Injection locking of oscillators

An oscillator can be locked in frequency by an external signal which is injected into the oscillator. In the oscillator model developed by Adler 1], the mechanism of the locking process depends upon the following. 1) The initial frequency difference between the oscillator and external signals. 2) The relative amplitude between the injected and the oscillator signals. 3) The circuit parameters. There are cases when the time required for locking must be known, particularly when an oscillator is being locked to a pulsed signal. In this paper, the work of Adler is extended to develop an equation which is useful for higher levels of locking signal, a case often encountered when an oscillator is being injection locked by a pulsed signal. Because the solution of this equation is unwieldy and difficult to understand intuitively, except in very special cases, curves describing the locking mechanism were obtained using a digital computer. These curves enable a designer to construct oscillators which will provide a desired performance. The curves were checked experimentally and showed a close agreement between predicted and measured results. The experimental data indicates that the theory describes the locking time remarkably well even at high levels of locking signal.