 using a shooting or an harmonic balance method. Having computed the Ik, we use (5.144)-(5.162) to obtain the term in (5.162). Averaging this term yields hq,T (q1). Here, averaging comes down to the selection of the DC component of the Fourier series expansion of with respect to T. 5.8.3 Experimental results The model extraction procedure was implemented in Matlab for both a single har- monic oscillator and an harmonic quadrature oscillator. In what follows, we compare the behavioral model's steady-state and transient behavior with results extracted from SPICE-like simulations. All computations were performed in Matlab running on a Pentium IV at 1.7 GHz. 5.8.3.1 Single harmonic oscillator In a first example, we construct a behavioral model for the harmonic oscillator shown in Fig. 5.30. The behavioral model is constructed by precomputing the right-hand side of the averaged ODEs (5.168) for 31 different values of the oscillation amplitude. Model evaluations are based on table lookup and interpolation in between these 31 precomputed values. The oscillator is designed to have its oscillation frequency near 1 GHz. Its feedback transistors are sized such that (5.175) The transistor's (VGs - Vth) - is set to 0.5 V. As shown in Fig. 5.30, the resonant tank model includes several parasitics for both the inductor and capacitor. The MOS tran- sistors are modeled using the EKV equations [Enz95] for a 0.5um CMOS technology. 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING 0.05 S 8.32 pF 0.05 O 1.5 nH 1.5 nH 2.28 S 0.4 L 0.4 O 0.2 pF 0.2 pF Figure 5.30: Harmonic oscillator with a single resonant tank. The tank in- cludes several components that model parasitic behavior of the inductor and capacitor. In a first step, we extract the characteristics of the resonant tank. Without transistor capacitances, the tank is characterized by: (5.176) e = 27/0C -8.04 (5.177) Taking the transistor capacitances into account changes the resonance frequency to fo = 0.986GHz. Note that these capacitances are automatically accounted for if we use the