Mitsuo Nakazawa

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>>

Stress-Compensated Quartz Resonators Having Ultra-Linear Frequency-Temperature Responses

A new family of stress compensated quartz resonators having cuts exhibiting an ultra-linear frequency vs. temperature characteristic. This family of resonators has an orientation defined with respect to the crystallographic axes by polar angles φ and θ, which angles lie on the locus where the second-order temperature coefficient of frequency is zero between the angles φ=20°±2° and θ=20°±5°, and in close proximity to the locus of zero coefficient of stress. In one preferred embodiment, the resonator comprises a plate whose angles of cut φ and θ are both substantially equal to 20°. In a second preferred embodiment an exact stress compensation is provided where φ is substantially equal to 20.8° and θ is substantially equal to 23.2°, and orientation where the locus of the zero coefficient of stress intersects the locus of the zero of the second-order temperature coefficient.

A theoretical study of quartz crystal resonators for chemical sensors, vibrating in C mode

The cut angles and their governing equation for quartz crystal resonators vibrating in C mode and having reliable frequency-temperature characteristics for high temperatures such as 200 degrees C are derived from the improved analytical theory with the piezoelectric effect. Lateral field excitation is discussed. It is concluded that the realization of stress-compensated quartz resonators with reliable frequency-temperature characteristics in the high temperature region can be predicted.<<ETX>>

New Quartz Resonators with Precision Frequency Linearity Over a Wide Temperature Range

Abstract : Quartz crystal resonators have been employed in a number of thermometer applications. We have recently discovered two new thermometric cuts; one exhibits a high degree of linearity over a wide temperature range; the other is located in the vicinity of the stress compensated locus. These doubly rotated cuts were found by calculations based on the thickness - vibration theory for ideal plates. This paper presents theoretical and experimental results concerning the frequency-temperature characteristics of these quartz resonators.

Two-dimensional analysis of thickness-shear and flexural vibrations in rectangular AT-cut quartz plates using a one-dimensional finite element method

The two-dimensional coupled vibrations of thickness-shear and flexure in miniature rectangular AT-cut quartz resonators are theoretically studied. The analysis is based on Mindlins plate equations. To calculate the mode chart, a one-dimensional finite element technique is used. It is shown that the theoretical curves match the experimental data well. It is found that most spurious resonances in strip type miniature resonators belong to the two-dimensional flexural family. The numerical method presented is well suited to determine the points at which these flexural modes will coincide with the fundamental main thickness-shear mode in the miniature resonators elongated along the X axis.<<ETX>>

Reliable quadric relationship of frequency turn-over temperature characteristics vs. electrode film thicknesses for quartz crystal tuning forks

A reliable quadric formula for frequency turn-over temperature vs. electrode film thickness in the quartz crystal tuning fork is proposed and the coefficients are experimentally determined by the least squares method. Reliable experiments with respect to frequency temperature characteristics for quartz crystal tuning forks are carried out. In particular, a new analysis for the Youngs modulus of the electrode film is also described, and it is expected to be valuable to film technology.

Analysis of film thickness dependence on electrical equivalent model for AT-cut resonators

This paper describes the theoretical analysis and experiment regarding film thickness dependence on an electrical equivalent model for AT-Cut resonators. Resonant frequencies were 10 MHz for fundamental waves vibrating in thickness shear C-modes. Measurements for electrical equivalent circuit constant characteristics versus film thickness were conducted by using a network analyzer. An equivalent model for film thickness plated on AT-Cut resonators in the neighborhood of resonance frequency was proposed and analyzed. By using the experimental frequency temperature characteristics, a quadric relationship between frequency turn-over temperatures and film thickness was also obtained. It was found that these theoretical and experimental results could be very useful in designing AT-Cut resonators, among other things.

Third overtone frequency turnover temperature-orientation characteristics for quartz plate resonator in the vicinity of AT-cut

This paper describes the third overtone frequency turnover temperature vs. orientation characteristics for quartz crystal plate resonator in the vicinity of AT-cut in the temperature range from -196 to 250/spl deg/C, and these characteristics are discussed in comparison with the frequency turnover temperature characteristics for the fundamental and fifth overtone modes. From the presented quadric relationships we can demonstrate the useful piezoelectric cuts of quartz for the resonators and sensors at the elevated temperature region. The quadric theory proposed in this paper is a simple and useful one and the coefficients of quadric can be experimentally determined by the least squares method. From these coefficients we can infer the frequency temperature coefficients.

An analysts of the longitudinal mode quartz tactile sensor based on the Mason equivalent circuit

A tactile sensor was developed by use of a longitudinal mode quartz crystal resonator. Its behavior in contact with viscoelastic mediums was analyzed based on the Mason equivalent circuit. The problem of acoustic impedance of an oscillating sphere in semi-infinite viscoelastic media has already been analyzed. On the assumption that the top shape of the quartz resonator is spherical, the Mason equivalent circuit was applied to this acoustic impedance. Finally, theoretical equations were obtained for frequency and impedance changes. The theoretical equation for frequency change includes both density and shear modulus of silicone rubbers as parameters. Shifts in frequency were correlated with measurements from both viscoelastic and rubber testers. The frequency changes were found to correspond to the hardness or softness of the rubbers. It has been confirmed that the theoretical equation for frequency change is in good agreement with experimental results.

Reliable quadratic for frequency-turnover temperature vs orientation of rotated Y-cut quartz plate resonator oscillating in c-mode

This paper describes the reliable quadratic for frequency-turnover temperature vs orientation of c-mode in the temperature range -196-300/spl deg/C. From the relation we can show the useful piezoelectric cuts of quartz for the resonator and sensor at the elevated temperature region. In particular, the experiments are carried out in the vicinity of AT-cut.<<ETX>>