TY - JOUR

T1 - Rigorous mathematical definitions of the hold-in and pull-in ranges for phase-locked loops

AU - Kuznetsov, N. V.

AU - Leonov, G. A.

AU - Yuldashev, M. V.

AU - Yuldashev, R. V.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Various ranges of frequency deviation are widely used by engineers to describe frequency deviations for which the PLL-based circuits achieve lock under some additional conditions. In engineering literature, as a rule, the non-rigorous explanations of such ranges are given. In this paper it is shown that the considered frequency deviation ranges need not be intervals and, strictly speaking, should be defined as sets. Rigorous mathematical definitions of hold-in and pull-in sets are given. Example, showing that the use of the term “range” need additional clarification for high order loop filters, is demonstrated.

AB - Various ranges of frequency deviation are widely used by engineers to describe frequency deviations for which the PLL-based circuits achieve lock under some additional conditions. In engineering literature, as a rule, the non-rigorous explanations of such ranges are given. In this paper it is shown that the considered frequency deviation ranges need not be intervals and, strictly speaking, should be defined as sets. Rigorous mathematical definitions of hold-in and pull-in sets are given. Example, showing that the use of the term “range” need additional clarification for high order loop filters, is demonstrated.

KW - hold-in range

KW - hold-in set

KW - linear analysis

KW - phase-locked loop (PLL)

UR - http://www.scopus.com/inward/record.url?scp=84992484471&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2015.09.272

DO - 10.1016/j.ifacol.2015.09.272

M3 - Article

AN - SCOPUS:84992484471

VL - 48

SP - 710

EP - 713

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8971

IS - 11

ER -