Trapped Energy Modes Research Articles

Use of Trapped-Energy Mode of Backward-Wave-Type Thickness Vibration for Liquid-Level Sensing

The authors have presented a new technique that employs a piezoelectric thickness vibrator operating in a trapped-energy mode for detecting a small-scale variation in liquid level. In this study, the feasibility of applying backward-wave-type energy trapping to liquid level sensing is investigated. It has been found that backward-wave-type energy trapping shows a sensing property slightly different from those obtained using conventional trapped-energy modes. Gradual variations in resonance characteristics with liquid level have been observed for backward-wave-type energy trapping when the liquid surface is in the surrounding electroded region.

Vibration Analysis of Thickness-Shear-Mode Trapped-Energy Resonators Excited by Parallel Electric Field

The energy trapping of thickness-shear vibrations that are excited by parallel electric field in a partially polarized piezoelectric-ceramic plate is analyzed by the finite element method (FEM), and characteristics of the thickness-shear-mode trapped-energy resonators for vibratory gyroscopes are theoretically revealed. The calculated results obtained by FEM agree well with the measured results with respect to the displacement and vibration energy distributions. It is shown from the results that the vibrational energy of trapped-energy modes is almost confined to the central region of a partially polarized piezoelectric-ceramic plate and the displacement distribution of the mode can be varied by adjusting electrode dimensions.

A piezoelectric double-mode filter using the complex-branch-type energy trapping

A piezoelectric double-mode filter using the complex-branch-type energy trapping, that is caused by contributions from the complex branches of dispersion curves is proposed, and its theoretical and experimental results are presented for the width-extensional modes in a thin piezoelectric ceramic strip. Characteristics of the symmetric and antisymmetric trapped-energy modes in this filter have some interesting features different from those of the usual trapped-energy modes, such as noticeable undulations in the resonant frequency spectrum and sinusoidally oscillating decay of displacement in the unelectroded region. Based on these results, double-mode filters with a center frequency of about 1 MHz and a 3-dB fractional bandwidth of 3% are constructed. The filters of this type are useful in the medium frequency range below several megahertz because of the miniature size and the ease of supporting.

An analysis of thickness-extensional trapped energy mode polarized ceramic transducers

An analysis of PZT-7A plates driven into thickness-extensional trapped energy vibrations by the application of a voltage to strip electrodes and radiating into an adjacent fluid is performed. All previous treatments of thickness-extensional trapped energy modes in piezoelectric plates have ignored the radiation into the surrounding medium and, hence, have been for resonators rather than transducers. The solution consists of a sum of a driven thickness solution and the pertinent plate eigensolutions for shorted electrodes in the electroded region and for zero surface charge in the unelectroded region, including in each instance the radiation into the adjacent fluid. Since the sum of the solutions in each region satisfies the differential equations and boundary conditions on the major surfaces including the fluid loading exactly, the substitution into the appropriate variational principle of linear piezoelectricity yields integral conditions across the thickness of the plate at the edge of the electrodes. The resulting system of inhomogeneous linear algebraic equations yields the response from very low frequency to slightly above the first thickness-extensional frequency of the unelectroded plate.

Design of bandpass ceramic filter with double-mode resonator

The design of a bandpass ceramic filter using a double-mode resonator vibrating in trapped energy modes is presented. The filter characteristics are related to the dimensions of the piezoelectric ceramic plate and electrode, the spacing between two electrode pairs, and the mass loading effect of the electrode. On the basis of a systematic investigation of theories and experiments, the optimal configuration of the device is determined. The designed ceramic filter exhibits a center frequency of 10.7 MHz, a 3-dB bandwidth of about 150-350 kHz, insertion loss close to 0 dB, spurious response larger than 35 dB, and temperature stability within 30 p.p.m./ degrees C.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An analysis of thickness-extensional trapped energy resonant device structures with rectangular electrodes in the piezoelectric thin film on silicon configuration

It has recently been shown that highly uniform thin layers can be etched in a small well-defined region of a silicon wafer and that good quality thin piezoelectric films such as zinc-oxide can be deposited along with the electrodes to form high frequency trapped energy resonant device structures. The accompanying analytical work has been for pure thickness vibrations only. In this work an analysis of essentially thickness-extensional trapped energy modes in the thin piezoelectric film on silicon composite structure is performed. It is shown that for small wavenumbers along the plate the dispersion equation is isotropic in the plane of the plate even though the silicon is severely anisotropic in that plane. From the resulting dispersion relation an asymptotic differential equation describing the mode shape along the surface of the composite plate vibrating in the vicinity of a thickness-extensional resonance is obtained along with the associated edge conditions. Since the mode is essentially thickness-extensional, trapping does not usually occur in the electroded regions for the fundamental mode of the flat composite plate. However, by appropriately thickening the silicon outside the electroded regions trapping in the electroded regions can be made to occur for the fundamental mode. Furthermore, in the case of zinc-oxide on silicon, trapping in the electroded regions can be made to occur for the fundamental mode of a flat plate simply by making the zinc-oxide sufficiently thicker than the etched silicon. The aforementioned asymptotic differential equation and edge conditions are applied in the analyses of the steady-state vibrations of trapped energy resonators and acoustically coupled two-pole resonator filters, both with rectangular electrodes. Lumped parameter representations of the admittance in the case of the single-pole device and admittance matrix in the case of the two-pole device, which are valid in the vicinity of resonances, are obtained. The analyses hold for the first few thickness-extensional modes and their accompanying lateral overtones.

