Total Variance, an Estimator of Long-Term Frequency Stability
Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to half the test duration.
Engineering topics
Publications and source records attributed to Howe, D. A..
Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to half the test duration.
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We give results of recent work on a newly developed frequency stability characterization, called Total variance, whose main advantages are improved confidence at and near the longest averaging time of half the data duration, and lower sensitivity to drift removal.
We evaluate with simulated data a new type of sample variance for the characterization of frequency stability. The new statistic (referred to as TOTALVAR and its square root TOTALDEV) is a better predictor of long-term frequency variations than the present sample Allan deviation. The statistical model uses the assumption that a time series of phase or frequency differences is wrapped (periodic) with overall frequency difference removed. We find that the variability at long averaging times is reduced considerably for the five models of power-law noise commonly encountered with frequency standards and oscillators.
A passive hydrogen maser employing a smaller microwave cavity than previous masers is described. The volume of the entire resonator package, including a conventional source, hexapole state selector, and four magnetic shields, is estimated at 20 liters. The techniques for constructing the ceramic cavity, coating it with FEP, and attaching the endcaps to achieve a stable container (to allow its use as a single vacuum system) are described in detail. Frequency stability measurements were made of four such masers, against an NBS-4 cesium primary standard, against each other, and against eight commercial cesium clocks; frequency stability level is reported as 1.7 x 10 to the -12th tau exp -1/2 from 1 to 100,000 sec, and no drift above 1 x 10 to the -15th/day was found. Pressure and temperature effects on frequency stability were found at the 1 x 10 to the -14th level. Noise behavior beyond 200,000 sec is characterized as random walk. The potential use of a compact stable maser as a clock is suggested.
The timekeeping ability of a prototype passive hydrogen maser which is a factor of 5 smaller in size, weight, and cost than any previously designed, was compared to UTC (NBS) based on 10 cesium frequency standards including a large primary standard, NBS-4. The frequency of the prototype was monitored as a function of source pressure, cavity temperature, microwave power, modulation width, and magnetic field. Based on these measurements, a frequency stability of better than 6 x 10 to the -15 power was expected, implying a timekeeping ability of order 0.5 ns/day. Measurements vs UTC(NBS) indicate a joint timekeeping a stability of order 1.2 ns/day. Simultaneous measurements made between NBS-4, UTC(6600), and the small passive me maser show peak to peak time variations of the small maser vs UTC(6600) was 10 ns for the full 32 days if the average rate and drift are considered. Frequency stability of the small prototype vs UTC (NBS) was to 1.1 x 10 to the -14th power for tau = 1 to 8 days.
The paper describes a compact passive hydrogen maser with unique features including a reduction in size. It uses a passive operation mode, permitting the use of a small microwave TE(011) cavity dielectrically loaded by a low loss alumina. The Teflon coated quartz bulb common in other masers has been replaced by a Teflon coating on the inside wall of the cavity producing a simpler designed and a more rugged H-maser package. The cavity and the attached endcaps comprise the vacuum envelope, allowing the use of a single vacuum system. The dimensional stability of the ceramic cavity under barometric changes is sufficiently within the range of the electronic cavity servo so that a second vacuum system is not required. For temperature control, a single oven is located in the magnetic shield nest.
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