 from the figure, if the simulation time span grows large, then SPICE-like simulations tend to take minutes and even hours while the behavioral model still evalu- ates within seconds or minutes. Hence, use of the behavioral model becomes more and more advantageous when the total simulation time span grows large. Lengthy (or large numbers of short) simulations frequently occur in design practice: just think about sys- tem optimization methods that require us to run simulations in a loop, system-level verifications that run over many periods of the high-frequency carrier (oscillation) sig- nal and the simulation of the startup behavior of oscillators with a really large settling time (e.g. when using a crystal resonant tank). As indicated by the dashed lines in Fig. 5.33: if, for the setup in this example, you want to avoid having to wait longer 5.8.3 Experimental results Figure 5.32: Harmonic oscillator startup behavior. The fast-oscillating line is the solution of the original circuit equations. The envelope solves the av- eraged system (5.179)-(5.180). The results agree to within 1%. CPU time 1000 minutes 100 minutes 10 minutes 1 minute 6 seconds Tsim/Toscillation 10000 Figure 5.33: CPU time versus the normalized length of the simulation time span. For lengthy or repetitive simulations that run over a large number of oscillation periods, use of the behavioral model reduces simulation times from hours to minutes. 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING Rloss Rloss HM M1 M2 -V- M1 M2 V1 Figure 5.34: Harmonic quadrature oscillator topology. Tank losses are mod- eled by means of the parallel resistor Rloss. than 10 minutes for the simulation results to be ready, then you should switch to the use of the behavioral model as soon as the simulation runs over a time span that exceeds 300 periods of the oscillation signal. 5.8.3.2 Harmonic quadrature oscillator In a second example, we construct a behavioral model for the harmonic quadrature oscillator in Fig. 5.34. The model corresponds to the linearized averaged ODEs