investigating the effect of voltage controlled oscillator delay on the stability of phase lock loops

In this paper, the effects of the delay caused by the frequency change in self-priming locking oscillators are investigated in the phase lock loops. self-injected locking phenomena in oscillators are used to reduce phase noise and more sustainability. instead of using an external signal in an intruder lock, part of the output signal itself is returned to the oscillator again. in this case, the time required to restore the circuit after the injection of the external frequency is important, especially when this oscillator is used in the shape of a phase lock loop. this delay has the ability to unstable the phase lock loop. in this paper, the stability requirements for phase locking loops with delayed oscillators are fully investigated and the results are validated by simulation.