 computational procedure outlined in section 5.8.2. Next, we construct the (normalized) equations that govern the behavior of the averaged state vector (5.178) This yields the system of ODEs (5.179) (= ho(A) (5.180) Note that averaging removes the right-hand-side's dependency on the phase 0. Fig. 5.31 plots both ha(A) and he(A) as a function of the averaged amplitude. The upper figure 5.8.3 Experimental results Figure 5.31: Right-hand sides of the ODEs (5.179) and (5.180) that gov- ern the behavior of the resonant tank's averaged amplitude and phase. The vertical line indicates the position of the stable operating point. shows ha(A) to contain two operating points: an unstable one at Aop = 0 and a stable one at Aop = 1.69. Only the latter is of interest. It is indicated by the vertical line in Fig. 5.31. For this operating point, we notice from equation (5.180) that A(t) = he (Aop) T. Hence, the interactions between the resonant tank and the feedback elements cause a slight shift in oscillation frequency. To verify the accuracy of the averaging method, we compare the oscillator's steady- state differential output voltage as computed using the (normalized) signal model xs(t)=A(t)cos(t+ ((())) (5.181) and the averaging transformation A(T) = (5.182) O(T) = (5.183) with the solutions of the original circuit equations. The latter are obtained by means of a SPICE-like algorithm. The transformation (5.182)-(5.183) is evaluated at the stable operating point Aop = 1.69. Table 5.2 lists the magnitudes of the fundamental tone and the first few odd harmonics (the even harmonics are negligible). The magnitude of the fundamental component is 1% (0.1 dB) accurate. The other components are 0.5- 1.5 dB accurate. This shows that the steady-state behavior of the averaged equations corresponds with that of the circuit equations. 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING Harmonic Averaged SPICE-like 4.58 dB 4.68 dB -33.2 dB -32.1 dB -46.8 dB -46.4 dB -60.6 dB -59.0 dB Table 5.2: Spectral components of the steady-state differential 