Bifurcation analysis for third-order phase-locked loops
Tipo
Carta ao editor
Data de publicação
2004
Periódico
IEEE Signal Processing Letters
Citações (Scopus)
31
Autores
Monteiro L.H.A.
Filho D.N.F.
Piqueira J.R.C.
Filho D.N.F.
Piqueira J.R.C.
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Resumo
Second-order phase-locked loops (PLLs) are extensively used in applications related to recovering clock signals for synchronous demodulation in telecommunication networks. In situations where an improvement of the transient response of the local clocks is necessary, third-order PLLs are employed. Here, we use concepts taken from dynamical system theory for analytically determining the capture range of three nonlinear third-order PLLs subject to a ramp input. We show that saddle-node, saddle-saddle, and Hopf bifurcations can be produced by varying the values of the input signal velocity and of the PLL parameters, providing criteria for designing such PLLs.
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Assuntos Scopus
Bifurcation analysis , Hopf bifurcation , Saddle-node bifurcation , Saddle-saddle bifurcation , Signal velocity , Third order phase locked loops , Transient response