mple, fo = 1 GHz. The input noise PSD was modeled as in (5.141) with fi/f set to 50kHz. The noise strength was chosen in order for the phase noise spectrum at 1 MHz to equal - 130 dBc/Hz. These values correspond to typical (recent) designs, e.g. [Demu02]. Fig. 5.27 plots Sx,1 (Af) for values of r anging from 0.5 Hz to 5 kHz. For small values of 8, i.e. for the second term in (5.141) becoming more 1/f-like, the very-close-in phase noise spectrum flattens with a steep edge mak- ing the transition from the DC level to the familiar 1/Af3 - 1/Af2 characteristic. In this example, this edge is located between 300 Hz and 1 kHz. 5.8 Harmonic oscillator behavioral modeling We end this discussion on oscillators with a method for the construction of compact behavioral models for harmonic oscillators and sets of coupled harmonic oscillators [Vana03b]. The models are useful to speed up lengthy or repetitive system-level ver- 5.8.1 Model extraction theory R10ss R10ss Figure 5.28: It is assumed that the oscillator circuit can be mapped onto a template consisting of K weakly interconnected lossless resonant tanks. The figure shows a template for K = 2. ification and trade-off analysis. The model extraction procedure builds on the theory outlined in previous sections. The resulting models capture an oscillator's dynamic behavior by means of the averaged state-changing equations. The computational cost needed to evaluate them is well below that of solving the original circuit equations. The models also separate slow- and fast-varying behavior. As a result, they can be integrated using a large time step. Experimental results are presented for both a single harmonic oscillator and a harmonic quadrature oscillator. 5.8.1 Model extraction theory The method assumes that the oscillator circuit can be mapped onto the template in Fig. 5.28. The template consists of K lossless resonant tanks and a number of controlled current sources. The current sources are assumed to be weak: the amount of energy they inject per oscillation period into th