NIST Technical Note 1337: Characterization of Clocks and Oscillators

270 A. L. LANCE, W. D. SEAL, AND F. LABAARThe sensitivity (noise floor) of the two-oscillator measurement systemincludes the thermal and shot noise of the mixer and the noise of the basebandpreamplifier (referred to its input). This noise floor is measured withthe oscillator under test inoperative. The measurement system sensitivity ofthe two-oscillator system, on a per hertz density basis (dBc/Hz) iswhere bL: n is the rms noise voltage measured in a one-hertz bandwidth.The two-oscillator system therefore yields the output noise from bothoscillators. If the reference oscillator is superior in performance, as assumedin the previous discussions, then one obtains a direct measure of the noisecharacteristics of the oscillator under test. If the reference and test oscillatorsare the same type, a useful approximation is to assume that the measurednoise power is twice that associated with one noisy oscillator. This approximationis in error by no more than 3 dB for the noisier oscillator. Substitutingin Eq. (80) and using the relationships in Eq. (56), we have, per hertz,(83)!t'(f)1 = 2[(6V rm Y/(VPIP)2](2njr d )2 (84)dImExamination of this equation reveals the following.(I) The term in the brackets represents the two-oscillator response.Note that this term represents the noise floor oj the two-oscillator method.Therefore, adoption of the delay-line method results in a higher noise by thefactor (2rr.jr d )2 when compared with the two-oscillator measurement method.The sensitivity (noise floor) for delay lines with different values of time delayare illustrated in Fig. 17.(2) Equation (84) also indicates that the measured value of !t'(f) isperiodic in w = 2rrf This is shown in Fig. 21. The first null in the responsesis at the Fourier frequency j = l/rd' The periodicity indicates that the calibrationrange of the discriminator is limited and that valid measurementsoccur only in the indicated range. as verified by the discriminator slope shownin Fig. 16. (See Fig. 23.)(3) The maximum value of (2rrjr d )2 can be greater than unity (it is 4 atj = 1'2r d )· This 6-dB advantage is utilized in the noise-floor measurement.However, it is beyond the valid calibration range of the delay-line system.The 6-dB advantage is offset by the line attenuation at microwave frequencies,as discussed by Halford (1975).The delay-line discriminator system has been analyzed in terms ofa powerlimitedsystem (a particular idealized system in which the choice of poweroscillator voltage. the attenuator of the delay line, and the conversion lossTN-221