NIST Technical Note 1337: Characterization of Clocks and Oscillators

FIGURE 8.9'With a PLL, ; f we can maKe the ser'llo timeconstant very lang, then the Pll bandWidth as afiller will be small.This may be done by loweringthe gain A of the loop amplifier. We want tovtranslate the phase modulation spectrum to basebandspectruJI 50 that it is easily measured on alow frequency spectrum analyler. With a PLLfilter, wemust keen in mind that the referenceoscillator sl10uld be as good or better than thetest oscil1ator.1h'iS is because the output ofthe PLL represents the noise from both oscillators.and if nat properly chasen, the reference can ha'llenoise maSKing the noise from the test osc'i 11 atar.Often 1the reference and test asci 11 aters are ofthe same type and have, therefore, apprOXimatelythe same noise. We can acquire a meaningfulmeaSurement by noting t~at the noise we measure isfrom two oscillators.Many times a good approximationis to assume that the noise power is twicethat which is associated with one oscillator.S$(f) is general notation depicting spectral d@nsityon a p@r hertz basis.A PLL filter outputnece$sar;ly yields noise from two oscillators.The output of thE! PLL filter at Fourierfr@quencies abov@ the loop bandwi dth is a vo 1tag@represent ing phase f1 uctuat ions oetwe@n referenceand test osc; 11 ator.1t ; s necessary to mak.e thetime"'constant of the loop long compar@d with th@inverse of th@ lowest Fourier fr@quency woe wiSh tom@asure. That is, te > 2n fclowest)· This meansthat if we want to measure S~(f) down to 1 Hz, theloop time-constant must be gr~~ter tha~ ~ Seconds.One can measur@ the time-constant byperturbing the loop (momentarily disconnecting thebattery is convE!n;@nt) and noting the time ittakes for tt1@contro1 \/01 tage to reach 70% of itsfinal valu@. Th@ signal from the mixer can thenb@ inserted into a spectrum analyzer. A preampmay be necessary before the 50ectrum analyzer.• See Appendix Note , 3*22The analyzer determines the mean square volts thatpass throug~the analyzerls bandwidth centeredaround a pre-chasen Fourier frequency f.desireable to normalize results to a 1 HzIt isbandwidth.Assuming white phase no; se ( ....hite PM),this can be done by dividing the mean squarevoltage by the analyzer bandWidth in Hz.One mayhave to approximate for ather noi!;e processes.(The phase noise sideband levels will usually beindiCAted in rms volts-per-root-Hertz on mostanalyzers. )B.2 Equipment for Frequency !Jomai n Stabi 1i tyMeasurements(1) low-noise mixerThis should be a high quality, douolebalancedtype.,but single-ended typesmay be used. The oscillators shouldhave ~ell-buffered outputs to b@able toisolate the coupling between the twoinput RF ports of the mixer. Results **that are too good may be obtained if th@two oscillators couple tightly viasignal injection through the inputports. We want the PLL to contrallocking. One should read t~e specificationsin order to prevent exceedingth@ maximum allowable input power to themixer.It is best to operate near th@maximum for b@st signal-to-nois@ out ofth@cases~IF port of the mixer and, in someit is possible to drive th@ mixerinto saturation without burning out thedevice.FIGURE 8.10(2) Law-noi,. DC amplifi.rThe amount of gain A needed in the toopvamplifie:r 'Will depend on the amplitudeof th! mixer output and the d@gree of•• See Appendix Note" 4TN-35