Title

Discrete phase-locked loop systems and spreadsheets

Date of this Version

1-1-2011

Document Type

Book Chapter

Publication Details

Citation only.

Abramovich, S., Kudryashova, E., Leonov, G. A., & Sugden, S. (2011). Discrete phase-locked loop systems and spreadsheets. In E. Zeraooulia (Ed.), Models and Applications of Chaos Theory in Modern Science (pp. 405-428). United States: Science Publishers.

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2011 HERDC submission. FoR code: 130208

© Copyright CRC Press, 2011

ISBN

978-1-57808-722-8

Abstract

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behavior interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behavior of systems with different types of non-linear characteristic.

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This document has been peer reviewed.