Tutorial on dynamic analysis of the Costas loop

Best, Roland; Kuznetsov, Nikolay V.; Леонов, Г. А.; Yuldashev, M. V.; Yuldashev, R. V.

doi:10.1016/j.arcontrol.2016.08.003

Cited by 59 publications

(51 citation statements)

References 27 publications

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“…It is also assumed that the initial states of LPF in the loop do not affect its stability (because for the properly designed filters, the effect of the initial states on the output decays exponentially with time) [32]. It is also assumed that the initial states of LPF in the loop do not affect its stability (because for the properly designed filters, the effect of the initial states on the output decays exponentially with time) [32].…”

Section: Phase-locked Loop In Phase Domainmentioning

confidence: 99%

“…The working ranges of PLLs under different conditions have been rigorously defined in [32]. Hence, Type-1 PLLs will have finite loop gain while PLLs of Type-2 and above will have infinite values, theoretically.…”

Section: Loop Gain and Working Rangesmentioning

confidence: 99%

“…The analysis in this work assumes that the phase d does not leave the range (− , ). It is also assumed that the initial states of LPF in the loop do not affect its stability (because for the properly designed filters, the effect of the initial states on the output decays exponentially with time) [32]. The characteristics are shown in Figure 4 where they can also be classified as non-monotonic, sector-bounded, and slope-bounded nonlinearities.…”

Section: Phase-locked Loop In Phase Domainmentioning

confidence: 99%

“…Hence, Type-1 PLLs will have finite loop gain while PLLs of Type-2 and above will have infinite values, theoretically. The working ranges of PLLs under different conditions have been rigorously defined in [32]. The work in this paper however narrows down to the condition where the interval of the working ranges contains frequency deviation of zero, which is of more practical interest.…”

Section: Loop Gain and Working Rangesmentioning

confidence: 99%

See 3 more Smart Citations

Robust stability analysis and improved design of phase‐locked loops with non‐monotonic nonlinearities: LMI‐based approach

Ahmad

2017

Circuit Theory & Apps

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Due to nonlinear nature of several phase detectors, linear approximation method often leads to performance degradation in many phase-locked loops (PLLs), particularly when the phase errors are sufficiently large. A third or higher order PLL, in spite of the ability to track a wider variety of inputs and having higher operatingfrequency range, requires more design attention in order to ensure stable tracking. In this work, with the nonlinearities inserted into the system's model, suitable criteria that take into account the nonlinearities' non-monotonicity, sector and slope bounds are employed to establish robust stability conditions. The result is applicable to any PLLs without order and type restrictions. For Type-1 PLLs, the resulting condition can be used to search for the maximum stable loop gain, which is also linked to the lock-in range of the system. In the later part of this work, the focus is devoted towards designing PLLs with high lock-in range, which is performed via mixing the proposed method with H ∞ synthesis. The searches for the parameters in both PLL analysis and design are expressed in terms of convex linear matrix inequalities, which are computationally tractable. To illustrate the improvement introduced via this approach, several numerical examples and simulations are included with comparisons over conventional methods. Remark 2Solving the optimization problem in (13) with c set to unity gives K L = k 0 . The significance of this is that it directly reduces the complexity of the LMI search for higher values of c where the solution is only k 0 c . This is useful particularly when n is large, which often leads to numerical issues.

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Section: Phase-locked Loop In Phase Domainmentioning

confidence: 99%

Section: Loop Gain and Working Rangesmentioning

confidence: 99%

Section: Phase-locked Loop In Phase Domainmentioning

confidence: 99%

Section: Loop Gain and Working Rangesmentioning

confidence: 99%

See 2 more Smart Citations

Robust stability analysis and improved design of phase‐locked loops with non‐monotonic nonlinearities: LMI‐based approach

Ahmad

2017

Circuit Theory & Apps

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“…For the past 50 years, the PLL has been contributing to the advancement of technology, particularly in the fields of communications and servo motor control systems [3]. PLLs can generally be used to demodulate a signal, track a carrier signal, synthesize a frequency, or distribute full-time clock pulses in microprocessors [4].Another PLL method is Costas loop and is currently used for wireless communications, Global Positioning Systems (GPSs), and others [5]. It is also utilized in the demodulation of the binary phase shift keying (BPSK) signals [1].…”

Section: Introductionmentioning

confidence: 99%

The Phase-Locked Loop and Costas Loop

Yakut

2017

ijcrr

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Abstract:In this study, the classical phase-locked loop (PLL) and Costas loop are investigated together. How the synchronization is obtained by the carrier recovery from the sinusoidal reference signal is mathematically shown with some assumptions and presented. It is concluded from this paper that Costas loop produces about half of the error signal produced by the PLL in the locked-stateoperation. This result may affect the decision whether the Costas loop will be used more frequently in the phase coherent communication systems in the future.

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