S. Goka

A dual mode oscillator based on narrow-band crystal oscillators with resonator filters

A dual mode crystal oscillator using two narrow-band transistor Colpitts circuits has been developed. This oscillator excites arbitrary two-modes in a common resonator even if the modes are close to each other. The practical circuit structure and analysis of the proposed oscillator, and the experimental results are described.

Fundamental study on multi-mode quartz crystal gas sensors

A quartz crystal microbalance (QCM) gas sensor using multiple resonant modes is studied. In this QCM sensor the absorbent is not fully deposited onto the plate surface as in the general QCM gas sensors. The absorbent is coated on the plate surface where the external-stress sensitivity difference between the two modes used is greatest. The external-stress sensitivity is measured by a semiconductor pulsed-laser system. To perform the fundamental experiments, that is, determining effectiveness of using external-stress sensitivity measuring in the design and fabrication of multi-mode QCM devices, a polyimide thin film is used as the adsorbent of carbon dioxide, and an 11 MHz AT-cut quartz resonator is used.

Decoupling effect of multi-stepped bi-mesa AT-cut quartz resonators

In this paper, we calculated the mode-coupling characteristics of multi-stepped bi-mesa resonators and compared them with beveled resonators. Calculation results showed that increasing the number of mesa steps reduced coupling between the thickness-shear and thickness-flexure modes. These results indicate that the multi-stepped bi-mesa resonator has a good mode-decoupling effect, and its performance characteristics approach those of the beveled resonator.

Frequency temperature behavior of bi-mesa shaped at cut quartz resonators

To confirm the effect of bi-mesa structures on the decoupling of thickness-shear (TS) and thickness-flexure (TF) modes, we measured the frequency-temperature behavior of bi-mesa shaped AT cut quartz resonators. The TF mode couples with the TS mode because the same displacement component is contained within the TS mode. This strong coupling cannot be eliminated as long as the plates have boundaries. Therefore, the temperature characteristics of the fundamental TS mode are clearly affected by the TF components. Bi-mesa structures have an energy trapping effect large enough to spatially separate the vibrational modes, so bi-mesa structures can decrease the effect of TF components. Therefore, the frequency-temperature behavior of a bi-mesa resonator is close to that of an infinite plate, which has no TF component effect. The bi-mesa resonators used in this study were fabricated using a wet etching process, and the fundamental TS frequency was 8.3 MHz. The frequency-temperature behavior was measured using a network analyzer. Results showed that bi-mesa resonators have temperature characteristics four times better than those of flat resonators, ranging from -20 to 85/spl deg/C. These results confirm the energy trapping effect of bi-mesa structures and their effectiveness in separating vibrational modes.

Three-dimensional analysis for rectangular AT-cut quartz plates with bi-mesa structure

This paper describes a method to analyze 3-D vibrations of rectangular AT-cut quartz plates with bi-mesa structure. The method is based on a classical approach. As in the 2-D analysis of the previous paper, the displacement field for each of thick and thin portions of a plate 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. We also incorporate a new expression for orthogonality relation of guided waves into the continuity condition of displacement and stress over part of a junction cross section. A computational advantage of this method is that it can greatly reduce matrix size compared with the 3-D FEM. As an example of calculation, the frequency spectrum for an X elongated plate of bi-mesa shape is presented along with one for a flat plate.

Frequency temperature characteristics of stepped bi-mesa-shaped AT-cut quartz resonators

To confirm the decoupling effect of stepped bi-mesa structures, 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 using stepped bi-mesa structures reduces the influence of mesa edges and improves the characteristics of bi-mesa resonators.

Frequency stability and phase noise characteristics of digital OCXOs using dual-mode excitation

A high-stability oven-controlled crystal oscillator (OCXO) (frequency stability; +/- 10 ppb from -30 to 70/spl deg/C) has been developed using a dual-mode SC-cut quartz crystal oscillator. The oscillators frequency stability includes a frequency-temperature hysteresis over the range of operational temperatures, and repeatability of frequencies after power is switched off then back on. In this OCXO a conventional oven-control system is used for coarse compensation and a digital correction system is used for fine compensation. The combination of these forms of compensation greatly improves the C-mode frequency stability and expands the operational temperature range with a very small additional requirement for electric power. Experimental results indicate that the frequency-temperature stability of the OCXO was 20 times better, and its operational temperature range 30 degrees wider, than the conventional OCXOs. We also measured the phase noise characteristics of this OCXO. The experimental results indicate that very low phase-noise (-157 dBc/Hz @ 10 kHz) can be obtained at the floor region. This noise level corresponds well with a calculation based on our dual-mode oscillator noise estimation.

Analysis of Frequency-Temperature Behavior of X-Cut LiTaO3 Strip Resonators.

We numerically study the frequency-temperature (f-T) behavior of a partially plated X-cut LiTaO 3 strip resonator operating in the fundamental thickness-shear fast mode. The plate orientation is designated by (XZt)ψ basedon the IEEE standard notation. The f-T curves are calculated as functions of the electrode length and the plate-orientation angle ψ. The results confirm that the turnover temperature of the f-T curve decreases with increasing electrode length. Furthermore, we find that the turnover temperature changes depending on the coupling between thickness shear and thickness width flexure through c 5 6 , and that it therefore depends on ψ An angle ψ = 40 that yields a turnover temperature in the range of 33-6.5°C is optimal for the material constants of [J. Appl. Phys. 42 (1971) 2219] because c 5 6 is zero. We also show that the external loading of both series and parallel capacitances can make the adjustment of turnover temperature of high electro-mechanical coupling resonators very simple.

Drive-level dependence of long-term aging in quartz resonators

To analyze the factors of frequency aging in ultra-stable quartz crystal oscillators, a novel system that continuously measures the stability in both resonant frequencies of the resonators and oscillation frequencies has been proposed. Experimental results show that the long-term drift of resonant frequency depends mainly on the amplitude of the crystal driving current and that the aging of the circuit partly affects the aging of oscillation frequency.

Three-dimensional analysis of forced piezoelectric vibrations of rectangular AT-cut quartz plates and X-cut LiTaO/sub 3/ plates

We have developed a method for analyzing 3D forced vibrations of rectangular piezoelectric plates. Since it utilizes only a 2D FEM, the matrix size required is much smaller than that required when using a 3D FEM. The 2D FEM was used to obtain a 2D forced solution satisfying the driving requirement and also to obtain a 3D free solution. The calculated capacitance characteristics of a rectangular AT-cut quartz plate agreed very well with measured data. We also showed a numerical example for a 3/spl deg/ rotated X-cut LiTaO/sub 3/ plate.