A New Type of Energy Trapping Caused by Contributions from the Complex Branches of Dispersion Curves

I- a - U. Abstract The energy trapping of width-extensional vibra- tions in a thin piezoelectric ceramic strip is studied, and it is shown that a new-type of energy trapping by contributions from complex branches oc- curs in the vicinity of the stationary points on dispersion curves. The trapped-energy modes have some interesting c haracteristics, such as: 1) The resonant frequency curves as a function of the electrode-length/strip-width ratio exhibit notice- able undulations. 2) The decay of displacements with distance from the electrode edge is accompanied by sinusoidal oscillations. 3) The ratio of capaci- tances becomes a minimum at an electrode length where the resonant frequency curve begins to undu- late, and increases abruptly as the electrode length grows larger. The existence of this type of energy trapping is also verified experimentally for thickness-extens ional vibrations in a piezoelectric ceramic plate.

Trapped-energy flexural mode filter

An electromechanical filter using trapped-energy flexural modes in a rectangular plate is proposed. The filter is amenable to fabrication by planar techniques and it can operate in the l.f. range, including the voice band. Bandwidth is easily controllable. A considerable gain in size can be obtained with respect to flexural bar filters.

Monolithic mosaic transducer utilizing trapped energy modes

A transducer array consisting of a large number of separated sets of electrodes plated on a single piezoelectric plate of uniform thickness is described. Each set of electrodes is made to act essentially independently by placing them sufficiently far apart and employing an essentially trapped energy mode. Experimental results obtained with a linear array on PZT-7A show that the isolation is very good over a bandwidth of about 14%, close to the calculated bandwidth of 12.8%.

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.

Exact equations for analysing thickness-twist trapped-energy modes in monolithic filters

Thickness-twist vibrations with energy trapping in a monolithic filter consisting of an infinite piezoceramic plate withN infinitesimally thin electrodes evaporated on to each face are analysed. By applying the Fourier transform technique, the linear three-dimensional equations for a piezoceramic plate are reduced to integral equations for the charge distributions on the electrodes. An approach for solving these equations and numerical results for a dual are given.

Trapped-Energy Modes in Quartz Filter Crystals

The behavior of thickness/shear-mode quartz resonators is explained both mathematically and experimentally in terms of lateral standing-wave trapped-energy modes. A cutoff phenomenon, similar to that occurring in optical total internal reflection, results in energy trapping or the restriction of vibratory energy almost exclusively to the electroded region of a resonator, with an energy distribution decreasing exponentially with distance from the electrode edge. Consideration of boundary conditions at the electrode edges of an idealized two-dimensional model yields an expression for the eigenfrequencies of symmetric inharmonic overtone modes (lateral standing waves) that can exist in the electroded region of fundamental- and harmonic-mode resonators. Design formulas for the suppression of these unwanted modes are included. They show that electrode thickness and lateral dimensions can be traded off against one another to obtain a wide range of motional parameters. Previously, unwanted responses were eliminated by restricting the electrode diameter to empirically established values. The present understanding has led to a reduction in resonant resistance and an increase in motional capacitance by at least a factor of four with hf and vhf fundamental- and harmonic-mode filter crystals. Experimental data that verify results predicted by energy-trapping theory are given, and application to design of single- and multi-electrode resonators is considered. Specific examples in the 10- to 180-MHz frequency range are given.

Multiple-Mode Piezoelectric Resonators

As a vibrator of continuum medium, a piezoelectric resonator has an infinite number of eigenmodes. Most resonators, however, have utilized one and only one mode of vibration. Novel quartz and ceramic resonators utilizing more than one mode have been developed. Such a resonator is useful as a filter element, because characteristics of a full lattice network with resonators in each arm can be realized by a single resonator. The frequency separation between modes to be utilized should be within the design limit of filters owing to the capacitance ratio of the resonator. Their motional inductances should be approximately equal in order to realize symmetrical bandpass characteristics. Their temperature coefficients should be approximately equal in order to realize a good stability. These criteria can be met by the following modes, which practically cover all the frequency range of interest. For the use at a high frequency, symmetric and antisymmetric trapped energy modes of thickness vibration in a thin plate are suitable. Quasidegenerative modes of longitudinal and flexural vibrations in a plate are useful at a medium frequency, while quasidegenerative modes of two mutually perpendicular flexural vibrations in a rod are useful at a low frequency.