5.32) (thin oscillating lines). The upper figure plots the differential output xd(T) while the lower one plots the common- mode output xcm(T). 5.6 AVERAGING emphasizes the fact that solutions to (5.92)-(5.94) average out the high-frequency com- ponents in the oscillator's dynamic behavior. With regard to computational complexity, (5.92)-(5.94) can be solved using a much larger timestep than the starting point equa- tions (5.28)-(5.32) since they directly model the behavior of the dominant slow-varying (averaged) components of the oscillator's dynamics. As a consequence, for this ex- ample, solving (5.92)-(5.94) runs 10 times faster than solving the original equations (5.28)-(5.32). The averaged equations (5.92)-(5.94) can be used for the computation of oscillator's operating point. The oscillator's (averaged) operating-point amplitude Aop and common- mode level Zop are obtained by equaling dA/dt and dz/dt to zero in (5.92) and (5.94). Hence, we solve Aop and Zop from (5.95) (5.96) For the numerical values used to obtain the results in Fig. 5.20, solving (5.95)-(5.96) yields Aop==1.30 (5.97) Zop 1.25 (5.98) By linearizing (5.92)-(5.94) in the neighborhood of these operating-point values, we obtain an affine system of differential equations that allows us to study the oscillator's local dynamic behavior, e.g. the stability of the operating point. As demonstrated in section 5.8, these linearized averaged equations can also serve as compact behavioral models useful for architectural-level exploration and verification. In some cases, the small variations that come on top of the averaged behavior are also of interest. They are, for instance, responsible for the high-order harmonics in the oscillator's output spectrum. Up to first order, these variations are determined by the second term in the averaging transformation (5.84). This term is solved from (5.87) and (5.91). This yields, for instance, (5.99) as an expression for the oscillator's steady-state common-mode behavior. Fig. 5.21 compares the steady-state common-mo