A Collocation-Based Algorithm for Analyzing Bifurcations in Phase Locked Loops with Tanlock and Sawtooth Phase Detectors
المؤلفون المشاركون
Harb, Bassam A.
Al-Ajlouni, Ahmad
Eyadeh, Ali
المصدر
Mathematical Problems in Engineering
العدد
المجلد 2018، العدد 2018 (31 ديسمبر/كانون الأول 2018)، ص ص. 1-7، 7ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2018-07-04
دولة النشر
مصر
عدد الصفحات
7
التخصصات الرئيسية
الملخص 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.
نمط استشهاد جمعية علماء النفس الأمريكية (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
نمط استشهاد الجمعية الأمريكية للغات الحديثة (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
نمط استشهاد الجمعية الطبية الأمريكية (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
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1209372
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر