Shigeo Kanna

IDT geometry and crystal cut effects on the frequency-temperature curves of a SAW periodic structure of quartz

Piezoelectric Lagrangian equations for the frequency-temperature behavior of quartz is presented. A finite element study of these Lagrangian equations is performed for a two-dimensional periodic SAW structure of quartz. Plane strain assumptions are used to enable a two-dimensional analysis of straight crested acoustic waves in the structure. Adaptive finite element meshes are employed to reduce the size of the finite element problem. The frequency-temperature characteristics of the two fundamental SAW modes are compared and contrasted. Numerical results are compared with experimental data for the ST- and K-cut of quartz. The finite element results for the turnover temperature and the 2nd temperature coefficient of the f-t curve as a function of the electrode height are found to compare well with the ST-cut experimental data. Similar numerical results for the change in frequency-temperature characteristics of the K-cut as a function of crystal cut angles phi is also found to be compare well with the experimental data. The experimental data are found to follow the lower bandgap frequency SAW1.

Temperature Stability of Surface Acoustic Wave Resonators on In-Plane Rotated 33° Y-Cut Quartz

ST-cut quartz has been widely used in surface acoustic wave (SAW) devices due to its good temperature stability. However, ST-cut SAW devices are still not as temperature stable as AT-cut quartz. Hence new SAW resonators with better temperature stability are needed. We present surface acoustic wave resonators on the in-plane rotated 33° Y-cut quartz with improved temperature stability. We calculated the frequency temperature characteristics of Rayleigh waves using the finite element method under the condition of Euler angle (0, 123, 39-44). The second-order temperature coefficients of less than -1.5×10-8/°C2 were achieved by calculations and experiments. Compared with the second-order temperature coefficients of ST-cut quartz (-3.4×10-8/°C2), these values are more than 50% smaller. The fabricated SAW resonators have good crystal impedance (resonance impedance) and Q-value.

A set of hierarchical finite elements for quartz plate resonators

Formulation of a finite strip element for high frequency quartz resonator plate vibrations is presented. The finite strip formulation is equivalent to the nth order Mindlin plate theory depending on the order of the strip in the thickness direction. Consequently the finite strip element could be used to model any high frequency resonator plate vibrations by choosing the appropriate nth order plate theory. This choice could be incorporated into the finite strip program so that the user may model higher overtones of thickness shear vibrations without regeneration of finite element meshes. This forms the basis of the set of hierarchical finite elements for high frequency quartz plate vibrations. The mass effect of electrodes is included in the formulation. Numerical results for the first and third order Mindlin plate theory are obtained and compared with Kogas experimental results. Good comparisons are obtained.

Finite element analysis of the substrate thickness effect on travelling leaky surface acoustic waves

A FE method is developed for analysis of travelling LSAWs. Because of the use of the general eigenvalue problem with Hermitian coefficient matrices needs to be solved. A publicly available eigenvalue solver ARPACK, together with the shift and invert spectral transformation, is used to solve the problem efficiently. The effect of the finite thickness of substrates on the dispersion behaviour of LSAWs is simulated.

Frequency-temperature effects in three-dimensional surface acoustic wave periodic structures

Numerical results on the resonant frequencies and their frequency-temperature behavior in a three-dimensional surface acoustic wave (SAW) periodic structure are presented. These results are compared with those of the quartz SAW resonator. The 3D FEM models of SAW periodic structures are useful in the analyses of IDT geometry and crystal cuts of SAW resonators which have power flows transverse to the SAW phase velocity. They are also useful for analyzing transversely coupled SAW resonators. Piezoelectric, Lagrangian equations for the frequency-temperature behavior of quartz are presented. Three-dimensional finite element results for a half wavelength SAW periodic structure are compared with measured data from a SAW resonator. The frequency characteristics of the fundamental SAW mode and its transverse overtones as a function of the electrode length W in the transverse direction are studied. Generally good results are obtained with the 3D FEM models when compared with measured values. Their frequency-temperature behavior are also studied and are reasonably well predicted by the 3D SAW periodic structure. The 2D FEM models are shown to yield results consistent with the 3D FEM models.

