Spectral Density Of Frequency Fluctuations Research Articles

Self-Oscillators Based on Surface Acoustic Waves (A Review)

Introduction. Modern precision radio systems impose stringent requirements on the quality of the reference signal sources used. Various approaches are used to create sources of reference signals in the microwave range – micro-wave self-oscillators (SO). A promising direction in the development of such SO is SO with frequency-setting elements based on surface acoustic waves (SAW).Aim. A review of international achievements in the development of frequency-setting elements based on SAW and respective SO.Materials and methods. The selection of materials for a comparative analysis and generalization was carried out using available sources published over the past 30 years in well-known engineering journals, advertising brochures and websites of the manufacturers of devices based on SAW. The selection criteria included low values of the power spectral density of the frequency fluctuations of the generated signal, the presence of vibration protection, the presence of a thermostat, as well as the miniaturization and originality of the design.Results. Specific features of various methods used for constructing microwave oscillators were analyzed. It is shown that the achievement of the best values of the power spectral density of frequency fluctuations in SO with frequency-setting elements on SAW is possible only with the use of two-port resonators. An analysis of the main technical characteristics of temperature-controlled vibration-resistant SO was carried out.Conclusion. Despite the large number of different manufacturers on the world market (more than 20 companies) and the variety of different models of oscillators with frequency-setting elements on SAW (more than a 100 different models), only two companies produce oscillators resistant to external vibrations and acoustic noise.

Nonwhite frequency noise in spin torque oscillators and its effect on spectral linewidth

We measure the power spectral density of frequency fluctuations in nanocontact spin torque oscillators over time scales up to 50 ms. We use a mixer to convert oscillator signals ranging from 10 GHz to 40 GHz into a band near 70 MHz before digitizing the time domain waveform. We analyze the waveform using both zero crossing time stamps and a sliding Fourier transform, discuss the different limitations and advantages of these two methods, and combine them to obtain a frequency noise spectrum spanning more than five decades of Fourier frequency $f$. For devices having a free layer consisting of either a single Ni$_{\text{}80}$Fe$_{\text{}20}$ layer or a Co/Ni multilayer we find a frequency noise spectrum that is white at large $f$ and varies as \emph{$1/f$} at small $f$. The crossover frequency ranges from $\approx\unit[10^{4}]{Hz}$ to $\approx\unit[10^{6}]{Hz}$ and the $1/f$ component is stronger in the multilayer devices. Through actual and simulated spectrum analyzer measurements, we show that $1/f$ frequency noise causes both broadening and a change in shape of the oscillator's spectral line as measurement time increases. Our results indicate that the long term stability of spin torque oscillators cannot be accurately predicted from models based on thermal (white) noise sources.

Fundamental limits on1/ffrequency noise in rare-earth-metal-doped fiber lasers due to spontaneous emission

It is proposed that observed $1/f$ laser frequency noise in rare-earth-metal-doped optical fiber lasers is caused by diffusion of local entropy fluctuations associated with random spontaneous emission events. This heat generation is directly associated with the broad emission spectrum of rare-earth-metal-doped laser glasses. Using data from a well characterized erbium-doped fiber laser, it is shown that the power spectral density of frequency fluctuations resulting from this mechanism is able to achieve excellent agreement with experiment. The proposed theory is expected to be generally applicable to broadly emitting solid-state gain media.

A Bayesian method for oscillator stability analysis

The power spectral density of frequency fluctuations of an oscillator is generally modeled as a sum of power laws with integer exponents (from -2 to +2). However, a power law with a fractional exponent may exist. We propose a method for measuring the level of such a noise process and determining the probability density of the exponent. This yields a criterion for compatibility with an integer exponent. This method is based on a Bayesian approach called the reference analysis of Bernardo-Berger. The application to a sequence of frequency measurement from a quartz oscillator illustrates this paper.

Measurement of the frequency fluctuations of a laser with a nonlinear-absorbing cell using the Bershtein method

We propose to use the method of I. L. Bershtein for measuring the frequency fluctuations of an arbitrary type oscillator from the error signal at the output of the phase locking system for a laser with internal absorbing cell. The spectral density of the frequency fluctuations of a single-frequency He-Ne/CH4 laser was measured. It is shown that in this case the method allows us to measure the low-frequency technical fluctuations of the laser frequency, which determine the width of the laser emission line. The measurements can be performed in the case of both suppression of low-frequency fluctuations of the laser frequency due to the phase locking system and the regime that is close to that of free generation. It is also shown that an increase in the operating frequency band of the phase locking system makes sense only in the case in which the reference spectral density of the laser frequency fluctuations multiplied by the slope of the frequency discriminator conversion (in this case, the power and photoreceiver peak) exceeds the noise level at the system input.

