NIST Technical Note 1337: Characterization of Clocks and Oscillators

given byREFV",(f) ]2(10)[G(f)~ P,IJMeasurement of Scp(f) lor Two AmplifiersS~lf). (-- V. )' ­~ G(')K. BW(often more than 20 dB). Termination of the mixer IFport with 50 n maximizes the IF bandwidth, however,termination with reactive loads can reduce the mixernoise by - 6 dB, and increase K dby 3 to 6 dB asshown in Fig. 3 [4J. Accurate determination of K dcan be achieved by measuring the slope of the zerocrossing in volts/radian with an oscilloscope orother recording device when the two oscillators arebeating slowly. For some applications the digitizerin the spectrum analyzer can be used to measure boththe beat period and the slope in Vis at the zerocrossing. The time axis is easily calibrated sinceone beat period equals 2~ radians. The slope involts/radian is then calculated with a typicalaccuracy of 0.2 dB. Estimates of K dobtained frommeasurements of the peak to peak output voltageinduced can introduce errors as large as 6 dB inS~(f) even if the amplitude of the other harmonics ismeasured unless the phase relationship 1s also takeninto account [4]. S~(f) can be made independent ofthe accuracy of the spectrum analyzer voltagereference by comparing the level of an externally IFsignal (a pure tone is best), on the spectrumanalyzer used to measure V nwith the level recordedon the device used to measure K d.Fig. 2. Precision phase measurement system featuringself calibration to 0.4 dB accuracy from dc to 0.1 vaFourier frequency offset from carrier. This systemis suitable for measuring signal handling equipment,multipliers, dividers, frequency synthesizers, aswell as passive components [4J.S0.8r--,.--,--r--r--,O.OlIJF~ 0.7 2mW MIXER DRIVE~>­!::0.6> 0.5i=fi)Z 0.4w«)0.3WIJJi4:J:a-0.210mW MIXER DRIVE0.11 2 5 10 202 51020 50 100FREQUENCY (kHz)Fig. 3. Double-balanced mixer phase sensitivity at 5KHz as a function of Fourier frequency for variousoutput terminations. The curves on the left wereobtained with 10 mlJ drive while those on the rightwere obtained with 2 mlol drive. The data demonstratea clear choice between constant, but low sensitivityor much higher, but frequency dependent sensitivity[4J.where V",(f) is the RKS noise voltage at Fourierfrequency f from the carrier measured after IF gainG(f) in a noise bandwidth RIJ. Obviously RIJ must besmall compared to f. This is very important whereS~(f) is changing rapidly with f, e.g., S~(f) oftenvaries as f- 3 near the carrier. In Fig. 1, theoutput of the second amplifiQr foLlovins the mixercontains contributions from the phase noise of theoscillators, the noise of the mixers, and the postamplifiers for Fourier frequencies much larger thanthe phase-lock loop bandwidth. In Fig. 2, the phasenoise of the oscillator cancQls out to a high degreelkQThe noise bandwidth of the spectrum analyzer alsoneeds to be verified. This calibration procedure issufficient for small Fourier frequencies but loosesprecision and accuracy due to the problemsillustrated in Fig. 3 and the variations of amplifiergain with Fourier frequency. If measurements need tobe made at Fourier frequencies near or below thephase-lock-loop bandwidth, a probe signal can beinjected inside the phase-lock-loop and theattenuation measured versus Fourier frequency.Some care is necessary to assure that the spectrumanalyzer is not saturated by spurious signals such asthe power line frequency and its multiples.Sometimes aliasing in the spectrum analyzer is aproblem. If narrow spectral features are to bemeasured it is usually recommended that a flat topwindow function (in the spectrum analyzer) be used.In the region where the measured noise is changingrapidly with Fourier frequency, the noise bandwidthshould be much smaller than the measurementfrequency. The approximate level of the noise floorof the measurement system should be measured in orderto verify that it does not significantly bias themeasurements or, if necessary, to subtract its effectfrom the results.Typical best performance for various measurementtechniques is shown in Fig. 4. The two oscillatorapproach exceeds the performance of almost allavailable oscillators from below 0.1 MHz to over 100GHz and is generally the technique of first choicebecause of its versatility and simplicity. Figs. 10- 12 give some examples. Phaae noise measurements onpairs of signal sources can be made with an absoluteaccuracy better than 1 d! using the above calibrationprocedure. Such accuracy is not always attainablewhen the phase noise of the source exceeds that ofthe added noise of the components under test (seeFig. 2). The use of specialized high level mixerswith multiple diodes per leg increases the phase tovoltage conversion sensitivity, K d and thereforereduces the contribution of IF amplifier noise 15] asshown in Fig. 4. Phase noise measurements Cangenerally be made at Fourier frequencies fromapproximately de to 1/2 the source frequency. The434