NIST Technical Note 1337: Characterization of Clocks and Oscillators

up an interesting hierarchy of kinds of measurementsystems: 1) those that can measure time, x(t); Z)those that can measure changes in time or timefluctuations ox(t); 3) those that can measurefrequency, v(y = (v-vo)/v ); and 4)othose that canmeasure changes in frequency or frequency fluctuations,ov (oy =ov/v o)' As depicted in table 2.1,if a measurement system is of status 1 in thishierarchy, i.e., it can measure time, then timefluctuations, frequency and frequency fluctuationscan be deduced. However, if a measurement systemis only capable of measuring time fluctuations(status 2 - table 2.1), then time cannot be deduced,but frequency and frequency fluctuationscan. If frequency is being measured (status 3 ­table 2.1), then neither time nor time fluctuationsmay be deduced with fidel ity because essentiallyall commercial frequency measuring devices have"dead time" (technology is at a point where thatis changing with fast data processing speeds thatare now available). Dead time in a frequencymeasurement destroys the opportunity of integratingthe fractional frequency to get to "true" timefluctuations. Of course, if frequency can bemeasured, then trivially one may deduce the frequencyfluctuations. Finally, if a'system canonly measure frequency fluctuations ~status 4 ­table 2.1), then neither time, nor time fluctuations,nor frequency can be deduced from the data.If the frequency stabil ity is the primary concernthen one may be perfectly happy to employ such ameasurement system, and similarly for the otherstatuses in this measurement hierarchy. Obviously,if a measurement method of Status 1 could beemployed with state-of-the-art precision, thiswould provide the greatest flexibility in dataprocessing. From section 1, the dual mixer timedifference system is purported to be such a method.Table 2.2 is a comparison of these differentmeasurement methods. The values entered arenominal; there may be unique situations wheresignificant departures are observed. The time andfrequency stabil iti es 1i sted are the nomi na 1second to second rms values. The accuracieslisted are taken in an absolute sense. The costslisted are nominal estimates in 1981 dollars.Figure 2.1 is a diagram indicating thesample time regions over which the various methodsNII