Handbook of Frequency Stability Analysis

The power spectral density of the phase fluctuations in units of rad²/Hz is given by S φ (f) = (2πν 0 )² · S x (f), where ν 0 =carrier frequency, Hz.PSD of Time Fluctuations S x (f)The power spectral density of the time fluctuations x(t) in units of sec²/Hz is given by S x (f) = h(β) · f β = S y (f)/(2πf)²,where: β = α−2. The time fluctuations are related to the phase fluctuations by x(t) = φ(t)/2πν 0 . Both are commonlycalled “phase” to distinguish them from the independent time variable, t.SSB Phase Noise £(f)The SSB phase noise in units of dBc/Hz is given by £(f) = 10 · log [½ · S φ (f)]. This is the most common function usedto specify phase noise.6.3. Phase Noise PlotThe following diagram shows the slope of the SSB phase noise, £(f), dBc/Hz versus log f, Fourier frequency, Hz forvarious power law noise processes.£(f),-60-80-100RWFM-40SSB Phase Noise Diagramα = -2FlickerFMS y(f) ∼ f αα = -1α = -1 -μS φ(f) ∼ f β β = α -2£(f) = 10·log 10[½· S φ(f)]-120dBc/Hz-140-160-30Slopes indB/decadeWhiteFM-20α = 0Flicker PM α = 1White PMα = 20 1 2 3 4 5log f, Hz-10Figure 31. SSB Phase Noise Plot.06.4. Spectral AnalysisSpectral analysis is the process of characterizing the properties of a signal in the frequency domain, either as a powerspectral density for noise, or as the amplitude and phase at discrete frequencies. Spectral analysis can thus be appliedto both noise and discrete components for frequency stability analysis. For the former, spectral analysis complementsstatistical analysis in the time domain. For the latter, spectral analysis can aid in the identification of periodiccomponents such as interference and environmental sensitivity. Time domain data can be used to perform spectralanalysis via the Fast Fourier Transform (FFT), and there is much technical literature on that subject [2,3]. While, inprinciple, time and frequency domain analyses provide equivalent information, in practice, one or the other is usually69