Search results for "Gardner problem on the lock-in range"

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The Egan problem on the pull-in range of type 2 PLLs

2021

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …

PLLtype IIelektroniset piiritEgan problem on the pull-in rangehold-in rangeEgan conjectureglobal stabilityharmonic balance methodsäätöteoriavärähtelyttype 2describing functionphase-locked loopnonlinear analysisGardner problem on the lock-in rangedifferentiaaliyhtälötLyapunov functions
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О проблеме Гарднера для систем управления фазовой автоподстройкой частоты

2019

This report shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loops systems. The development of analogs of classical stability criteria for the cylindrical phase space made it possible to obtain analytical estimates of the lock-in range for third-order system. peerReviewed

säätöteoriaphase-locked loopselektroniset piiritnonlinear analysisGardner problem on the lock-in rangefrequency stability criteria
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