NIST Technical Note 1337: Characterization of Clocks and Oscillators

112u·2-2Fig. 1. I'- -a mapping.-~Fig. 3. Bias function B,(T, p.).ferent parameter, such as in the use of an o"cilJator inDoppler radar measurements or in clocks..(tr:(N2,T., T.» = (::YFig. 2. Function B,(N, T = I, 1'-).. [BI(N., r., /-l)B.(r., I-')J< '(N T » (32)B.(N" T" I-')B.(r" 1-') tr. I, I, TI ,where Tl = Tt/·f'I and r2 = TdT2.3) General: While it is true that the concept of thebias functions B 1 and B 2 could be extended to otherprocesses besides those with the power-law types ofspectral densities, this generalization has not been done.Indeed, spectra of the form given in (28) [or superpositionsof such spectra as in (26)] seem to be themost common types of nondeterministic noises encounteredin signal generators and associated equipment. For-Qther types of fluctuations (such as causally generatedperturbations), translations must be handled on an in­.dividual basis.VI. ApPLICATIONS OF STABILITY MEASURESObviously, if one of the stability measures is exactlythe important parameter in the use of a signal generator,-the stability measure's application is trivial. Some non­.trivial applications arise when one is interested in a dif­A. Doppler Radar1) General: From its transmitted signal, a DopplNradar receives from a moving target a frequency-shiftedreturn signal in the presence of other large signals. The"elarge signals can include clutter (ground return) andtransmitter leakage into the receiver (spillover). Instabilitiesof radar signals result in noise energy on theclutter return, on spillover, and on local oscillators inthe equipment.The limitations of subclutter Yisibility (SCV) rejertionsdue to the radar signals themselves are related tothe RF power spectral density Sv (f). The quantity typicallyreferred to is the carrier-to-noise ratio and can bemathematically approximated by the quantityThe effects of coherence of target return and otherradar parameters are amply considered in the literature[14]-[17].2) Special Case: Because FM effects generally predominateover AM effects, this carrier-to-noise ratio isapproximately given by [6](33)for many signal sources provided If - vol is sufficientlygreater than zero. (The factor of t arises from the factthat Sip (f) is a one-sided spectrum.) Thus, if f - Vll isTN-IS3