Chaos and bifurcation in a third-order digital phase-locked loop

Banerjee, Tanmoy; Sarkar, B. C.

doi:10.1016/j.aeue.2007.03.001

Cited by 23 publications

(14 citation statements)

References 15 publications

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“…Besides in conventional analog PLLs, the phase locking principle based systems are implemented using charge pump type filters or digital building blocks. The dynamics of these charges pump PLLs and digital PLLs in third order varieties has been extensively studied in the literature [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Oscillations in a Third Order PLL in the Face of Two Co - Channel Signals and Its Control

Sarkar¹,

Chakraborty²

2015

JESTR

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A third order phase locked loop incorporating a resonant type second order filter is a conditionally stable system and shows complicated dynamics including chaotic oscillations for a range of loop parameters. In the face of two co-channel signals, an otherwise stable loop may be thrown into a chaotic state, depending on the relative strength and mutual frequency offset of the input signals. We have predicted the parameter zone for chaotic state of the loop through numerical studies and verified the prediction by hardware experiment. Then we modify the loop structure to incorporate an additional control signal which stabilizes the loop dynamics and removes the chaotic oscillations. The improved response of the loop is established numerically and experimentally.

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Section: Introductionmentioning

confidence: 99%

Chaotic Oscillations in a Third Order PLL in the Face of Two Co - Channel Signals and Its Control

Sarkar¹,

Chakraborty²

2015

JESTR

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“…Although PLL-based circuits are essentially a nonlinear control systems, in modern engineering literature, devoted to the analysis of PLL-based circuits, the main direction is the use of simplified linear models, the methods of linear analysis, empirical rules, and numerical simulation (see a plenary lecture of D. Abramovich at American Control Conference 2002 (Abramovitch, 2002)). While the linearization and analysis of linearized models of control systems may lead to incorrect conclusions 1 , the attempts to justify the reliability of conclusions, based on the application of such simplified approaches, are quite rare (see, e.g., (Suarez and Quere, 2003;Margaris, 2004;Feely, 2007;Banerjee and Sarkar, 2008;Feely et al, 2012;Suarez et al, 2012)). Rigorous nonlinear analysis of PLL-based circuit models is often very difficult task, so for analysis of nonlinear PLL models, numerical simulation is widely used (Troedsson, 2009;Best, 2007;Bouaricha et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Phase-frequency Domain Model of Costas Loop with Mixer Discriminator

Kuznetsov

Леонов

Neittaanmäki

et al. 2013

Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics

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Problem of rigorous mathematical analysis of classical Costas Loop for non-sinusoidal signals is considered. The analytical method for phase detector characteristics computation is proposed and new classes of phase detector characteristics are computed for the first time. Effective methods for nonlinear analysis of Costas Loop are discussed. 1 see, e.g. counterexamples to filter hypothesis and to Aizerman's and Kalman's conjectures on absolute stabil

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“…[28]. Many studies on DPLL reveal that the following variants of DPLLs show chaos and bifurcations: positive zero-crossing DPLL (ZC1-DPLL) [1,3,5,7,17], uniform sampling DPLL [28], bang-bang DPLL [11], dual sampler-based zero crossing DPLL (ZC2-DPLL) [4] and tanlock DPLL [6,13]. Although several variants of DPLLs exist in the literature but zero-crossing DPLL (ZC-DPLL), which is a non-uniform sampling DPLL, is the most popular one due to their less circuit complexity.…”

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confidence: 99%

Application of Time-Delayed Feedback Control Techniques in Digital Phase-Locked Loop

Banerjee

Sarkar

2016

Advances and Applications in Nonlinear Control Systems

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In this chapter we investigate how time-delayed feedback control (TDFC) techniques can be exploited in controlling chaos and bifurcation in a digital phaselocked loop (DPLL) and thus improve its system response. We use both the TDFC techniques: The conventional one and its extended version. Using local stability analysis, two parameter bifurcation studies and two parameter Lyapunov exponent spectrum we explore the nonlinear dynamics of conventional and controlled DPLLs. A condition for the optimum value of the system control parameter is derived analytically for a TDFC based DPLL. We describe the implementation of the extended time-delayed feedback control (ETDFC) technique in a DPLL. It is observed that the application of the delayed feedback control technique on the sampled values of the incoming signal results in the nonlinear time-delayed feedback control on the phase error dynamics. We establish that, for some suitably chosen control parameters, an ETDFC based DPLL has a broader stability zone in comparison with a DPLL and its TDFC version. IntoductionControl of chaos and bifurcation has been an active field of research for the last two decades [9,10,19,25]. By controlling chaos and bifurcation one can suppress the chaotic behavior where it is unwanted (e.g., in power electronics [14,24] and mechanical systems [9]), and on the other hand in electronic systems one can exploit chaos in chaos-based electronic communication systems [15]. The methodology of controlling chaos in dynamical systems was first introduced in [21] and is well known as the OGY method. In the OGY method, a physically accessible parameter is perturbed to stabilize a desired unstable periodic orbit (UPO) embedded in the phase

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Chaos and bifurcation in a third-order digital phase-locked loop

Cited by 23 publications

References 15 publications

Chaotic Oscillations in a Third Order PLL in the Face of Two Co - Channel Signals and Its Control

Chaotic Oscillations in a Third Order PLL in the Face of Two Co - Channel Signals and Its Control

Phase-frequency Domain Model of Costas Loop with Mixer Discriminator

Application of Time-Delayed Feedback Control Techniques in Digital Phase-Locked Loop

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