The effect of the forcing function on disruption of a phase-locked loop (PLL)

S. M. Booker*, P. D. Smith, P. Brennan, R. Bullock

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper we compare the disruption of a second-order type II phase-locked loop (PLL) by two different waveforms: a sinusoid and a sawtooth. The choice of these two waveforms results from a novel approach to the problem of determining an appropriate forcing function for studying the disruption of such systems. It is shown that the sawtooth is the better disruptor for low frequencies of modulation, i.e. in the regime of physical interest. Analytical, numerical and experimental results are reported which support this conclusion. The paper presents the first results of a sawtooth modulated PLL, which viewed as a nonsmooth dynamical system with a nonsmooth forcing function is a problem of considerable theoretical interest. This paper demonstrates that forcing functions can be designed for nonlinear dynamical systems which are well suited to the study of certain aspects of the system dynamics, and significantly better than the conventional choice of a simple sinusoid.

Original languageEnglish
Pages (from-to)2099-2117
Number of pages19
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number9
Publication statusPublished - Sep 2000
Externally publishedYes


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