Paul Lesage

Characterization of Frequency Stability: Analysis of the Modified Allan Variance and Properties of Its Estimate

An analytical expression for the modified Allan variance is given for each component of the model usually considered to describe the frequency or phase fluctuations in frequency standards. The relation between the Allan variance and the modified Allan variance is specified and compared with that of a previously published analysis. The uncertainty on the estimate of the modified Allan variance calculated from a finite set of measurement data is discussed.

Effect of Dead-Time on the Estimation of the Two-Sample Variance

Expressions for the averaged two-sample variance as well as expressions for the uncertainty on its estimation are given, in cases where dead time is present between measurements. The effect of this dead time on the precision of the time domain measure of frequency stability, in the presence of a limited number of data, is specified. The possibility to distinguish between white and flicker noises is pointed out.

Characterization of Frequency Stability: Bias Due to the Juxtaposition of Time-Interval Measurements

The characterization of frequency stability is usually achieved by means of numerically processed time-interval measurements. In the present paper, we study the bias occurring in the frequency stability measure when successive data with the same mean durations are added in order to get different sets of samples with various mean durations. The effect of a dead time between the data involved in the considered algorithm is pointed out. An experimental analysis is presented which checks the theoretical results for several noise processes in different experimental conditions.

Frequency stability of an oscillating maser: Analysis of the effect of an external feedback loop

The noise temperature of the microwave cavity of an oscillating maser operated with an external feedback loop is given. The theoretical frequency stability of the signal delivered by the maser is deduced and the effect of the external feedback loop is discussed. Short- and mid-term frequency stabilities achievable with a conventional hydrogen maser with and without an external feedback loop and with a compact hydrogen maser operated either in active or in passive modes are given.

Experimental Study of the Frequency Stability of a Maser Oscillator Operated with an External Feedback Loop

In this paper, we report the results of an experimental study of the short-and mid-term frequency stability for both a hydrogen maser and a rubidium maser operated with an external feedback loop to modify the cavity quality factor. A revised version of the theoretical expression of the frequency stability for this type of maser is given and a numerical solution for various maser parameters is calculated. The predicted frequency stability exhibits an optimum when the cavity Q is varied. The experimental results presented in this study agree with this conclusion.

Measurement of the Effect of Thermal Noise on the Amplitude of Oscillation of a Maser Oscillator

Experimental verification of the effect of thermal noise on the oscillation amplitude of a maser is described. Two different masers are considered, the H maser with an homogeneous atomic line and the Rb maser with an inhomogeneous line. The effect is characterized by the spectral density of the relative amplitude fluctuations and this parameter is measured with a conventional superheterodyne AM receiver for various maser saturation factors. Experimental results show good agreement with theoretical predicted values. At high saturation factors, a peak appears with a maximum at a frequency close to the Rabi frequency. Observed values at high Fourier frequencies allow a measurement of the atomic power by the knowledge of the absolute temperature of the cavity and the prediction of the oscillator short-term frequency stability. Furthermore, the effect on amplitude and on frequency noise of an external feedback loop used to increase the cavity quality factor is discussed.

Studies of dielectrically loaded cavities for small size hydrogen masers

A dielectrically loaded cavity made of a hollow alumina cylinder, which is used to reduce hydrogen maser size, is considered. The results of a theoretical study of the effect of the cavity geometry on the frequency stability capability of the maser are reported. The active mode as well as the passive mode of operation are considered and the achievable performances are compared. It is shown that the frequency stability capabilities do not differ very much for both modes of operation with, however, a slight advantage to the active mode. >

Theory of Hydrogen-Maser Auto-Tuning Systems Based on the Frequency or the Phase Method

A theoretical analysis of auto-tuning systems for actively operated hydrogen (H) masers is presented. Tuning procedures based on changes in the frequency or the phase of oscillation are considered and compared. The analysis takes into account the basic results of sampling theory. The condition which should be satisfied when the reference frequency source is perturbed by white or flicker phase noise is specified. It is shown that the phase method should give better results than the frequency method when the reference source is a good quartz crystal oscillator.