Frequency Pulling of the van der Pol Oscillator

Abstract

<p> The frequency pulling of the van dcr Pol nonlinear oscillator due to an external forcing signal is investigated. The nonlinearity is of the zero-memory symmetric-cut-off type following a cube law.</p> <p> An experimental oscillator was built, and curves of the frequency shift of the oscillator fundamental against the magnitude of the input forcing signal are shown, both for a sinusoidal input and for a narrow band noise input. An empirical result is derived.</p> <p> The case of the sinusoidal input is examined theoretically. The importance of harmonic and intermodulation frequencies in the oscillator output is shown, and relations giving the oscillator frequency shift are given for small forcing amplitudes and for large amplitudes when the oscillator is nearly synchronized.</p>