Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large
Leonov, G.A., Kuznetsov, N., Yuldashev, M., & Yuldashev, R. (2015). Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large. Signal Processing, 108(March 2015), 124-135. https://doi.org/10.1016/j.sigpro.2014.08.033
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Signal ProcessingDate
2015Copyright
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC
BY license.
The analysis of the stability and numerical simulation of Costas loop circuits for highfrequency
signals is a challenging task. The problem lies in the fact that it is necessary to
simultaneously observe very fast time scale of the input signals and slow time scale of
phase difference between the input signals. To overcome this difficult situation it is
possible, following the approach presented in the classical works of Gardner and Viterbi,
to construct a mathematical model of Costas loop, in which only slow time change of
signal's phases and frequencies is considered. Such a construction, in turn, requires the
computation of phase detector characteristic, depending on the waveforms of the
considered signals. While for the stability analysis of the loop near the locked state (local
stability) it is usually sufficient to consider the linear approximation of phase detector
characteristic near zero phase error, the global analysis (stability in the large) cannot be
accomplished using simple linear models.
The present paper is devoted to the rigorous construction of nonlinear dynamical
model of classical Costas loop, which allows one to apply numerical simulation and
analytical methods (various modifications of absolute stability criteria for systems with
cylindrical phase space) for the effective analysis of stability in the large. Here a general
approach to the analytical computation of phase detector characteristic of classical Costas
loop for periodic non-sinusoidal signal waveforms is suggested. The classical ideas of the
loop analysis in the signal's phase space are developed and rigorously justified. Effective
analytical and numerical approaches for the nonlinear analysis of the mathematical model
of classical Costas loop in the signal's phase space are discussed.
...
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Elsevier BV; European Association for Signal ProcessingISSN Search the Publication Forum
0165-1684Keywords
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Except where otherwise noted, this item's license is described as © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC
BY license.
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