Ultrahigh-spectral-purity laser for the VIRGO experiment

We report on the frequency stabilization and on the measurement of the spectral density of frequency fluctuations (range 20 Hz to 20 kHz) and of the Allan variance (0.02 ms to 10(5) s) of a Nd:YAG laser for the VIRGO interferometric detector of gravitational waves. The short-term frequency fluctuations presented here compare favorably with those of other known oscillators. The Allan variance is better than 10(-14) for all measurement times below 0.1 s.

Characteristics of the relaxation oscillating SQUID with tunnel junctions

The authors describe a relaxation oscillating superconducting quantum interference device (SQUID) fabricated using the Nb/AlO/sub x//Nb Josephson tunnel junction technique. It is demonstrated that this SQUID transfers flux changes into frequency changes. The relative linewidth of the frequency spectrum is on the order of 10/sup -5/. The spectral density of frequency fluctuations is 2*10/sup 4/ Hz/sup 2//Hz at both 10 kHz and 100 kHz. A method to evaluate the flux resolution of relaxation oscillating SQUIDs without a flux-locked loop is also proposed; the result is S/sub phi /(f)=2.1*10/sup -14/ phi /sub 0//sup 2//Hz at both 10 kHz and 100 kHz. The advantage of the relaxation oscillating SQUID is that it does not suffer from amplifier noise as long as the signal is treated in the frequency domain. >

Frequency stabilization of a continuous-wave Ti:sapphire laser

Measurements of the spectral density of frequency fluctuations are reported for an actively stabilized cw Ti:sapphire laser. For a servo loop incorporating an intracavity translatable mirror and an external-cavity acousto-optic modulator, a linewidth of 1.0 kHz rms is obtained for the fluctuations of the laser frequency as recorded within the servo loop. The modulation index associated with the frequency deviations is considerably less than one over most of the Fourier spectrum, indicating operation in a domain of small phase noise for the fluctuations of the electric field.

Modeling resonator frequency fluctuations induced by adsorbing and desorbing surface molecules

Resonator frequency fluctuations due to adsorption and desorption of molecules on plate electrodes are studied using the principle of mass-loading effects of adsorbed molecules. The study is based on a 525 MHz, AT-cut quartz resonator enclosed in a small crystal holder. Equations relating the surface adsorption rates of the crystal holder to pressure were derived and found to be quadratic polynomial functions of the adsorption rates. Calculations based on these equations show that a contaminant gas with a higher desorption energy creates larger changes in pressure when the temperature is varied. The function describing the frequency fluctuations due to any one contaminant site is a continuous-time Markov chain. Kolmogorov equations and an autocorrelation function for the Markov chain are derived. The autocorrelation and spectral density function of resonator frequency fluctuations are derived. The spectral density of frequency fluctuations at 1 Hz is studied as a function of pressure, temperature, and desorption energy of molecules. The noise levels for a contaminant gas with one type of molecules are found to be lower for lower desorption energies, and higher at lower pressures.

Resonator surface contamination-a cause of frequency fluctuations?

The mass loading effects of adsorbing and desorbing contaminant molecules on the magnitude and characteristics of frequency fluctuations in a thickness-shear resonator are studied. The study is motivated by the observation that the frequency of a thickness-shear resonator is determined predominantly by such mechanical parameters as the thickness of the resonator, elastic stiffnesses, mass loading of the electrodes, and energy trapping. An equation was derived relating the spectral density of frequency fluctuations to: (1) rates of adsorption and desorption of one species of contaminant molecules; (2) mass per unit area of a monolayer of molecules: (3) frequency constant; (4) thickness of resonator; and (5) number of molecular sites on one resonator surface. The induced phase noises were found to be significant in very-high-frequency resonators and are not simple functions of the percentage of area contaminated. The spectral density of frequency fluctuations was inversely proportional to the fourth power of the thickness if other parameters were held constant.

1/f frequency fluctuations in quartz acoustic resonators

The level of 1/f frequency fluctuations has been measured on numerous quartz surface acoustic wave resonators. When these results are combined with existing data for quartz bulk acoustic wave resonators it becomes clear that the 1/f process is essentially the same in both types of devices. Furthermore, the power spectral density of frequency fluctuations shows a clear power law dependence that is very close to 1/Q4u , where Qu is the unloaded Q. However, the observed dependence on loaded Q is weak.

1/f frequency fluctuations of a quartz oscillator and temperature fluctuations

AbstractWe have investigated correlations between an ambient temperature and a frequency of a 5‐MHz, 5th overtone IC‐cut plano‐convex quartz oscillator. We found that the spectral density of frequency fluctuations is composed of three parts over a fluctuation frequency from 10−6 to 10−2 Hz; in the lowest frequency part it is proportional to 1/f2, which continues to 1/f and eventually to f0. the 1/f2 and f0 spectra are caused by ambient temperature fluctuations. Thus we have found that the 1/f spectrum has nothing to do with temperature fluctuations, which, therefore, provides a limit for frequency stability of a quartz oscillator.