Melnikov Analysis for a Second Order Phase-Locked Loop in the Presence of a Weak CW Interference

Hisa-Aki Tanaka, Shin'ichi Oishi, and Kazuo Horiuchi
IEICE Trans. Fundamentals, Nov. 1994


phase-locked loop, CW interference, Melnikov analysis


This letter presents the results of an analysis concerning the global, dynamical structure of a second order phase-locked loop (PLL) in the presence of the PLL equation are focused and analyzed as to how they are extended from the hyperbolic periodic orbits. Using the Melnikov integral which evaluates the distance between the stable manifolds and the unstable manifolds, the transversal intersection of these manifolds is proven to occur under some conditions on the power of the interference and the angular frequency difference between the signal and the interference. Numerical computations were performed to confirm the transversal intersection of the system-generated invariant manifolds for a practical set of parameters.

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