Behavioral modeling of (coupled) harmonic oscillators

Abstract

A new approach is presented for the construction of behavioral models for harmonic oscillators and sets of coupled harmonic oscillators. The models can be used for system-level simulations and trade-off analysis. Besides the steady state behavior, the model also takes the transient behavior of the oscillation amplitudes and phase differences into account. This behavior is modeled using a set of linear differential equations. Their extraction from a netlist description is based upon the ideas of perturbation analysis and stochastic averaging. The modeling equations are valid in the neighbourhood of the oscillator's steady-state operating point and can be evaluated at very low computational cost. Another major advantage of the approach is that it explicitely separates the fast-varying steady-state behavior and the slow varying transient behavior. This allows for straightforward application of multi-rate simulation techniques, greatly boosting simulation speeds. The technique is illustrated for a quadrature oscillator.