NDLI: PLL bifurcation analysis via smooth periodic extension

Content Provider	IEEE Xplore Digital Library
Author	Stensby, J.
Copyright Year	2012
Description	Author affiliation: University of Alabama in Huntsville (Stensby, J.)
Abstract	To aid the acquisition process in an out-of-lock PLL, an external sweep voltage can be applied to the VCO. The goal is to sweep the system state towards a stable lock point. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep rate magnitude, denoted as R $rad/sec^{2},$ for which phase lock is guaranteed. If the actual VCO sweep rate magnitude is less than R, the loop cannot sweep past a stable phase-lock state without locking correctly. This is not true for a sweep rate greater than R. As the sweep rate increases through R, an unstable phase plane 2π-periodic limit cycle bifurcates from a 2π-periodic separatrix cycle. This separatrix cycle must be approximated in order to approximate R. This task is made difficult by the fact that the separatrix cycle has a discontinuous first derivative at each saddle point. To eliminate this problem, the 2π-periodic separatrix cycle is used to construct a smooth (i.e., has a continuous derivative) 4π-periodic solution of an equation derived from the PLL dynamic model. This smooth periodic extension is approximate accurately by a simple finite Fourier series, and an approximation is derived for R.
Starting Page	30
Ending Page	33
File Size	224566
Page Count	4
File Format	PDF
ISBN	9781457714924
ISSN	00942898
e-ISBN	9781457714931
DOI	10.1109/SSST.2012.6195115
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-03-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Phase locked loops Voltage-controlled oscillators Limit-cycles Mathematical model Fourier series Differential equations
Content Type	Text
Resource Type	Article

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