Synchronization of Oscillators by Periodically Interrupted Waves

This paper describes the principles, methods, circuit applications, and the theoretical basis of the synchronization of LC oscillators by interrupted wave trains. The synchronizing process is shown to depend upon the transient behavior of the phase angle between two vectors which represent, respectively, the instantaneous voltage of the oscillator and the corresponding instantaneous voltage of the injected synchronizing signal. This phasing action is employed in the derivation of formulas by means of which it is possible to define the regions of synchronization due to each of the several significant frequency components of the interrupted wave train. The term interrupted wave train as used herein refers to a cw signal which is interrupted (gated) in a periodic manner. The resultant signal, as herein demonstrated by theoretical and experimental means, can produce a form of synchronization such that the average frequency of the oscillator is identically equal to the fundamental component of the synchronizing signal or to any selected sideband. Phase modulation of determinable magnitude is shown to exist in the synchronized oscillator and analyses are included which permit evaluation of the frequency spectrum of the output. Particular emphasis is given to the band of synchronization due to a cw signal of the same amplitude as the interrupted signal. This band, a measure of frequency, is used as a convenient unit when comparing the synchronizing action of various forms of synchronizing signals.