hase differences. A second com- ponent contains the common-mode phase 0. Writing the system of ODEs (5.162), governing the behavior of the state vector q=[q]e], in terms of q1 and 0 yields (5.167) Here, we deliberately partitioned the right-hand side in two terms. The first one, hq,T , is typically largest in magnitude and captures the action of tank losses, non-stochastic transistor currents and resonant frequency mismatches. This component is periodic in the normalized time variable T with a period T = 2 The second component, Ahq, is typically much smaller than hq,T and captures, for instance, (transistor) noise or other signal sources. The averaged ODEs corresponding to (5.167) are (5.168) Since hq,T (q1, T+0) is periodic in T, the average of the first term does not explicitly depend on the common-mode phase 0. For stable oscillators, the averaged oscillation amplitudes and phase differences, i.e. the elements of q1, converge to the neighborhood of a constant operating point value q1,op* This operating point is solved from hq1,T (11,op) =0. (5.169) Here hq1,7 contains the first (2K - 1) rows of hq,T. Near the operating point, we capture the oscillator's dynamic behavior by means of approximations of the averaged equation (5.168). The simplest approximation is based on linearization. Section 5.8.3.2 illus- trates the accuracy of these linearized models for an harmonic quadrature oscillator. More sophisticated approximators use multivariate polynomial regression, radial basis functions or support vector machines. 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING V2 I2 Figure 5.29: Harmonic quadrature oscillator measurement setup. Here, the voltage sources V1 and V2 are introduced for the purpose of extracting the resonant tank characteristics and the currents t) ex- changed between the resonant tanks and the remainder of the circuit. The voltage sources should therefore not be considered as part of the oscillator circuit. 5.8.2 Numerical computations Finally, we discuss the numerics that are needed to put the above th