de behavior predicted using (5.99) with that computed by solving (5.28)-(5.32). The figure illustrates a clear correspondence be- tween both results. Deviations are due to perturbation effects of second and higher order that are not accounted for by the first-order analysis presented in this text. In magnitude, the RMS value of this error equals about 1/Q of the RMS value of the high-frequency steady-state common-mode variations z(T) - Zop. Hence, in this exam- ple, due to the low Q-factor, use of first-order analysis introduces an error with an en- ergy that lies about a factor 10 below that contained in the high-frequency variations. Figure 5.21: Common-mode steady-state variations respectively obtained us- ing first-order averaging (solid line) and by solving (5.28)-(5.32) (dashed line). The dashdot line denotes the averaged operating-point common-mode level Zop. By taking a closer look at the harmonic content of the common-mode steady-state variations, it is observed that the error energy is mainly located at high frequencies. Table 5.1 lists the energy contained in the first couple of even harmonics (the odd ones are negligible). Values are given based on results respectively predicted by first-order averaging and SPICE-like evaluation of (5.28)-(5.32). These results clearly indicate good agreement for the low-order harmonics. Significant deviations only occur from the 6th harmonic on. A final example that demonstrates the accuracy of the equations (5.92)-(5.94) follows from (5.93). This equation models the impact that perturbations have on the oscillator's phase and frequency. For example, the averaged unnormalized effective oscillation frequency equals (5.100) where wo = 1/VLC. Up to first order, the small (transistor) capacitances C (see Fig. 5.9) decrease the oscillation frequency by woCg/4C. This corresponds with Weffective 1 (5.101) Here, instead of being treated as perturbations, the C8 are taken into account as part of the resonant tank capacitance. 5.7 OSCILLATOR PHASE (NOISE) ANALYSIS Harmonic Aver