Asymptotic formulas in nearly sinusoidal nonlinear oscillators

We give an iterative procedure for calculating the steady-state output waveform of nearly sinusoidal nonlinear feedback-oscillators whose order as well as the shape and the degree of the nonlinearity is assumed to be of the greatest generality. The procedure inherits its foundation from the classical perturbation theory and makes it possible to determine both the frequency and the complex amplitude of the harmonics of the oscillation by very simple recurrence formulas, by which a complete analytical representation of the nonlinear oscillation is obtained. These asymptotic formulas are valuable for both the analysis and synthesis purposes. The application of the above formulas to some typical oscillator circuits is given to show their usefulness in practical problems.