DESIGN AND STABILITY OF PHASE LOCKED LOOPS.
Abstract
It is shown that phase-locked loops with noise corrupted inputs can be represented by non-linear differential equations with randomly varying coefficients. Conditions for the stability of the linearized form of these equations are determined. The method used in the stability analysis is that of bounding the nth order system impulse response with that of a first order system, and determining where the first order system is stable. This is the method developed by Bershad. The results of this analysis are then applied to second and third order systems to determine their stability regions. These stability regions are experimentally verified. Parameter optimization, utilizing the stability criterion as a constraint, is then performed upon the second and third order systems to minimize their steady-state error to a noise-free ramp phase input. The results of this procedure yield the optimum filters for second and third order phase-locked loops. A comparison is then made to determine which of the two loops has a smaller steady state error to a ramp phase input. Experimental results are given for a phase-locked loop with an optimum filter designed by the above procedure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1964
- Accession Number
- AD0612036
Entities
People
- Lawrence H. Michaels
- Paul M. Derusso
- Williamg. Tuel Jr.
Organizations
- Rensselaer Polytechnic Institute