NIST Technical Note 1337: Characterization of Clocks and Oscillators

648IEEE TRANSACTIONS ON ULTRASONICS. FERROELECTRICS. AND FREQUENCY CONTROL. Val. UFFC-'4. NO.> 6. NOVEMBER 1987y( t)+ FREQUENCY OFFS£1OSCILLATOR, au RB H H< o. ) CS""1(a)J•TE,*"ERATU~ESE"fStrIvITY / d.g KFig. 2. Nominal values for temperature coefficient for frequency standards:QU = quanz crystal. RB = rubidium gas cell. H = active hy.drogen maser. H(pas) = passive hydrogen maser. and CS = cesiumbeam.OSCILLATOR, au RB H H< ce)I.~I •CSINEGATIV£ FREQuENCY DRIFT(b)Fig. l. Frequency y(1) and time x(t) deviations due to frequency offsetand to frequency drift in clock. (a) Fractional frequency error versustime. (b) Time error versus time.of reasons. the first being systematics such as frequencydrift (D). frequency offset ( Yo), and time offset (xo). Inaddition. there are systematic deviations that are often environmentallyinduced. The second category is the randomdeviations E( n. which are usually not thought to bedeterministic. In general. we may writex(r) = Xo + -,"or + 1/2 Dr;' + €(r). (5) *Though generally useful, the model in (5) does not applyin all cases~ e.g.. some oscillators have significant frequency-modulationsidebands, and in others the frequencydrift D is not constant. In some clocks and oscillators.e.g.. cesium-beam standards, setting D = 0 isusually a better model.Note that the quadratic D term occurs because x (r) isthe integral of y (t), the fractional frequency. and is oftenthe predominant cause of time deviation. In Fig. 1 wehave simulated two systematic-error cases: a clock withfrequency offset. and a clock with negative frequencydrift. Figs. 2-6 summarize some of the important systematicinfluences on precision clocks and oscillators. In additionto Figs. 1-6, important systematic deviations mayinclude modulation sidebands, e.g., 60 Hz, 110 Hz, daily.and annual dependences, which can be manifestations ofenvironmental effects such as deviations induced by vibrations.shock. radiation, humidity, and temperature... See Appendix Note # 12,.'1,-11,.­1.­1·Fig. 3. Nominal values for magnetic field sensitivity for frequency standards:QU = quartz crystal. RB = rubidium gas cell, H = active hydrogenmaser. H (pas) = passive hydrogen maser. and CS = cesiumbeam.OS:: I ~.L A TOR, au RB H H < os ) CS•••.8I,Fig. 4. Nominal capability of frequency standard to reproduce same frequencyafter period of time for standards: QU = quartz crystal. RB =rubidium gas cell. H = active hydrogen maser. H (pas) = passive hydrogenmaser. and CS = cesium beam...­ '"I1OSCilLATORau RB H H ( o.) CSABSOLUTE AC:uRACYFig. 5. Nominal capability for frequency standard to produce frequencydetermined by fundamental constants of nature for standards: QU =quartz crystal. RB = rubidium gas cell. H = active hydrogen maser.H (pas) = passive hydrogen maser. and CS = cesium beam.TN-122