Algorithm for solving a class of phase-lock-loop equations

Hasan, P.

doi:10.1049/el:19830107

Cited by 5 publications

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“…A comparative evaluation of α for the triangular and the sawtooth PD nonlinearities has revealed appreciable differences only for low-gain phase-locked loops (β/2<ζ<β) with low damping factors. The worst-case estimate of the normalized frequency acquisition time eo n t w has been evaluated via numerical solutions to the nonlinear integral equation of the acquisition process for N =100 equally spaced samples of the initial phase [8], and the normalized FAR a(i w = i 0 ) has been calculated by an iterative procedure. 3 and 4 for the common damping of ζ = 0.707 apply equally to both the piecewise linear PD characteristics considered.…”

Section: Frequency Acquisition Rangementioning

confidence: 99%

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On the Frequency Acquisition Performance Evaluation of Phase-Locked Loops

Hasan¹

1990

Frequenz

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The statistical definition of the frequency acquisition range (FAR) is introduced. The superiority of the newly proposed performance measure over the traditional pull-in limits is demonstrated, and the frequency acquisition performance of second-order phase-locked loops is evaluated via the FAR. The results obtained using a simple approximate method are confirmed by the exact time domain analysis of the acquisition process.Übersicht: Die statistische Definition des Einrastbereichs (FAR) wird eingeführt. Die Vorzüge des letzthin vorgeschlagenen Bewertungsmaßes gegenüber den traditionellen Pull-in-Grenzen werden bewiesen, und das Einrastverhalten von Phasenregelkreisen zweiter Ordnung wird durch den Einrastbereich abgeschätzt. Die mit einer einfachen approximativen Methode gewonnenen Ergebnisse werden durch die exakte Analyse des Einrastvorgangs im Zeitbereich bestätigt.Für die Dokumentation:

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Section: Frequency Acquisition Rangementioning

confidence: 99%

“…The ratio £ = «PLgm «S (8) where « PL and a s apply to the piecewise linear and the sinusoidal PD characteristics, respectively, is for ω η ί 0 >10 practically independent of f 0 . In the limiting case β->0, Χς = \/2ζω η ί 0 [2], and Ε approaches the asymptotic value En=-…”

Section: Frequency Acquisition Rangementioning

confidence: 99%