A theoretical analysis of phase shift in pulse injection-locked oscillators

In this paper, the amount of phase shift with result of the pulse injection is derived mathematically and verified by simulation. The resultant phase shift is proportional to injection pulse width, and inversely proportional to on-resistance of the switch and total capacitance parallel to injection transistor. In addition, phase shift has sinusoidal form with two times the oscillation frequency. Furthermore, locking range can be estimated using the amount of the maximum resultant phase shift. Thereby, it is verified that pulse injection-locked oscillators using shorting scheme have two locking points in one period.