NIST Technical Note 1337: Characterization of Clocks and Oscillators

198 SAMUEL R. STEINknow the time of a clock, one needs to perform the integration in Eq. (12-1l).The missing frequency measurements must be bridged by estimating theaverage frequency over the gap, resulting in a time error that is propagatedforever. Thus, it is preferable to always make measurements at a level of themeasurement hierarchy equal to or above the level corresponding to thequantity of principle interest. In the past this was rather difficult to do.Measurement systems constructed from simple commercial equipment sufferedfrom dead time, that is, they were inactive for a period after performinga measurement. To make matters worse, methods for measuring time orphase had considerably worse noise performance than methods for measuringfrequency. As a result, many powerful statistical techniques weredeveloped to cope with these problems (Barnes, 1969: Allan, 1966). The effectof dead time on the statistical analysis has been determined (Lesage andAudoin, 1979b). Other techniques have been developed to combine shortdata sets so that the parameters of clocks over long periods of time could beestimated despite missing data (Lesage, 1983). The rationale for theseapproaches is considerably diminished today. Low-noise techniques for themeasurement of oscillator phase have been developed. Now, commercialequipment is capable of measuring the time or the total phase of an oscillatorwith very high precision. Other equipment exists for measuring the timeinterval. These devices use the same techniques that were previouslyemployed for the measurement of frequency and are very competitive inperformance.The proliferation of microcomputers and microprocessors has had anequally profound effect on the field of time and frequency measurement.There has been a dramatic increase in the ability of the metrologist to acquireand process digital data. Many instruments are available with suitablestandard interfaces such as IEEE-583 or CAMAC (IEEE, 1975) andIEEE-488 (IEEE, 1978). As a result, there has been a dramatic change indirection away from analog signal processing toward the digital, and thisprocess is accelerating daily. Techniques once used only by nationalstandards laboratories and other major centers of clock development andanalysis are now widespread. Consequently, this chapter will focus first onthe peak of the measurement hierarchy and the use of digital signalprocessing. But the analysis is directed toward estimating the traditionalmeasures of frequency stability. Considerable attention will be paid toproblems associated with estimating the confidence of these stability measuresand obtaining the maximum information from available data.The IEEE has recommended as its first measure of frequency stability theone-sided spectral density Sy(f) of the instantaneous fractional-frequencyfluctuations J(t). It is simply related to the spectral density of phase fluctuationssince differentiation of the time-dependent functions is equivalent toTN-68