Yu.S. Shmaliy

Kalman filtering of a frequency instability based on Motorola Oncore UT GPS timing signals

The paper presents the application results of different types of optimal and quasi optimal Kalman filters looked after the oven controlled crystal oscillator (OCXO) with reference timing signals of GPS Motorola Oncore UT+ Timing Receiver. Some simple algorithms have been studied for different definitions of filter coefficients, thereupon we showed that optimal, and quasioptimal ones have the similar asymptotic levels with t/spl rarr//spl infin/ but different output noises and transfer times of covariance function.

Flicker noise conversion in crystal oscillator

A single port 1/f model is examined of a crystal oscillator combined with a resonator and an equivalent negative resistance of amplifier. Intrinsic 1/f flicker fluctuations of resonator and amplifier amplitude and phase are converted to the oscillator amplitude and phase, and the proper transformation coefficients are applied. An analysis of the oscillator phase power spectral density is provided in detail for the particular case of a resonator excited in oscillator at various frequencies. Conformity with the Leesons model is shown.

An influence on eigenvibrations in resonators of anisotropy of boundary surface of piezoelectric plate with variable convexity

The report addresses an analysis of the transversely varying thickness modes in a piezoelectric resonator caused by the convex anisotropic boundary surface in a piezoelectric plate. We show that the anisotropy of the boundary surface greatly influences the frequency spectrum of the eigenvibrations of the resonator. The relations to calculate the frequency spectrum and the relative amplitudes of the vibrations are derived.

The lateral field excited anharmonic mode vibrating SC-cut resonators application in oscillators

The SC-cut anharmonic mode 301 and 310 resonators have been presented over past several years at the EFTF. Compared to main mode lateral field excited resonators, the anharmonic mode resonators exhibit a lower motional resistance and few times higher motional capacitance. For this reason, it is inherently easier to make frequency calibration and control of an anharmonic mode based oscillator. At the Tele and Radio Research Institute, lateral field excited resonators employing the main mode 300 and the anharmonic modes 301 and 311 were designed and manufactured. The same swept quartz material was used for all resonators, and the manufacture was based on the same technological process. The resonators were mounted in oscillators. Then the short term instability, the long term drift and the thermal frequency offset were measured, using conventional methods of measurement. Measurements of the long term frequency drift were carried out in the laboratory with constant ambient temperature 20/spl plusmn/1/spl deg/C. Moreover the long term frequency drift was corrected for atmospheric pressure and air humidity. As a result of the measurements, the short term instability of 7+10/spl times/10/sup -13//1s range and the long term drift of in 5+20/spl times/10/sup -11//day, after 1 month were achieved. The influence of the parameters of electronic components utilized in oscillators on oscillator parameters was observed. After changing the components that exhibited the highest instability the short and long term instability measurements were repeated. The measured long term drift was in the region of 1+6/spl times/10/sup -11//day. The parameters of anharmonic mode lateral field excited resonators are presented. The short term and long term instability and thermal frequency offset of oscillators utilizing lateral field anharmonic mode resonators are compared with those of oscillators utilizing classical lateral field excited SC cut resonators.

An analysis of frequency spectrum of the convex piezoelectric resonator of thickness-shear vibrations

The mathematical model is discussed of the lateral field excited crystal resonator employing thickness-shear vibrations of the even anharmonic mode. The resonator is combined with a convex piezoelectric plate and with two one-sided electrodes of the relevant shape. The influence of the electrode boundaries on the frequency spectrum is taken into account based on perturbation theory, which allows consideration of arbitrary electrode shapes. We show that the theoretical model fits well with the experimental data provided in ITR for the crystal resonator with lateral excitation field.

Frequency spectrum of localized vibrations of piezoelectric resonator

The paper addresses the frequencies /spl omega//sub kln/ of localized vibrations of a piezoelectric resonator accounting for the nonequidistance of spectrum by squared frequency. The formulas obtained for /spl omega//sub kln/ with high accuracy (/spl sim/10/sup -4/-10/sup -3/) describe the vibration frequencies of an AT-cut quartz crystal resonator, which were observed experimentally. The influence produced by the electrodes boundaries on the frequency spectrum has been studied.

Evaluation of the tie of a crystal clock by gps measurements with negative sawtooth correction and unbiased fir filtering

The local crystal clock performance is evaluated in terms of the time interval error (TIE) that is a measure of inaccuracy in timekeeping. In this paper, we apply the unbiased FIR filter to examine the TIE by the GPS timing receiver with and without the negative sawtooth correction. The rubidium clock is used as a reference source of 1 PPS signal for the local crystal clock. We show that the unbiased FIR estimate is comparable to measurements with the sawtooth correction. Herewith, the estimate becomes much more accurate when the TIE changes with time very slowly.