NIST Technical Note 1337: Characterization of Clocks and Oscillators

12 FREQUENCY AND TIME MEASUREMENT223the signal from the mixer can be used to estimate the spectral density of thefrequency fluctuations:1S7(!) ~ C' t )2 Sv,vo(f) for f 4, I/1tC d • (12-64)... 7tVo dFrequency discriminators are applied in an analogous fashion. A resonantcircuit is often used to provide discrimination since it produces a phase shiftproportional to the frequency deviation from the resonant frequency. Forexample, the phase shift on reflection from a resonance with loaded qualityfactor Qis¢ = arctan(2Qy) ~ 2Qy, (12-65)provided that the frequency deviation is small compared to the bandwidth ofthe resonance and the applied signal is nearly at the center frequency of thediscriminator. This can be accomplished either manually or with a frequencylockedloop. The design of such a loop is similar to the phase-locked loop ofthe next section. Once again, one can spectrum analyze the signal from themixer to obtainfor f 4, vo/Q· (12-66)The noise floor for measurements made with either a delay line or discriminatornormally results from white voltage noise in the analysis circuitry andis independent of the Fourier frequency. We denote the noise floor Sv,vo(minimum) and find the noise floor for frequency or phase measurements by2 2vvSq,(noise limit) = f~ S7(noise limit) = P(;Q)2 Sv/Vo(minimum).(12-67)Consequently, the discriminator or delay-line technique is limited in sensitivitysince the output voltage is proportional to the frequency deviations.Greater sensitivity is possible using two oscillators in a phase-locked loop.The noise in the reference is an important consideration, even though thereference is passive in the case of a discriminator or a delay line. If theoscillator has sufficiently low noise, then the circuits described measure thevariations of the discriminator center frequency or the delay variations in thedelay line.12.3.2.2 PHASE-LOCKED LOOPThe block diagram for the most general phase-locked loop that will beconsidered here is shown in Fig. 12-20. The noise voltage summed into theloop is a schematic way of representing ¢nU), the open-loop phase noise of theTN-93