H.F. Tiersten

Guided acoustic‐surface‐wave filters

A number of filter structures utilizing acoustic surface waveguides and periodic arrays of reflecting strips to form multimoded resonant configurations are described. The devices described are analogous to the monolithic crystal filter in that an array of acoustically coupled resonators is obtained from a structure placed on a single substrate. The coupling between resonators is described in terms of trapped energy modes of the surface‐waveguiding structures.

Zero temperature coefficient of delay for surface waves in quartz

Some new orientations and propagation directions possessing zero temperature coefficients of delay for surface waves in quartz with somewhat better electromechanical coupling than the ST cut are reported. One of the orientations also exhibits an almost‐zero power flow angle. The results have been obtained using a nonlinearly based formalism in which the reference geometry, which remains fixed as the temperature is varied, may be employed.

An analysis of the normal acceleration sensitivity of contoured quartz resonators rigidly supported along the edges

The authors perform an analysis of the normal acceleration sensitivity of contoured quartz resonators rigidly supported along rectangular edges. Calculated biasing deformation fields are used in an existing perturbation equation along with the equivalent trapped energy mode shapes for the contoured resonator to calculate the normal acceleration sensitivities. It is shown that the normal acceleration sensitivity vanishes for certain values of the planar aspect ratio for all modes considered in both the AT and SC cuts. In addition, the sensitivity has been calculated as a function of the orientation of the rectangle with respect to the nodal lines of the anharmonics of the contoured resonator for the case of square AT- and SC-cut plates. The calculations reveal that the SC cut has zero-crossings for this case while the AT cut does not and that the sensitivity is consistently lower for the square SC cut than the AT cut.<<ETX>>

Acceleration sensitivity of surface acoustic wave resonators

The acceleration sensitivity of acoustic surface wave resonators (and delay lines) on quartz substrates supported uniformly at the base has been calculated. For normal acceleration the calculated sensitivity is almost two orders of magnitude lower than the lowest published measurements. For in‐plane acceleration the calculated sensitivity is comparable to the best published measurements. This causes us to believe that uniform base support has not been realized in practice and, in fact, may be impossible to achieve. For normal acceleration and nonuniform base support the calculations indicate that increasing the thickness of the substrate decreases the acceleration sensitivity. Experimental verification of this is presented. However, for in‐plane acceleration the calculations indicate that increasing the thickness of the substrate increases the acceleration sensitivity.

On the Temperature Dependence of the Velocity of Surface Waves in Quartz

Abstract : The first temperature derivatives of the fundamental elastic constants of quartz are employed along with the thermally-induced biasing strains in the equation for the first perturbation of the eigenvalue for the linear electroelastic equations for small fields superposed on a bias to calculate the resulting change in surface wave velocity with temperature. Since the description employed is referred to a fixed reference state, the geometry does not change and the temperature coefficient of velocity is the negative of the temperature coefficient of delay.

Ultrasonic imaging using trapped energy mode Fresnel lens transducers

A focusing transducer utilizing trapped energy modes can be easily fabricated by plating a number of concentric rings of electrodes on a suitable piezoelectric plate of uniform thickness. The concentric ring structure acts as a Fresnel lens and can be used to obtain excellent lateral focusing of ultrasonic waves. Several transducers operating in the 2–5 MHz range have been produced using PZT-7A as the piezoelectric material. The near field radiation pattern has been observed directly in front of the plate using the first order diffraction peak from a laser probe. It is confirmed that there is good acoustic isolation between the rings and that they radiate in the trapped energy mode. The ultrasonic radiation pattern of the Fresnel lens has been observed at various distances from the plate and compared with computed results which show excellent agreement. Furthermore, the axial diffraction pattern of the lens can be optimized by adjusting ring spacings. During the course of this study a new, previously unreported mode of energy trapping has been discovered. The explanation for this method of trapping is briefly discussed. Finally an acoustic through-transmission imaging system incorporating one focusing transducer is used for imaging of flaws in composite materials.

Ultrasonic Imaging Using Monolithic Mosaic Transducer Utilizing Trapped Energy Modes

A transducer array utilizing trapped energy modes can be fabricated simply by plating a large number of separate electrodes on a single piezoelectric plate of uniform thickness. Several two dimensional arrays operating in the frequency range 2–5 MHz have been fabricated using PZT-7A. Experimental results showing the three dimensional radiation pattern of these transducers will be presented. The radiation pattern was determined from a computer aided reconstruction of data obtained from an acousto-optic diffraction measurement. The transducer elements are found to act independently over a higher bandwidth if electronic matching is employed. Preliminary results of ultrasonic imaging using a two dimensional mosaic transducer will also be presented.

A Variational Analysis of the Reflection of Surface Waves by Arrays of Reflecting Grooves

Abstract : A system of approximate surface wave equations and edge conditions in one scaler variable is derived from Hamiltons principle for linear piezoelectric media by assuming suitable depth behavior and integrating with respect to depth. The assumed behavior with depth is determined from the known surface wave solutions of the three-dimensional equations for both the plated and uplated substrate. The influence of the inertia, stiffness and electrical shorting of the film is included in the analysis. The approximate equations are expressed in terms of the known fundamental material constants and no measurement of model parameters is required. Bulk wave scattering is not considered. The approximate equations, which admit of a transmission line representation, are applied in the analysis of surface wave reflection by both uniformly and nonuniformly spaced arrays of reflecting strips plated on various substrates. Among other things, the calculated reflection curves indicate a slight asymmetry for heavier film materials on account of the dispersion caused by the strips. Although this effect has been observed experimentally, it has not been reproduced by other analytical models. (Author)

Enhanced Trapped Energy Mode Array Transducer Using Thickness Overtones

A trapped energy mode of thickness-extensional (TE) vibrations is shown to exist at certain overtones in various materials. Utilization of such a mode, which results in improved isolation between elements in a transducer array, is demonstrated. Knowledge of the dispersion curves (frequency vs. lateral wave number) for unelectroded and fully electroded plates, along with an understanding of the manner in which they determine trapped energy modes, is essential in order to choose a suitable overtone: one which, first, will exhibit TE energy trapping, and second, will allow for large imaginary wave numbers in the unelectroded region of the plate. Dispersion curves for PZT-7A and Z-cut lithium tantalate are examined and found to possess suitable overtones. Improved trapped energy mode spatial confinement is confirmed.

A Hybrid Trapped Energy Mode Transducer Array

Spatial confinement of the mode shape for thickness-extensional (TE) vibrations of the trapped energy mode is influenced by the form of the dispersion curve for the material in between the electroded elements. In previous treatments the authors have studied trapping in plates of uniform thickness. In this paper the authors examine hybrid devices employing a small amount of plate notching. Provided these notches are not too deep their effect can enhance the trapping resulting from electrode shorting and mass loading. Special problems arise, however, with deep notches due to lateral vibrations within the elements themselves.