Nonlinear Dynamics and Chaos in Second Order ZC1- DPLLs with Inherent Time Delay
Madhusudan Ghosh1, Tanmoy Banerjee2, Bishnucharan Sarkar3
1Madhusudan Ghosh, Assistant Professor, Department of Physics, Maulana Azad College, 8, R.A. Kidwai Road, Kolkata , (W.B.), India.
2Tanmoy Banerjee, Assistant Professor, Physics Department, University of Burdwan, Burdwan, (W.B.), India.
3Bishnucharan Sarkar, Professor, Physics Department, University of Burdwan, Burdwan ,(W.B.), India.
Manuscript received on July 17, 2012. | Revised Manuscript received on August 25, 2012. | Manuscript published on August 30, 2012. | PP: 235-242 | Volume-1 Issue-6, August 2012.  | Retrieval Number: F0674081612/2012©BEIESP

Open Access | Ethics and Policies | Cite
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (

Abstract: The present paper examines the dynamics of a delayed second order zero crossing digital phase locked loop (DSZC1-DPLL). Some inherent time delay is inevitable in the loop response due to the non-ideal behaviour of loop digital filter and other constituent blocks. The possibility of chaos and bifurcation in the system has been investigated analytically and numerically. Since the order of the second order loop increases due to loop time delay, the stability limit of the loop will be decreased. Further the inherent time delay in the loop results in period doubling route to chaos. The stability and nonlinear dynamical behaviour of the delayed system has been investigated through standard technique of stability analysis. Chaotic dynamics of the system has been quantified with the help of nonlinear dynamical measures like bifurcation diagram, Lyapunov exponent, Correlation dimension, Kolmogorov entropy etc. 
Keywords: ZC1-DPLL, Loop time delay, Stability Zone, Bifurcation Diagram, Layapunov Exponent, Correlation dimension, Kolmogorov entropy.