Unlock Characteristics of the Optimum Type II Phase-Locked Loop

1 March 1964

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Navigational Electronics

Vol. ANE-11 (1) , 15-24
https://doi.org/10.1109/TANE.1964.4502150

Abstract

This paper describes a study of the statistical unlock characteristics of the commonly used optimum type II phase-locked loop taking into account the nonlinearity of the phase detector. The unlock behavior is investigated by simulating the loop with random noise inputs on a digital computer. A criterion of loop unlock is evolved using the phase portrait of the loop and consists of crossing of separatrices by loop error and a measure of loop error rate. Approximately 100 statistically independent trials were made for each of a number of combinations of initial phase error, initial frequency error, and input noise amplitude. From these computer runs, cumulative frequency distributions of unlock time and curves of mean time to unlock were obtained and are presented. The phase portrait of the loop containing time information also is included in the paper, along with a plot of capture characteristics for large initial frequency offsets.

Keywords

This publication has 3 references indexed in Scilit:

Phase-Lock Loop Frequency Acquisition Study
IRE Transactions on Space Electronics and Telemetry, 1962
Design and performance of phase-lock circuits capable of near-optimum performance over a wide range of input signal and noise levels
IRE Transactions on Information Theory, 1955
Mathematical Analysis of Random Noise
Bell System Technical Journal, 1945