NIST Technical Note 1337: Characterization of Clocks and Oscillators

7. PHASE NOISE AND AM NOISE MEASUREMENTS 257rms voltage, the noise voltage is in units of volts per square root hertz. whichmeans volts per square root bandwidth. Therefore,Shv(f) = [JVrm,,,,,/B] = (t5v rm ,)2,B, (57)where B is the noise power bandwidth used in the measurement.Because it was assumed that the reference oscillator did not contribute anynoise, the voltage fluctuations V rms represent the oscillator under test, andthe spectral density of the phase fluctuations in terms ofthe voltage measurementsperformed with the spectrum analyzer, in radians squared per hertz, isEquation (46) is sometimes expressed asS•.p(f) = H(l5v rms)2/B{Vrms)2]. (58)5h4>(f) = Shv(f)/K 2 , (59)where K is the calibration factor in volts per radian. For sinusoidal beatsignals. the peak voltage of the signal equals the slope of the zero crossingin volts per radian. Therefore, (V p )2 = 2(V.ms)2, which is the same as thedenominator in Eq. (56).The term S'(f) = 20 log(bvrms) - 20 log(V.ms) - 1010g(B) - J. (60)A correction of 2.5 is required for the tracking spectrum analyzer used inthese measurement systems. !f(f) differs by 3 dB and is expressed in decibels(carrier) per hertz as!f(f) = 20 log(bvrms) - 20 10g(V.ms) - 10 10g(B) - 6. (61)A. Two NOISY OSCILLATORSThe measurement system of Fig. 6 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 oscillators are the same type, a useful approximationis to assume that the measured noise power is twice that associatedwith one noisy oscillator. This approximation is in error by no more than3 dB for the noisier oscillator, even if one oscillator is the major source ofnoise. The equation for the spectral density of measured phase fluctuationsin radians squared per hertz isSh