NIST Technical Note 1337: Characterization of Clocks and Oscillators

7. PHASE NOISE AND AM NOISE MEASUREMENTS271of the mixer are limited by the capability of the mixer) by Tykulsky (1966),Halford (1975), and Ashley et al. (1977). For this particular case. Eq. (83)indicates that an increase in the length of the delay line (to increase 'd fordecorrelation of Fourier frequencies closer to the carrier) results in anincrease in attenuation of the line, which causes a corresponding decreasein V ptp ' The optimum length occurs where'd is such that the decrease inV ptp is approximately compensated by the increase in (2nf'd)' i.e., where~ 2nf'd = O. (85)d'd V plPThis condition occurs where the attenuation of the delay line is 1 Np(8.686 dB). However, when the system is not power limited, the attenuationof the delay line is not limited, because the input power to the delay line canbe adjusted to maintain V ptp at the desired value. The optimum delay-linelength is determined at a particular selectable frequency. However, sincethe attenuation varies slowly (approximately proportional to the square rootof frequency), this characteristic allows near-optimum operation over aconsiderable frequency range without appreciable degradation in themeasurements.A practical view of the time delay ('d) and Fourier-frequency functionalrelationship can be obtained by reviewing the basic concepts of the dualchanneltime-delay measurement system discussed by Lance (1964). If thedifferential delay between the two channels is zero, there is no phase differenceat the detector output when a swept-frequency cw signal is appliedto the system. Figure 16 shows the detected output interference display whena swept-frequency cw signal (zero to 4 MHz) is applied to a system that has1+----- 360" ~ IoTd = 1500 nsec:f = 2 MHzf = 4 MHzFIG. 16 Swept-frequency interference display at the output of a dual-ehannel systemwith a differential delay of 500 nsee.TN-222