NIST Technical Note 1337: Characterization of Clocks and Oscillators

7. PHASE NOISE AND AM NOISE MEASUREMENTS245Voga:w~0..FIG.4A power density plot.The spectral density is the distribution of total variance over frequency. Theunits of power spectral density are power per hertz; therefore. a plot of powerspectral density obtained from amplitude (voltage) measurements requiresthat the voltage measurements be squared.The spectral density of power versus frequency, shown in Fig. 4, is a twosidedspectral density because the range of Fourier frequencies f is fromminus infinity to plus infinity.The notation 5if) represents the two-sided spectral density of fluctationsof any specified time-dependent quantity get). Because the frequency bandis defined by the two limit frequencies of minus infinity and plus infinity,the total mean-square f1uctilation of that quantity is defined by+OOGsideband = _ 00 5if) df. (13)fTwo-sided spectral densities are useful mainly in pure mathematical analysisinvolving Fourier transformations.Similarly, for the one-sided spectral density,J+OOGsideband = 0 5 9 (/) df. (14)The two-sided and one-sided spectral densities are related as follows:592 df = 2 {+oo S92 df = {... co 5 dj, (15)91f+oo-00 Jo Jowhere g I indicates one-sided and g2 two-sided spectral densities. It is notedthat the one-sided density is twice as large as the corresponding two-sided