oint values. The initial phase difference deviates 10% from its steady-state value. It is observed that the results predicted by the model are in good agreement with circuit- level behavior (to within 5%). Furthermore, simulations run about 30 times faster when using the behavioral model. Hence, use of the behavioral model significantly boosts simulation speed, even when compared to circuit simulations that use low- complexity transistor models (MOST level 1) instead of sophisticated models (BSIM4, MOS Model 11). Finally, as an interesting application of the behavioral model (5.187)-(5.188) we men- 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING -0.05 -0.15 Re(E) Figure 5.36: Loci of the oscillator eigenvalues (of the matrix Amodel) plotted in the complex plane for y=0.5 = and m = 0 4. The locus of the third eigen- value, indicated by the crosses, lies entirely on the real axis. The hatched area marks the region of instability. If one of the eigenvalues enters this region, then the operating point around which linearization took place is unstable. tion its use as an aid to optimize the design of an oscillator's dynamic behavior. With regard to this issue, it is particularly interesting to plot the loci of the eigenvalues of the matrix Amodel in (5.187)-(5.188) [Vana01c]. As illustrated in Fig. 5.36, this is ac- complished by computing Amodel and its eigenvalues over a range of values for one of the design parameters Q, Y or m. The eigenvalues of Amodel entirely characterize oscillator's dynamics near the corresponding operating point. Their real values corre- spond to the oscillator's settling time while their complex parts, for instance, indicate the presence of ringing Furthermore, if one of the eigenvalues enters the right half of the complex plane (the hatced area in Fig. 5.36), then this indicates that the operating point around which linearization took place is unstable. Hence, loci like the ones in Fig. 5.36 are of great value in making design decisions, e.g. in determining a suitable value for the coupling pa