NIST Technical Note 1337: Characterization of Clocks and Oscillators

7. PHASE NOISE AND AM NOISE MEASUREMENTS243where y(c) is the instantaneous fractional frequency deviation from thenominal frequency Vo 'A. NOISE SIDEBANDSNoise sidebands can be thought of as arising from a composite of lowfrequencysignals. Each of these signals modulate the carrier-producingcomponents in both sidebands separated by the modulation frequency, asillustrated in Fig. 2. The signal is represented by a pair of symmetricalsidebands (pure AM) and a pair of antisymmetrical sidebands (pure FM).The basis of measurement is that when noise modulation indices aresmall, correlation noise can be neglected. Two signals are uncorrelaced iftheir phase and amplitudes have different time distributions so that they donot cancel in a phase detector. The separation of the AM and FM componentsare illustrated as a modulation phenomenon in Fig. 3. Amplitude fluctuationscan be measured with a simple detector such as a crystal. Phase or frequencyfluctuations can be detected with a discriminator. Frequency modulation(FM) noise or rms frequency deviation can also be measured with an amplitude(AM) detection system after the FM variations are converted toAM variations, as shown in Fig. 3a. The FM-AM conversion is obtainedby applying two signals in phase quadrature (90°) at the inputs to a balancedmixer (detector). This is illustrated in Fig. 3 by the 90° phase advances ofthe carrier.B. SPECTRAL DENSITYStability in the frequency domain is commonly specified in terms ofspectraldensities. There are several different, but closely related, spectral densitiesthat are relevant to the specification and measurement of stability of thefrequency, phase, period, amplitude, and power of signals. Concise, tutorialCARRIERCARRIERVoCARRIERv v v y, V nIf -Yo VnRADIAN FREQUENCY RADIAN FREQUENCY RADIAN FREQUENCYlal Ib) (c)FIG.2 (a) Carrier and single upper sideband signals; (b) symmetrical sidebands (pureAM); (0) an antisymmetrioal pair of sidebands (pure FM).IN-194