6533b7ddfe1ef96bd1274bf0
RESEARCH PRODUCT
The Egan problem on the pull-in range of type 2 PLLs
Nikolay V. KuznetsovMikhail Y. LobachevMarat V. YuldashevRenat V. Yuldashevsubject
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 functionsdescription
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 which an infinite hold-in range implies an infinite pull-in range. Using the direct Lyapunov method for the cylindrical phase space we suggest a sufficient condition of the pull-in range infiniteness, which provides a solution to the Egan problem. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-01-01 |