Interaction of additive and quantization noises in digital PLLs

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dc.contributor.advisor Mulchrone, Kieran F. en Ó Tuama, Cillian 2015-06-02T13:58:45Z 2015-06-02T13:58:45Z 2014 2014
dc.identifier.citation Ó Tuama, C. 2014. Interaction of additive and quantization noises in digital PLLs. PhD Thesis, University College Cork. en
dc.identifier.endpage 194
dc.description.abstract Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions. en
dc.description.sponsorship Science Foundation Ireland (02/IN.1/IM062, 06/IN.1/I366) en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher University College Cork en
dc.rights © 2014, Cillian Ó Tuama en
dc.rights.uri en
dc.subject Nonlinear dynamics en
dc.subject Phase jitter en
dc.subject Phase-locked loops en
dc.subject Noise en
dc.subject Difference equations en
dc.title Interaction of additive and quantization noises in digital PLLs en
dc.type Doctoral thesis en
dc.type.qualificationlevel Doctoral en
dc.type.qualificationname PhD (Science) en
dc.internal.availability Full text available en No embargo required en
dc.description.version Accepted Version
dc.contributor.funder Science Foundation Ireland en
dc.description.status Not peer reviewed en Mathematics en
dc.check.type No Embargo Required
dc.check.reason No embargo required en
dc.check.opt-out Not applicable en
dc.thesis.opt-out false
dc.check.embargoformat Not applicable en
dc.internal.conferring Summer Conferring 2014

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