THE ANALYSIS OF SYNCHRONIZED OSCILLATORS BY USE OF PHASE-LOCKED-LOOPS.

The synchronization behavior for an electronic oscillator is examined by the use of a first-order phase-lock-loop PLL model for the oscillator. A Hilbert transform relationship is obtained which relates a known beat waveform between the oscillator and a locking-signal to the other possible beat waveforms as described by Huntoon and Weiss and others. The equivalence between an oscillator and a PLL is established in terms of equivalent locking characteristics. Using this PLL model, beat waveforms are obtained for some specified locking signals. The locking phenomenon between two oscillators is also examined by the use of a PLL model for each oscillator. Finally, the locking characteristics for an oscillator which is frequencly-modulated by a feedback signal is studied, and it is shown that the lock-in width may be increased over that for the oscillator without feedback, or, alternately, the lock-in width may be reduced to zero. This is accomplished with relative ease by adjustment of the feedback parameters. All of the results of this report are verified experimentally as well as theoretically. Author