title: Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous  mathematical definitions and limitations of classical theory
metadata.name: dc.contributor.author
metadata.value: G. A. Leonov
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: N. V. Kuznetsov
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: M. V. Yuldashev
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: R. V. Yuldashev
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-07T20:35:34Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-07T20:35:34Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2015-05-16
metadata.lang: -
metadata.name: dc.identifier
metadata.value: 10.1109/TCSI.2015.2476295
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 10.1109/TCSI.2015.2476295
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 10.1109/TCSI.2015.2476295
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1958
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The terms hold-in, pull-in (capture), and lock-in ranges are widely used by
  engineers for the concepts of frequency deviation ranges within which PLL-based
  circuits can achieve lock under various additional conditions. Usually only
  non-strict definitions are given for these concepts in engineering literature.
  After many years of their usage, F.~Gardner in the 2nd edition of his
  well-known work, Phaselock Techniques, wrote "There is no natural way to define
  exactly any unique lock-in frequency" and "despite its vague reality, lock-in
  range is a useful concept." Recently these observations have led to the
  following advice given in a handbook on synchronization and communications "We
  recommend that you check these definitions carefully before using them." In
  this survey it is shown that, from a mathematical point of view, in some cases
  the hold-in and pull-in "ranges" may not be the intervals of values but a union
  of intervals and thus their widely used definitions require clarification.
  Rigorous mathematical definitions for the hold-in, pull-in, and lock-in ranges
  are given. An effective solution for the problem on the unique definition of
  the lock-in frequency, posed by Gardner, is suggested.
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - Dynamical Systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - Dynamical Systems
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous  mathematical definitions and limitations of classical theory
metadata.lang: en_GB
resources.filename: tcasi.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1958/2/tcasi.pdf
resources.format: Adobe PDF
resources.size: 6,57 MB