Response of a first-order phase locked loop to two sinusoidal inputs

Phase locked loops (PLLs) exhibit various tracking phenomena when subject to an input consisting of the sum of a desired and an interfering sinusoidal signal. Previous analysis of the first-order phase locked loop response has defined values of amplitude ratio and frequency difference for which the PLL tracks either the desired signal, the interfering signal or neither (Oie, T. et al., IEICE Trans. Fundamentals, vol.E77-A, no.11, p.1771-6, 1994). However, the previous analysis is incomplete and we present a further analysis of the first order PLL response to the sum of sinusoidal signals. Specifically, the nature of the PLL at points of saddle-node bifurcation when tracking the desired and interfering signals, and the Poincare map, are analyzed.