NIST Technical Note 1337: Characterization of Clocks and Oscillators

222SAMUEL A. STEINThe analysis of phase noise is accomplished by arranging that¢IO - ¢20 = n/2, which can be achieved with a phase shifter. Then,(12-59)There are various methods by which one can control the signal V 2(c) so that"10 = \120 without producing significant correlation between ¢2(t) and ¢I(t).When anyone of these methods is used, it is possible to use Vet) as a measureof ¢(t). Two methods, delay lines and phase-locked loops (Gardner, 1966), aredescribed below.12.3.2.1 DISCRIMINATOR AND DELAY LINEThe circuit of a discriminator or delay-line system for measuring phasenoise is illustrated in Fig. 12-19. The delayed signal is given byV 2 (t) = VIet - rd) = V 20 sin[21t\lIo(t - rd) + ¢,(r - Cd) + ¢10 + ¢.J.(12-60)When the phase shifter is set for quadrature, ¢. -2n\'10td = n.'2 andV2(r) = V 20 sin[l1t\l'or + ¢,(r - rd) + ¢'O + 1!,'2J. (12-61)The output of the phase detector is given bySubstituting Eq. (12-62) into Eq. (12-20), we obtain(12-62).nr - t d : r) = - V(r)/21t\·0 VOrd (12-63)and we see that the delay-line method can be used to produce samples of.~imro) by varying the delay time. However, the technique is used morefrequently with a fixed delay by restricting its application to the region of rmuch greater than the delay time, so that .Wt - td: r) is a good approximationfor the instantaneous frequency. Under this assumption spectrum analysis ofPHASE SHIFTERfaVIltl DISCRIMINATOR ORDELAY LINEOSCILLATORFIG. 12-19 A delay-line phase-noise-measurement system. When the phase shifter isadjusted so that 1'2(r) is in phase quadrature with Volt), the output of the phase detector isapproximately equal to the instantaneous frequency deviation of the oscillator. The spectraldensity of the source may be estimated for Fourier frequencies smaIl compared to the inverse ofthe delay' lime.TN-92