NIST Technical Note 1337: Characterization of Clocks and Oscillators

:l frequcllcy ~eparatioll froll1 the carrier, the carrier-tonoiseratio at that point is approximatelyB. Clock Ermrs1) Gel/eral: A clock is a device that counts the cyclesof a periodic phenomenon. Thus, the reading error x(t)of a clock run from the signal given by (2) is'P(t).r(l) = -'J­-?l'Vo(35)and the dimensions of .r(t) are seconds.If this clock is a secondary standard, then one couldhave available some past history of x(t), the time errorre)ati"e to the standard clock. It often occurs that oneis interested in predicting; the clock error x(t) for somefuture date, say t" + T, where to is the present date.Obviously, this is a problem in pure prediction and canhe handlrd by cOll\"entional methods [3].2) Special Case: Although one could handle the predictionof clock errors by the rigorous methods of predictiontheory, it is more common to use simpler predictionmethods [10], [11]. In particular, one often predicts a clockerror for the future by adding to the present error acorrection· that is derived from the current rate of gain(or loss) of time. That is, the predicted error £(t o + T)is related to the past history of x(t) byiLlY(t). One of the most common techniques is a heterodyneor beat frequency technique. In this method, the signalfrom the oscillator to be tested is mixed with a referencesignal of almost the same frequency as the test oscillatorin order that one is left with a lower average frequencyfor analysis without reducing the frequency (or phase)fluctuations themselves. Following Vessot et al. [18],consider an ideal reference oscillator whose output signalisV,(t) = Yo, sin 211"1' 0 t (40)and a second oscillat