Hitoshi Sekimoto

Mode Shape Measurement of Piezoelectric Resonators Using Image Processing Technique.

An image processing technique for measuring the mode shapes of piezoelectric resonators is described. Laser speckle interference, a periodic resonator excitation and charge coupled device (CCD) image captures are effectively combined in this method. The experimental results for three kinds of AT-cut quartz resonators demonstrate the applicability of the proposed method.

Visualization of Mode Patterns of Piezoelectric Resonators Using Correlation Filter

The application of a two-dimensional correlation filter to the mode shape visualization of piezoelectric devices is described. The filter extracts the vibrational patterns from two laser-speckle images of the driven and resting phases. The experimental results demonstrate clearly the feasibility of the proposed technique.

Three-Dimensional Analysis of Spurious Vibrations of Rectangular AT-cut Quartz Plates

We have developed a technique for the three-dimensional (3-D) analysis of all the spurious vibrations of rectangular AT-cut quartz plates. The 3-D displacements are described with a linear combination of modes guided along the X crystal axis of an AT-cut quartz strip. We accurately calculate each guided mode by applying the one-dimensional finite element method to the two-dimensional strip waveguide problem. To uniquely determine the amplitudes of guided modes in the 3-D solutions we employ the variational expression for the stress-free conditions on the X-length edges. The present technique makes it possible to perform 3-D analysis of spurious vibrations within a reasonable computational time. Frequency spectra for rectangular AT-cut quartz plates are computed as a numerical example and are compared with the numerical results obtained using an extended version of the previous method and with Kogas experimental data. Vibrational patterns of spurious modes are shown, and a convergence study is carried out.

Forced vibrations of thickness-flexure, face-shear and face-flexure in rectangular AT-cut quartz plates

The two-dimensional spurious vibrations of thickness-flexure, face-shear and face-flexure in a rectangular AT-cut quartz plate are theoretically studied. The input capacitance characteristics and the equivalent inductance are calculated, and compared with the experimental data.<<ETX>>

Nonscanning measurements for determining in-plane mode shapes in piezoelectric devices with polished surfaces

A nonmechanical scanning method has been developed for the visualization of the in-plane mode shapes of piezoelectric devices with polished surfaces. By taking into account the reflection versus laser-wavelength characteristics of the material of the electrodes, the in-plane motion can be measured even if the surface of the measurement plane is polished like a mirror. This method is based on laser speckle interference and two-dimensional correlation filtering that effectively enhance the mode-shape visualization for bulk and surface acoustic wave devices. Although this method cannot directly measure absolute displacement, the simple measurement system and high speed measurement more than offset this disadvantage. The experimental results for fundamental thickness-shear and nearby inharmonic modes in a bimesa-shaped rectangular AT-cut quartz resonator have been presented. The results of the experiments and the analyses obtained by the three-dimensional finite element analyses correlate well and show the advantages and validity of the proposed technique.

Phase noise measurements in dual-mode SC-cut crystal oscillators

This paper describes the phase-noise characteristics and the analysis model of an SC-cut dual-mode oscillator. The C mode phase-noise sideband levels of -124 dBc at 10 Hz and -154 dBc at 10 kHz have been demonstrated using a dual-mode oscillator that simultaneously excited the C and B mode of a 10-MHz, third overtone, SC-cut crystal resonator. Based on Leesons model, a phase-noise analysis model for dual-mode oscillators has been proposed also. Actual phase-noise levels of the C mode in dual-mode oscillation corresponded well to results calculated from the proposed model.

Effect of Stepped Bi-Mesa Structures on Spurious Vibrations of AT-Cut Quartz Plates

In this paper, the effect of stepped bi-mesa structures on the coupling of vibrations in AT-cut quartz plates is analyzed theoretically. Since strong coupling of thickness-flexure modes are of interest, straight-crested waves propagating along the X axis are treated. Calculated results for the stepped bi-mesa structure show that the coupling strength as estimated from its mode chart decreases to about one-third that of a bi-mesa resonator. The characteristics of bi-mesa structures appear to be amenable to further improvement by the use of a stepped bi-mesa structure.

Method based on laser speckle interferometry for measuring absolute in-plane vibrational distribution of piezoelectric resonators

A full-field imaging method has been developed for rapidly measuring the absolute in-plane vibrational distribution of piezoelectric resonators. This method is based on the synchronized laser speckle method. To confirm the measurement accuracy, a quartz plate with a small mirror attached to a lateral surface is used. The plate is excited by an external ceramic vibrator, and the absolute vibrational displacement is measured with a Michelson interferometer with optical components, including the small mirror. The amplitude of the in-plane displacement is obtained from this data and the statistical processing of the captured speckle images and is compared with the displacement obtained with the Michelson interferometer. Experiments showed good agreement between the two displacements, validating the proposed method.

Frequency-Temperature Behavior of Stepped Bi-Mesa-Shaped AT-Cut Quartz Resonators

To confirm the effect of stepped bi-mesa structures on the decoupling of thickness-shear and thickness-flexure modes, we fabricated stepped bi-mesa resonators and measured their frequency-temperature behavior. The results showed that stepped bi-mesa resonators have better temperature characteristics than bi-mesa resonators. These results confirmed that the stepped bi-mesa structure can reduce the influence of mesa edges and improve the characteristics of bi-mesa resonators.

Analysis of 3-D vibrations of rectangular AT-cut quartz plates with a bi-mesa structure

A method to analyze 3-D vibrations of rectangular AT-cut quartz, bi-mesa-shaped plates is developed. The method is based on a classical approach. As in 2-D analysis, the half structure of a plate is separated into a thick bi-mesa and a thin-side portion, and the displacement field of each region is represented by a linear combination of guided waves. In the 3-D analysis, we apply the 2-D finite element method (FEM) to obtain the waves guided by two pairs of parallel surfaces. The orthogonal property of guided modes is incorporated to approximately fulfil the continuity conditions at the interface between the thick and thin portions. The stress-free conditions on the plate edges are satisfied by employing the method of weighted residuals (MWR). The computational advantage of this method is that it can greatly reduce the matrix size compared with the 3-D FEM. As a numerical example, the frequency spectra are calculated for X-elongated plates of bi-mesa shape, and the strong energy-trapping effect on the fundamental thickness-shear (TS) resonance is verified.