Arthur Ballato

The Force-Frequency Effect in Doubly Rotated Quartz Resonators

Precision frequency control requirements for digital communication and position location systems currently undergoing development make it imperative that crystal resonator performance be improved in a number of aspects. Accordingly, the potential of doubly rotated quartz cuts has begun to be explored (EerNisse, 1975, 1976; Ballato and Iafrate, 1976). For cuts on the upper zero temperature coefficient locus in general (theta approximately equal to +34/sup 0/), and in the neighborhood of the SC-cut in particular (phi approximately equal to 21.9/sup 0/, theta approximately equal to +33.9/sup 0/), a variety of effects having their bases in nonlinear elasticity have been shown, or are predicted, to be reduced below the corresponding AT-cut values. In addition, the static frequency-temperature behavior shows some improvement. The force-frequency effect which has thus far not been investigated in any detail for doubly rotated quartz plate vibrators is studied. This effect relates the initial stress produced by the mounting supports to resonance frequency changes; it contributes to long-term aging and is also related to the frequency excursions produced by accelerations encountered in shock and vibration environments. Results are reported.

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.

Measurements of acceleration-induced phase noise in surface acoustic wave devices

Measurements of the acceleration sensitivities of a group of surface acoustic wave (SAW) resonators developed for a low-noise radar application are presented. The SAW resonator designs were systematically varied in order to obtain the best possible phase noise in a quiescent environment. A block diagram of the test system used is shown. Sample data obtained using the measurement system are shown. The maximum and minimum values obtained at each acceleration frequency tested are shown as a function of the test frequency. The relationships between the design changes and the vibration induced phase noise are discussed. It is suggested that careful control of transducer and busbar metallization may be used to optimize for acceleration induced phase noise without seriously compromising quiescent phase noise.<<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.

Electronic desensitization of resonators to accelerations

A compensation technique to electronically reduce the acceleration sensitivity, gamma, in crystal resonators is presented. Tests performed on both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators are described. For devices where the mode shape would not be expected to change very much with frequency adjustment, e.g. SAW delay lines, changes in the sensitivity coefficient are minimal. Some representative examples of the SAW devices tested are shown. A portion of the change in the gamma coefficient is shown to be a structure resonance, but the mode shape change is large. A twenty-fold improvement in gamma with electronic tuning is shown. It is possible to design resonators of each type so that the mode shape is more sensitive to frequency offsets to maximize the effect.<<ETX>>

A comparison of predicted and measured properties of doubly-rotated lithium tetraborate resonators

The authors previously presented calculations of the properties expected for doubly rotated lithium tetraborate resonators. The loci of cuts processing both first- and second-order temperature compensation for the simple thickness modes of plate resonators driven by thickness-directed electric fields were identified. Lithium tetraborate plates cut to the nominal orientations of these loci have since been obtained and measurements have been undertaken to verify the predictions. The mode spectra, equivalent circuit parameters, and frequency-temperature behavior have been examined for the first, third, and fifth harmonics for all three simple thickness modes of the resonators. The observed values of constants and piezocoupling are in good agreement with the predicted values. The measured temperature coefficients agree less well with the predicted values.<<ETX>>

Thermal expansion of alpha quartz

Existing data for thermal expansion of alpha quartz (between -50 degrees C and 150 degrees C) have been critically analyzed. A recommended best set of values was received, as were third-, and fourth-, and fifth-order power series expansions for the coefficients of thermal linear expansion (CTE), referenced to 0 degrees C. To fully utilize the results, relationships between the CTEs and the thermal expansion coefficients ( alpha /sub ij/) were derived and alpha /sub ij/ referenced to 25 degrees C were obtained. Based on the results, an additional analysis to third order in alpha /sub ij/ values allow direct comparison with previously published thermal expansion coefficients. The influence of the new alpha /sub ij/ on determinations of quartz material temperature coefficients and on the calculation of temperature coefficients of frequency for the case of the AT-cut are discussed.<<ETX>>

Determination of the limiting factors in the absolute phase noise of an L-band dielectric resonator oscillator

In an attempt to better understand the noise performance of a state-of-the-art two-stage L-band dielectric resonator oscillator (DRO), a single-stage DRO was constructed for comparison. The results of this investigation are presented. The discussion begins with a brief analysis of the design and temperature performance of the one- and two-stage DROs. The residual and absolute phase noise performance are discussed. The measured data demonstrate the low phase noise capability and excellent frequency stability of the two-stage, 2-GHz DRO.<<ETX>>

Lateral- and thickness-field coupling in lithium tetraborate

Calculations have previously been made for rotated y-cuts, including the regions where the quasi-extensional and quasi-shear thickness modes have zero temperature coefficients of frequency. This work extends the calculations to doubly rotated bulk-wave resonators, and computes the coupling factors for the three simple-thickness modes driven by thickness (TE) and lateral (LE) quasistatic electric fields as a function of the orientation angles phi and theta , and the direction of the applied lateral field psi . Because of the temperature coefficients of the piezoelectric coupling factors, the temperature coefficient of a resonator depend not only upon orientation, but also upon harmonic number and location of the resonator operating point on the immittance circle. These considerations are addressed.<<ETX>>

Thin rotated Y-cut quartz resonators vibrating in b-mode over a wide temperature range

The authors present both theoretical analyses and experimental results with reference to developing thin rotated Y-cut quartz resonators vibrating in b-mode which can show reliable frequency-temperature characteristics under high temperature. The fundamental equation relating the turnover temperature and the angle of cut for the thin rotated Y-cut quartz crystal resonator vibrating in b-mode over a wide temperature range is presented. Both theoretical and experimental results on the frequency-temperature characteristics of the crystal resonators in which Taylor expansion theory is used are presented. The resonator vibrating in b-mode has a greater frequency constant than a quartz crystal resonator vibrating in c-mode. This is an important advantage at the highest frequency.<<ETX>>