NIST Technical Note 1337: Characterization of Clocks and Oscillators

From: Proceedings of the 35th Annual Symposium on Frequency Control, 1981.PROPERTIES OF SIGNAL SDURCE~MEASUREMENT METHODSiANDD. A. Howe, D. W. Allan, and J.IA. BarnesSummaryThis paper is a review of frequency stabilitymeasurement techniques and of noise properties offrequency sources.First, a historical development of the usefulnessof spectrum analysis and time domain measurementswi 11 be presented. Then the rati ana1e wi 11be stated for the use of the two-sample (Allan)variance rather than the classical variance.Next, a range of measurement procedures wi 11 beoutlinea with the trade-offs given for the various,-echni ques emp 1oyed. Methods of i nte,,:lreti ng themeasurement results will be given. In particular,the five commonly used noise models (white PM,flicker PM, white FM, flicker FM, and random walkFM) and thei r causes wi 11 be di scussea. Methodsof characterizing systematics will also be given.Confidence intervals on the various measures willbe discussed. In addition, we will point outmethods of improving this confidence interval fora fixed number of data points.Topics will be treated in conceptual detail.Only light (fundamental) mathematical treatmentwi 11 be gi ven.Although traditional concepts. will be detailed, two new topi cs will be introduced in thi spaper: (1) accuracy limitations of digital andcomputer-based analysis and (2) optimizing theresults from a fixed set of input data.The final section will be devoted to fundamental(physical) causes of noise in commonly usedfrequency standards. Also transforms from time tofrequency domain and vice-versa will be given.Key Words. Frequency stabil ity; Oscill ator noi semodeling; Power law spectrum; Time-domain stabi1ity; Frequency-domain stabil ity; White noise;Flicker noise.IntroductionPrecision oscillators play an important rolein high speed communications, navigation, spacetracking, deep space probes and in numerous otherimportant applications. In this paper, we willrevi ew some preci sian methods or measuri ng thefrequency and frequency stability of precisionoscillators. Development of topics does not relyheavily on mathemati cs. The equipment and set-upfor stabi 1i ty measurements are out1i ned. Ex amp 1esand typical results are presented. PhysicalTime and Frequency Divis~onNational Bureau of Standa~dsBoulder, Colorado 8030B,interpre~ations of common noise processes arediscusseb. A table is provided by which typicalrrequencw domain stability characteristics may beitranslated to time domain stability characteristicsand vicetversa.L THEI SINE WAVE AND STABILITYA , Is i ne wave signal generator produces avoltage [that· changes in time in a sinusoidal wayas show~ in figure 1.1. The signal is an oscillatingsi;gna1 because the sine wave repeats itself.A cycle! of the oscillation is produced in oneperi ad 'rr". The phase is the ang1 e ""," wi thi n acycle c~rresonding to a particular time "t"..,,: FIGURE 1.1Itiis convenient for us to express angles inradians! rather than in units of degrees, andpositi\(~ zero-crossings will occur at even multip1es!orinumber iorrecipro~a1express{on!sine wa~en-radi ans. The frequency: "u" is thecycles in one second, which is theof period (seconds per cycle). Thedescribing the voltage "V" out of asignal generator is given by Vet) ::: V pis the peak voltage amplitUde.sin ["'(t)] where VipEquival+nt expressions are1TN-14