A Collocation-Based Algorithm for Analyzing Bifurcations in Phase Locked Loops with Tanlock and Sawtooth Phase Detectors
Joint Authors
Harb, Bassam A.
Al-Ajlouni, Ahmad
Eyadeh, Ali
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-07-04
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Analysis of bifurcation of second-order analog phase locked loop (PLL) with tanlock and sawtooth phase detectors is investigated.
Both qualitative and quantitative analyses are carried out.
Qualitatively, the basin boundaries of the attractors were constructed by plotting the stable and the unstable manifolds of the system.
The basin boundaries show that the PLL under consideration for certain loop parameters has a separatrix cycle which terminates the limit cycle (out-of-lock state) and the loop pulls-in.
This behavior is known in literature as homoclinic bifurcation and the value of the bifurcation parameter where this process occurs is called the pull-in range.
Quantitatively, we propose a collocation-based algorithm to compute the separatrix cycle and the pull-in range.
The separatrix cycle is approximated by a finite set of harmonics N with unknown amplitudes and by utilizing the fact that this limit cycle bifurcates from a separatrix cycle, a system of nonlinear algebraic equations is derived.
For given values of filter parameters and gain, the algorithm numerically solves for the unknown amplitude of the harmonics and the value of the pull-in range simultaneously by evaluating the system at the collocation points.
Results demonstrate that phase locked loop with sawtooth phase detector characteristics has the wider pull-in range followed by tanlock and sinusoidal, respectively.
American Psychological Association (APA)
Harb, Bassam A.& Al-Ajlouni, Ahmad& Eyadeh, Ali. 2018. A Collocation-Based Algorithm for Analyzing Bifurcations in Phase Locked Loops with Tanlock and Sawtooth Phase Detectors. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-7.
https://search.emarefa.net/detail/BIM-1209372
Modern Language Association (MLA)
Harb, Bassam A.…[et al.]. A Collocation-Based Algorithm for Analyzing Bifurcations in Phase Locked Loops with Tanlock and Sawtooth Phase Detectors. Mathematical Problems in Engineering No. 2018 (2018), pp.1-7.
https://search.emarefa.net/detail/BIM-1209372
American Medical Association (AMA)
Harb, Bassam A.& Al-Ajlouni, Ahmad& Eyadeh, Ali. A Collocation-Based Algorithm for Analyzing Bifurcations in Phase Locked Loops with Tanlock and Sawtooth Phase Detectors. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-7.
https://search.emarefa.net/detail/BIM-1209372
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209372