NIST Technical Note 1337: Characterization of Clocks and Oscillators

ALLAN: PRECISiON CLOCKS AND OSCILLATORS-10-i5ACTIVE H MASERRb GAS cru,...........'.....---­-16:-_--;__---;.__--:-__-+-__--!-_~I 2 3 4 6lO:; TAU (s.econds)Fig. 10. Square root of Allan variance for variety of state-of-the-an precisionoscillators including NBS-6. NBS primary frequency standard.-6-7II'sRMS TIME DEVIATION&/~f7.//'Cs653minimum O',(T) value. We would then change the temperatureto the other value and repeat the measurementwith the same criteria and note the Ayr.. between the twooptimally detennined frequency values. If these two stepsare repeated several times, an arbitrarily good precisionfor the temperature coefficient is achieved if it is linear.The uncertainty is approximately given by (J,(7 )/JP,mwhere P is the number of Ayr.. values obtained fromswitching back and forth. Knowing the characteristics ofboth the random and the systematic deviations of precisionclocks and oscillators clearly is useful to the designer,the manufacturer, the planner, and the user as wellas the vendor of these devices.The aforementioned procedures usually work well if theclocks or oscillators are in a reasonable environment. Ifthe environment is adverse, other procedures and analysismethods may have to be employed. As a general rule it isoften useful to analyze the data in the frequency domainas well as the time domain. The frequency domain is especiallyuseful if there are bright lines, i.e., sidebands tothe carrier frequency, The effect of a modulation sidebandfm on 0', (7) can be calculated, and is given by [18](15)-130~=~-~--':-3----J4'---..,:---~---:!lOG TAU p (seconds)Fig. I I. From frequency stability characterization shown in Fig. 10, optimumprediction algorithms to minimize time error can be obtained.Based on oplimum prediction procedures rms time prediclion error forprediction inlerval T p can be calculated for each oscillator shown in Fig.10 and corresponding values are plotted in Fig. II.state-of-the-art oscillators, and Fig. 11 shows the nns timeprediction errors for the same set of oscillators.CONCLUSIONIn conclusion, it is clear that classical statistics do notallow characterization of common kinds of random signalvariations found in precision oscillators. The two-sampleAllan variance provides a valuable and convergent measureof the power-law spectral-density models useful incharacterizing random deviations for most oscillators andclocks, Once characterized, we can calculate optimumtime and frequency estimates as well as predicted values.Characterizing the random variations also provides nearoptimumestimation of systematic effects, which oftencause the predominant time and frequency deviations. ForeX:lmple, if we wanted to optimally detennine the statictemperature dependence with the temperature set at twodifferent values, we would stabilize the oscillator at onetemperature and measure the frequency against a referencefor a time T"'" corresponding to the T for the nominalwhere x pp is equal to the peak-to-peak or twice the amplitudeof the time-deviation modulation.If one is trying to estimate the power-law spectral behaviorbetween a pair of oscillators or clocks using O'y (7),it is apparent from (15) that if significant modulationsidebands are present on the signal, these can seriouslycontaminate that estimate. However, if a O"y( 7) plot displaysa character as given by (15), then the amplitude andfrequency of that modulation sideband can be estimatedfrom this time-domain analysis technique. In practice, thisapproach is often used, but these modulation sidebandscan be more efficiently estimated in the frequency domain.If the measurement sampling rate 1/70 is set equalto 1m' then the modulation sideband is aliased away andhas no effect on l1y ( 7).The best rule in all analysis is to use common sense.Very often the most revealing information may be in aplot of the raw time (phase) difference or frequency-differenceresiduals after some trend has been removed. Sucha plot is usually the first thing to look at when characterizingclocks and oscillators. Caution here 'is also importantas a pure random walk on the time residuals (whiteFM) may be visually interpreted as having frequencysteps. This is especially true for flicker FM as often seenin quartz-crystal oscillators. Following the time-residualplot with a l1 y ( 7) analysis often answers the question asto whether or not such steps are statistically significant.ACKNOWLEDGMENTBecause the paper is mainly a review, the author is indebtedto a large number of people-many of whom arereflected in the references. Specifically. sincere appreciationis expressed to Dr. James A. Barnes, Mr. Dick D.IN-127