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.