Mason model for acoustic resonators. Their simpler fabrication process is counterbalanced by the high acoustic attenuation of suitable coupler materials. At high levels of attenuation, both the phase and the acoustic impedance must be treated as complex quantities to accurately predict the filter insertion loss. We demonstrate that the typically poor near-band rejection of coupled resonator filters can be improved at the die level by connecting a small capacitance between the input and output of the filter to produce a pair of tunable transmission minima. We make use of these theoretical findings to fabricate coupled resonators filters operating at 2.45 GHz.     

耦合共振型进气消声器声学特性分析

为了拓宽消声频带、提高消声量,克服传统串并联腔体结构安装空间大等缺点,研究了一种新型耦合共振型进气消声器．利用一维平面波理论探究了Helmholtz消声器的消声机理;为准确模拟消声器突变结构处的高阶次声波,建立了并联共振腔结构和新型结构Helmholtz消声器的声学有限元计算模型;计算、分析、比较了各结构的消声特性,重点研究了新型结构尺寸参数对其共振频率与传递损失的影响．计算结果表明：由于腔体间空气耦合共振作用,两腔耦合共振型Helmholtz消声器具有3个共振频率;两共振腔连接管的长度与直径是影响该结构消声性能的关键尺寸,减小连接管长度或者增大直径都可以拓宽消声器的消声频带,提高消声性能．这将为主动、被动耦合共振型进气消声器的设计提供重要参考．     

Cooled, ultrahigh Q, sapphire dielectric resonators for low-noise, microwave signal generation

Ultra-high Q, X-band resonators, used in a frequency discriminator for stabilization of a low-noise signal generator, can provide a means of obtaining significant reduction in phase noise levels. Resonator unloaded Qs on the order of 500 K can be obtained in sapphire dielectric resonator (DR) operating on a low-order (i.e. TE(01)) mode at 77 K and employing high-temperature superconducting (HTS) films installed in the DR enclosure covers. Rigorous analysis for the determination of resonator frequency, modes, and unloaded Q have been carried out using mode matching techniques. Trade-off studies have been performed to select resonator dimensions for the optimum mode yielding highest unloaded Q and widest spurious mode separation. Field distributions within the resonator have been computed to enable practical excitation of the required mode. The results of both analysis and prototype device evaluation experiments are compared for resonators fabricated using enclosures consisting of conventional, metal sidewalls and covers employing HTS films as a function of cover conductivity.     

K-cut quartz SAW resonators for stable frequency sources

A new type of quartz SAW resonator for use as a stable frequency source has been developed. It was studied from the point of view of frequency instability caused by transient thermal behavior, and a new angle of cut named the K-cut for quartz SAW resonators was found. The static and dynamic frequency temperature coefficients are both zero at a room temperature. Taking into consideration the influence of the electrode-film thickness, the width modes of the waves, and power-flow angles, optimized resonators and oscillators were designed. These devices had frequency stability of 2x10(-10) for the mean time of 0.01 s.     

Thermal transient model of a crystal resonator employing thickness-shear vibrations

This paper presents an improved model of thermally induced frequency transients in vacuum-enclosed thickness-shear mode quartz crystal resonators. The response times to temperature changes for different parts of the resonator and resulting thermal dynamic coefficients are examined and are related to Ballato's coefficient through a function defined by the resonator design, dependent on thermal response times only. A method is worked out for response time calculations for the different contributions to the static and dynamic temperature behavior of general and anharmonic modes. The model has been used to examine thermally induced frequency transients of the AT-cut resonator h(513) anharmonic mode excited by the modulational method within an ovenized Colpitts oscillator. A good agreement is shown between the predicted curves and experimental data over a variety of temperature ranges.     

An X-ray double crystal topographic assessment of defects in quartz resonators

This paper describes an X-ray double crystal topographic study of defects in eighteen quartz resonators designed to operate at 1.4 MHz. The types of defects found in quartz are described, together with their reported effects on resonator performance. The mode of operation of the bulk resonator and the technique of X-ray double crystal reflection topography are outlined. Topographs reveal the electrode structures and surface features of the resonators together with the presence of growth defects such as dislocation cells, sub-boundaries, growth striations and growth sector boundaries. Spurious flexure modes in two resonators are also shown. It is demonstrated that a correlation exists between the presence of growth striations (and probably sub-boundaries) and a higher equivalent series resistance of the resonators. It is shown that such defects change the contributions to the losses, possibly by changing the nature of the vibration pattern of the resonator.     

Phononic plate waves

In the past two decades, phononic crystals (PCs) which consist of periodically arranged media have attracted considerable interest because of the existence of complete frequency band gaps and maneuverable band structures. Recently, Lamb waves in thin plates with PC structures have started to receive increasing attention for their potential applications in filters, resonators, and waveguides. This paper presents a review of recent works related to phononic plate waves which have recently been published by the authors and coworkers. Theoretical and experimental studies of Lamb waves in 2-D PC plate structures are covered. On the theoretical side, analyses of Lamb waves in 2-D PC plates using the plane wave expansion (PWE) method, finite-difference time-domain (FDTD) method, and finite-element (FE) method are addressed. These methods were applied to study the complete band gaps of Lamb waves, characteristics of the propagating and localized wave modes, and behavior of anomalous refraction, called negative refraction, in the PC plates. The theoretical analyses demonstrated the effects of PC-based negative refraction, lens, waveguides, and resonant cavities. We also discuss the influences of geometrical parameters on the guiding and resonance efficiency and on the frequencies of waveguide and cavity modes. On the experimental side, the design and fabrication of a silicon-based Lamb wave resonator which utilizes PC plates as reflective gratings to form the resonant cavity are discussed. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs were applied.     

Equivalent circuit modeling of coupled resonator filters

Using the stacked crystal filter (SCF) concept, a coupled resonator filter (CRF) can be interpreted as a device in which 2 piezoresonators are stacked on top of each other in such a way that a certain degree of acoustic interaction occurs. The work presented in this paper reports a novel all-electrical model for the CRF. The model associates acoustical coupling with an equivalent electrical coupling between resonators. The resulting equivalent circuit makes it possible to apply classical filter synthesis techniques directly based on the coupling control between resonators. It complements with a synthesis approach the analysis approach of the Mason model.     

Selective excitation of eigenmodes in a multilayer thin film resonator on bulk acoustic waves

We consider a method of control over the operating frequency of a resonator on bulk acoustic waves, which is based on the selective excitation of eigenmodes. The frequency switching is achieved by using several layers of a ferroelectric in the paraelectric state and applying a control voltage of appropriate magnitude and polarity to each layer. The principle of selectivity is formulated and the criterion function is defined, which ensure the most effective excitation of a selected eigenmode with the possible suppression of parasitic modes. An example of using this function for a resonator switched between four eigenmodes is presented.