me variable t. For sufficiently large Af, (5.139) can be further approximated as (5.140) This expression is consistent with the well-known 1/Af3-1/Af2 characteristic. More- over, (5.139) unifies the two distinct high- and low-frequency asymptotes presented in [Dem98] in a single expression. For slow-varying (1/f) input noise sources, the validity of (5.139) -and therefore also that of the low-frequency asymptote in [Dem98]- breaks down for small frequency offsets Af. For such cases, we propose (again, see [Vana03c]) a method that refines (5.139) by means of a routine based on exponential data fitting. In performing the numerical computations, the PSD of the averaged noise process () is assumed to equal a combination of white and 1/f noise, i.e. (5.141) Here, fi/f is the input noise 1/f corner frequency, i.e. the frequency (in Hz) beyond which the PSD of the 1/f input noise drops below the white noise level. Furthermore 4This expression is somewhat different from the one presented in [Vana03c]. These differences arise from the fact that, contrary to [Vana03c], this dissertation performed computations with respect to the normalized time variable T = 2ft. We therefore need some de-normalizations to obtain the phase-noise spectrum. 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING Y=5 kHz r=500 Hz y=50 Hz y=5 Hz y=0.5 Hz Figure 5.27: Phase noise spectrum Sx, (Af) around carrier frequency. The spectrum is shown for different values of y For small values of Y, the very close-in phase noise spectrum flattens with a steep edge that makes the tran- sition from the DC-level to the familiar 1/Af3-1/Af2 - characteristic. the parameter Y represents the frequency whereby, for f -> 0, the characteristic of the second term in (5.141) goes over into a flat one with Snn(0) = N [1+4f1/f/Y] This 1/f noise model was borrowed from [Dem98, Kae90]. The algorithm mentioned above was used to compute Sx,1(Af), the phase-noise spec- trum around the carrier frequency. The computation of a single spectrum finished in less than a minute. In this exa