NIST Technical Note 1337: Characterization of Clocks and Oscillators

major difficulty is designing a mixer terminations toremove the source frequency from the output signal,which would generally saturate the low noiseamplifiers following the mixer. without degrading thesignal-to-noise ratio. As mentioned earlier thephase noise spectrum is quite likely asymmetric whenf exceeds the bandwidth of the tuned circuits in thedevice under test. For example one expects that thephase noise at 1/2vo is different than the phasenoise at 3/2v o .Comparison of Noise Floorfor Different Techniquesreference source is also higher at the multipliedfrequency as shown in Section III.F below.III, B Enhanced PerfOrmance Using CorrelationTechniquesThe resolution of the many systems can be greatlyenhanced (typically 20 dB) by using correlationtechniques to separate the phase noise due to thedevice unde·r test from the noise in the mixer and IFamplifier [5, 11].For purposes of illustration, consider the schemeshown in Fig. 5. At the output of each doublebalanced mixer there is a signal which isproportional to the phase difference, A~, between thetwo oscillators and a noise term, V R• due tocontributions from the mixer and amplifier. Thevoltages at the input of each bandpass filter areVI(BP filter input) = GIA~(t) + C1V.I(t) (11)V 2 (BP filter input) = G 2 A~(t)+ C 2V. 2(t).where VRI(t) and V. 2 (t) are substantiallyuncorrelated and C I and C 2are constants. Eachbandpass filter produces a narrow band noise functionaround its center frequency f:VI(BP filter output) = G I [S.(f)]· B I ' cos [2Kft +~(t)](12)V 2 (BP filter output) G 2 [S.(f)]· B 2 ' cos [2lfft +.p(t)]Fig. 4.Curve A.The noise floor S¢(f) (resolution) oftypical double balanced mixer systems (e.g.Fig. 1 and Fig. 2) at carrier frequenciesfrom 0.1 MHz to 26 GHz. Similarperformance possible to 100 GHz [5J.Curve B. The noise floor, S~(f), for a high levelmixer [5 J .Curve C. The correlated component of S.(f) betweentwo channels using high level mixers [5].Curve D. The equivalent noise floor S.(f) of a 5 to25 MHz frequency multiplier.Curve E. Approximate phase noise floor of Fig. 8using a 500 ns delay line.Curve F. Approximate phase noise floor of Fig. 8where alms delay has been achieved byencoding the signal on an optical carrierand transmitted it across a long opticalfiber to a detector.OOM,REfMost double balanced mixers have a substantial nonlinearitythat can be exploited to make phasecomparison between the reference source and oddmultiples of the reference frequency. Some mixerseven feature internal even harmonic generation. Themeasurement block diagram looks identical to that ofin Fig. 1, except that the source under test is at anodd (even) harmonic of the reference source. Thismethod is relatively efficient (as long as theharmonics fall within the bandwidth of the mixer) formultiples up to x5 although multiples as high as 25have been used. The noise floor is apprOXimatelydegraded by the amount of reduction in the phasesensitivity of the mixer. The phase noise of theFig. 5.Correlation phase noise measurement system.where B I and B 2are the eqUivalent noise bandwidthsof filters 1 and 2 respectively. Both channels arebandpass filtered in order to help eliminate aliasingand dynamic range problems. The phases ~(t), n, (t)and n 2(t) take on all values between 0 and 2lf withequal likelihood. They vary slowly compared to 11fand are substantially uncorrelated. When these twovoltages are multiplied together and low passfiltered, only one term has finite average value.435