David W. Allan

Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators

A tutorial review of some time-domain methods of characterizing the performance of precision clocks and oscillators is presented. Characterizing both the systematic and random deviations is considered. The Allan variance and the modified Allan variance are defined, and methods of utilizing them are presented along with ranges and areas of applicability. The standa,rd deviation is contrasted and shoun not to be. in general. a good measure for precision clocks and oscillators. Once a proper characterization model has been developed, then optimum estimation and prediction techniques can be employed. Some important cases are illustrated. As precision clocks and oscillators become increasingly important in society. communication of their characteristics and specifications among the vendors, manufacturers. design engineers. managers, and metrologists of this equipment becomes increasingI> important.

Should the classical variance be used as a basic measure in standards metrology

Since a measurement is no better than its uncertainty, specifying the uncertainty is a very important part of metrology. One is inclined to believe that the fundamental constants in physics are invariant with time and that they are the foundation upon which to build internationl system (SI) standards and metrology. Therefore clearly specifying uncertainties for these physical invariants at state-of-the-art levels should be one of the principal goals of metrology. However, by the very act of observing some physical quantity we may perturb the standard, thus introducing uncertainties. The random deviations in a series of observations may be caused by the measurement system, by environmental coupling or by intrinsic deviations in the standard. For these reasons and because correlated random noise is as commonly occurring in nature as uncorrelated random noise, the universal use of the classical variance, and the standard deviation of the mean may cloud rather than clarify questions regarding uncertainties; i.e., these measures are well behaved only for random uncorrelated deviations (white noise), and white noise is typically a subset of the spectrum of observed deviations. The assumption that each measurement in a series is independent because the measurements are taken at different times should be called into question if, in fact, the series is not random and uncorrelated, i.e., does not have a white spectrum. In this paper, studies of frequency standards, standard-volt cells, and gauge blocks provide examples of long-term random-correlated time series which indicate behavior that is not “white” (not random and uncorrelated). This paper outlines and illustrates a straightforward time-domain statistical approach, which for power-law spectra yields an alternative estimation method for most of the important random power-law processes encountered. Knowing the spectrum provides for clearer uncertainty assessment in the presence of correlated random deviations, the statistical approach outlined also provides a simple test for a white spectrum, thus allowing a metrologist to know whether use of the classical variance is suitable or whether to incorporate better uncertainty assessment procedures, e.g., as outlined in the paper.

Measurements of frequency stability

The characterization of frequency stability in the time domain and frequency domain are briefly defined and their relationships explained. Techniques for making precise measurements of frequency fluctuations in oscillators, multipliers, dividers, amplifiers, and other components are discussed. Particular attention is given to methods of calibration which permit accuracies of 1 dB or better to be achieved when measuring in the frequency domain. Common pitfalls to avoid are also covered, and efficient time-domain techniques are explained.

A Method for Estimating the Frequency Stability of an Individual Oscillator

A method is given for estimating the intensity of random noise frequency modulation of an individual oscillator, using data obtained by comparing it with two or more other osci l la tors . This method is appropriate even if the oscillators available for comparison are less stable than the oscillator being evaluated, but their frequency fluctuations must be independent. The statistical uncertainty of the resul ts i s d iscussed briefly.

A frequency-domain view of time-domain characterization of clocks and time and frequency distribution systems

The authors discuss the characterization of frequency standards, clocks, and associated systems. These associated systems may include time and frequency measurement systems, time and frequency transmissions systems, time and frequency comparison systems, and telecommunication networks. No single characterization is suitable. However, three time-domain statistical measures cover most of the situations encountered in actual practice. The selection of the appropriate time-domain measure is a function of the types of noise characteristic of the process being investigated, as well as whether the time stability or the frequency stability is to be studied. The three statistical measures are recast into the frequency domain. The authors treat each of these measures as a digital filter and study their transfer functions. This type of measure is related to the passband characteristics of a given system.<<ETX>>

