Forced oscillations in oscillator circuits, and the synchronization of oscillators

The behaviour of a feedback oscillator circuit under the influence of an injected tone having a frequency close to the natural frequency of oscillation is considered from the point of view of the steady-state equilibrium of the loop transmission circuit. The conditions for the absence or suppression of the free oscillation and for the stability of the forced oscillation are found. The application of the principles to certain common types of oscillator is discussed, and the effect of impurities in the injected tone is outlined.