Chaotic behaviour of first order zero crossing digital phase locked loop

The main objective of this paper is to analyze nonuniform zero crossing digital phase locked loop (ZCDPLL) in the unstable (non-convergent) region of its operation. The non-linear behaviour of ZCDPLL shows period doubling or bifurcation instabilities to its route to chaos. The loop has two or more fixed points and the chaos behaviour depends primarily on the values of gain in the loop filter and input frequency offset from the locking value. The chaotic behaviour has been confirmed through the use of phase error spectrum, bifurcation diagram and Lyapunov exponent