NIST Technical Note 1337: Characterization of Clocks and Oscillators

7. PHASE NOISE AND AM :>lOISE MEASUREMENTS 283The low-noise amplifiers preceding the digital signal analyzer are usedwhen performing measurements at Fourier frequencies from 1 Hz to 25 kHz.The amplifiers are not used when performing measurements below theFourier frequency of 1 Hz.2. Calibrating the Dual Delay-Line SystemEach delay line in the system is calibrated separately following the samebasic procedure set forth in Section IV.B. The Hewlett-Packard 5420measures the one-sided spectral density of frequency fluctuations in hertzsquared per hertz. The spectral density of phase fluctuation in radianssquared per hertz can be calculated asand(99)(l00)per hertz. The Hewlett-Packard 5420 measurement ofSJy(f) in Hz 2 /Hz must,therefore, be corrected by 1/2f2. However, the f2 correction must be enteredin terms of radian frequency (w = 2rr.j). This conversion is accomplished by5£(f) = SJy(f)(1/2f2)(4rr. 2 /4rr. 2 ) = [2rr. 2 SJy(f)]/(W)2per hertz since Eq. (100) can be stated in the following terms:[2rr. 1 SJy(f)]/4rr.2f 2.(LOllSignal-to-noise enhancement greater than 20 dB has been obtained usingthe dual-channel delay-line system.D. MILLIMETER-WAVE PHASE-NOISE MEASUREMENTSI. Spectral Density of Phase FluctuationsThe delay line used as an FM discriminator is based, in principle, on anondispersive delay line. However, a waveguide can be used as the delayline because the Fourier frequency range of interest is a small percentageof the operating bandwidth (seldom over 100 MHz), and the dispersion canbe considered negligible.The calibration and measurement are performed as set forth in SectionIV.B. The modulation index m is usually established using the carrier-tosidebandratio that uses amplitude modulation because millimeter sourcesare either unstable or cannot be modulated. The two approaches to measurementsat millimeter frequencies are shown in Figs. 25 and 26. Figure 25shows the direct measurement using a waveguide delay line. This systemoffers improved sensitivity if adequate input power is available. The rf bridgeand delay-line portion of the system differs from Fig. 18 because pre- andTN-234