Temperature stability of surface acoustic wave resonators on the in-plane rotated 33/spl deg/Y-cut quartz

We present surface acoustic wave resonators on the in-plane rotated 33/spl deg/Y-cut quartz with improved temperature stability. We calculate the frequency temperature characteristics of Rayleigh waves using finite element method under the condition of Euler angle (0, 123, 39-44). We confirmed the accuracy of calculated temperature coefficients by experiments. We also measured the resonance characteristics of prototype SAW resonators.

Effects of periodically missing fingers and periodically shifted fingers on SAW propagation in quartz resonators

A finite element study of a 3-electrode finger periodic SAW structure of ST-cut quartz was studied. This multi-period analysis allows more interaction of the bulk acoustic wave modes with the surface acoustic wave modes. Plane strain assumptions were used to enable a two-dimensional analysis of straight crested acoustic waves in the structure. Adaptive finite element meshes were employed to reduce the size of the finite element problem. The results of this study may be useful for a full-scale finite element modeling of SAW resonators and filters. The effects of periodically missing or shifted fingers may be useful for generating/controlling leaky SAW. The physical difference between the modes shapes of the two fundamental SAW modes were compared and contrasted. The numerical results of frequency spectrum versus electrode geometry and electrode height, respectively, confirms empirical experience with these SAW modes. Possible couplings of the SAW modes with the BAW modes are shown. These couplings lead to SAW modes with some BAW mode characteristics. The couplings may be useful for improving frequency temperature behavior or generation of leaky SAW modes. On the other hand, they may lead to poor frequency temperature behavior or low Q devices.

High-stability SAW oscillators with cubic frequency temperature curve and excellent aging characteristics

We describe the realization of oscillators combined with quartzs innate excellent long-term stability of frequency and frequency temperature characteristics by optimization of SAW oscillators design conditions using quartz crystal substrates in application on groove structure. As a result, we could realize SAW oscillator with cubic frequency temperature curve, inflection point temperature of 28°C at is close to a room temperature and extremely small frequency variation of 11ppm in wide temperature range between −40°Cand +85°C. Further, we could get excellent long-term stability lower than 3ppm of frequency variation in 2000 hours high temperature environment test with 85°C. SAW resonator that is making up oscillator has gained good resonance characteristics such as Q=14,700 and CI=12Ω with 400MHz. We realized high-performance SAW oscillator on practical use with characteristics such as low jitter and low phase noise, in addition excelling in frequency temperature characteristics and frequency long-term stability by oscillating fundamental wave in high-frequency range with 100MHz to 700MHz.

A New Thickness Shear Mode Vibratory Gyroscope with Acoustic Gaps Between Pairs of Electrodes

A new thickness shear mode vibratory gyroscope which employed the thickness shear mode at both the driving and sensing electrodes was presented. The thickness shear mode shape changed slightly with the Coriolis force, and this change could be detected by the sensing electrode separated from the driving electrode by an acoustic gap. Vibrating tines normal to the plate surface were placed along the acoustic gap. These tines were tuned to resonate with the harmonic Coriolis force caused by the angular rotation of the plate about its plate thickness axis. The change in vibration of the tines with the Coriolis force caused a change in charge or voltage at the sensing electrodes. Since the AT-cut resonators are known to have good f-T curves and long term aging, the new AT-cut gyroscope would have the advantages of a highly stable quartz AT-cut resonator.

P2E-7 A Novel AT-Cut Gyroscope, Its Analysis and Design

A novel AT-cut quartz vibratory gyroscope with a sensitivity to angular velocity of 1.3 mV/deg/s was presented. The gyroscope employed the thickness shear mode as the driving mode and the flexure mode of tines as the sensing mode. The tines are placed normally on the AT-cut quartz plate surface. These tines were tuned to resonate with the harmonic Coriolis body force caused by the angular rotation of the plate about its plate thickness axis. The flexure mode of the tines changed with the angular velocity about the thickness axis of the plate. The change in the flexure mode of the tines could be detected by the sensing electrode separated from the driving electrode by an acoustic gap. Since the AT-cut resonators are known to have good f-T curves and long term aging, the new AT-cut gyroscope would have the advantages of a highly stable quartz AT-cut resonator.