Behavioral modeling of (coupled) harmonic oscillators

This paper presents a method for constructing behavioral models for harmonic oscillators and sets of coupled harmonic oscillators. These models are useful for system-level simulations and tradeoff analysis. The modeling method allows capturing the steady-state and transient behavior of the target oscillators through a sequence of transformations of the circuit equations. Model extraction is based on ideas of perturbation analysis and averaging. The resulting models are evaluated at a computational cost that is well below that of solving the original circuit equations. Another major advantage of the approach is the explicit separation of the slow- and fast-varying components of the oscillator's behavior. This allows using a much larger time step during numerical simulations. The technique is illustrated for both a single harmonic oscillator and a harmonic quadrature oscillator.