Measurement of the Unperturbed Hydrogen Hyperfine Transition Frequency

The results of a joint experiment aimed primarily at the determination of the frequency of the H1 hyperfine transition (F = 1, mF = 0) ? (F = 0, mF = 0) is reported. In terms of the frequency of the Cs133 hyperfine transition (F = 4, mF = 0) ?(F = 3, mF = 0), defined as 9192 631 770 Hz, for the unperturbed hydrogen transition frequency the value ?H = 1420 405 751.768 Hz is obtained. This result is the mean of two independent evaluations against the same cesium reference, which differ by 2 × 10-3 Hz. We estimate the one-sigma uncertainty of the value ?H also to be 2 × 10-3 Hz. One evaluation is based on wall-shift experiments at Harvard University; the other is a result of a new wall-shift measurement using many storage bulbs of different sizes at the National Bureau of Standards. The experimental procedures and the applied corrections are described. Results for the wall shift and for the frequency of hydrogen are compared with previously published values, and error limits of the experiments are discussed.

Millisecond Pulsar PSR 1937+21: A Highly Stable Clock

The stable rotation and sharp radio pulses of PSR 1937+21 make this pulsar a clock whose long-term frequency stability approaches and may exceed that of the best atomic clocks. Improvements in measurement techniques now permit pulse arrival times to be determined in 1 hour at the Arecibo radio telescope with uncertainties of about 300 nanoseconds relative to atomic time. Measurements taken approximately every 2 weeks since November 1982 yield estimates of fractional frequency stability that continue to improve with increasing averaging time. The pulsars frequency stability is at least as good as 6 x 10-14 for averaging times longer than 4 months, and over the longest intervals the measurements appear to be limited by the stability of the reference atomic docks. The data yield a firm upper limit of 7 x 10-36 gram per cubic centimeter for the energy density of a cosmic background of gravitational radiation at frequencies of about 0.23 cycle per year. This limit corresponds to approximately 4 x 10-7 of the density required to close the universe.

Around-the-World Relativistic Sagnac Experiment

In 1971 Hafele and Keating carried portable atomic clocks east and then west around the world and verified the Sagnac effect, a special relativity effect attributable to the earths rotation. In the study reported here observations of the effect were made by using electromagnetic signals instead of portable clocks to make clock comparisons. Global Positioning System satellites transmit signals that can be viewed simultaneously from remote stations on the earth; thus an around-the-world Sagnac experiment can be performed with electromagnetic signals. The effect is larger than that occurring when portable clocks are used. The average error over a 3-month experiment was only 5 nanoseconds.

The NIST automated computer time service

The NIST Automated Computer Time Service (ACTS) is a telephone time service designed to provide computers with telephone access to time generated by the National Institute of Standards and Technology at accuracies approaching 1 ms. Features of the service include automated estimation by the transmitter of the telephone-line delay, advanced alert for changes to and from daylight saving time, and advanced notice of insertion of leap seconds. The ASCII-character time code operates with most standard modems and computer systems. The system can be used to set computer clocks and simple hardware can also be developed to set non-computer clock systems.

A study of the NBS time scale algorithm

A study is made of the various aspects of the algorithm theoretically, comparing the NBS (US National Bureau of Standards) algorithm with a Kalman filter to discuss questions of optimality. It is shown that since the time of a clock is not measured, but only the time difference between clocks, a time scale should not attempt to optimize time accuracy, since that has no meaning. However, time uniformity and frequency stability can be optimized. The authors further study the practice of monitoring the clocks in a time scale for frequency steps, and removing a clock from the scale when a step has been detected until the new frequency is learned. The authors show that the effect of this practice on the algorithm is to translate random walk behavior in the individual clocks, due to the frequency steps of the clocks, to flicker noise for the ensemble. The implication is that careful monitoring of the scale can significantly improve its long-term performance. >