NIST Technical Note 1337: Characterization of Clocks and Oscillators

230 SAMUEL R. STEINThe combination of oscillator, frequency synthesizer, and mixer functions asa divider and scaler I functions as the system clock, recording elapsed time inunits of cycles of oscillator 1.The signals from oscillators 1 and 2 are represented according to Eq.(12-52) with 4>J 0 = 4>20 = 0, and the signal from the synthesizer is writtenv,,(t) = v"o cos[2XVsof + 4>.(r)]. (12-85)The phase of the synthesizer retards nearly linearly in time compared to thephase of oscillators 1 and 2. At time t..., the synthesizer reaches phasequadrature with oscillator I and the beat signal crosses zero (in the positivedirection), producing a pulse from the zero-crossing detector and startingthe time-interval counter. At a later time t N the continued sweep of thesynthesizer has brought it into quadrature with oscillator 2, and a pulse isproduced that stops the time-interval counter. The phase difference betweenthe oscillators can be written in terms of the three counter readings:(12-86)where N is the reading of scaler 2, M the reading of scaler 1, P the reading ofthe time-interval counter, and '0 the period of its time base (Stein er aI., 1983).Comparison with Eq. (12-45) for direct time-interval measurements revealsthat the role of the scalers is to accumulate the coarse phase differencebetween the oscillators, while the time-interval counter provides fine-grainresolution of the fractional cycle. This process is illustrated in Fig. 12-28. Theadvantage of the technique over direct time-interval measurements is that thenoise performance is improved by the large heterodyne factor, allowing timeresolution of 0.1 psec to be obtained. The synthesizer degrades the noiseperformance very little since it contributes to the noise only over the interval'eP'_______ .1:--- -o:~""bJI 000III0000000TIMEFIG.12-28 Total elapsed phase measured b} the dual-mixer system of Fig. 11-17 (solidlinel. This phase mea~urement consists of two components: the number of full cycles that haveelapsed is [he step function ploned as a dashed line: the fractional cycle is the saw-tooth functionploned as open circles.TN-lOO