Exploitation of the phasor approach for closed-form solution of the Van der Pol's oscillator and sinusoidal oscillators with high-order nonlinearity

In this paper the phasor approach is applied to find the solution of the well-known Van der Pol's equation for both quasi-sinusoidal and relaxation oscillation regimes. It allows to find simple closed-form relationships for the output harmonics of a LC oscillator whose behavior is described by the Van der Pol's equation. Furthermore, the validity of the phasor approach is extended to analyze also oscillators with nonlinearity of order higher than three. As an example a LC oscillator with a polynomial nonlinearity of fifth order is considered and closed-form relationships for the output harmonics are found. The analysis developed, both for the Van der Pol's equation and for oscillators with high-order nonlinearity, is verified by means of simulations performed with Spectre.