The stability of a first-order phase-locked loop with interfering signal input

This paper is concerned with the stability of a first-order phase-locked loop (PLL) with an input consisting of a desired and an undesired (interfering) sinusoidal signal. This PLL is analyzed for the value of the normalized PLL detuning parameter w_Δ´ < 1. This case has been neglected in previous studies. Intuitively, for w_Δ´ < 1, phase lock to the desired signal can never be achieved. However, by using numerical methods, the author shows that in some situation, this PLL is stable for a range of w_Δ´ < 1, and the difference between the two input sinusoidal signals in the initial phase has no effects on the stability of the PLL. It is concluded that phase lock can possibly be achieved even if w_Δ´ < 1.