IX. POWERLAW NOISE PROCESSES Powerlaw noise processes are models of precision oscillator noise that produce a particular slope on a spectral density plot. We often classify these noise processes into one of five categories. For plots of Sf (f), they are: 1.Random walk FM (random walk of frequency), Sf plot goes down as 1/f^{4}. 2.Flicker FM (flicker of frequency), Sf plot goes down as 1/f^{3}. 3.White FM (white of frequency), Sf plot goes down as 1/f^{2}. 4.Flicker PM (flicker of phase), Sf plot goes down as 1/f. 5.White PM (white of phase), Sf plot is flat. Power law noise processes are characterized by their functional dependence on Fourier frequency. Equation 8.7 relates Sf (f) to S_{y}(f), the spectral density of frequency fluctuations. Translation of S_{y}(f) to timedomain data s _{y}(t ) for the five model noise processes is covered later in section XI. Figure 9.1: Powerlaw noise is indicated by a particular slope in the phasenoise measurement. The spectral density plot of a typical oscillator's output usually is a combination of different powerlaw noise processes. It is very useful and meaningful to categorize the noise processes. The first job in evaluating a spectral density plot is to determine which type of noise exists for a particular range of Fourier frequencies. It is possible to have all five noise processes being generated from a single oscillator, but, in general, only two or three noise processes are dominant. Figure 9.1 is a graph of Sf (f) showing the five noise processes on a loglog scale. Figure 9.2 shows the spectral density of phase fluctuations for a typical highquality oscillator. Figure 9.2: Different powerlaw noises have different causes in an oscillators output signal.
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