A Software Dened Phase Locked Loop

This report summarizes a software de…ned phase locked loop and its connection to standard second-order loop design parameter for a integrating VCO and DDFS frequency synthesizer. 1 Introduction Phase locked loops (PLLs) have been used since the early development of radio. Critical paper collections [1] and books [2] cover the subject matter, which includes nonlinear feedback and stochastic di¤erential equations. Contributions have been made by information theory pioneers such as H. L. Van Trees and A. J. Viterbi. The subject matter can be intimidating, but software-de…ned radio makes it possible to explore PLLs with compact easily constructed simulations. This report summarizes my own experience with software de…ned PLLs. I bene…ted from blogs posted by Paul Lutus 1 and Joseph D. Gaeddert 2 . My implementation is structured only for software implementation. Input digital data streams are prerecorded. Paul Lutus’s development is structured for realtime digital processing. Gaeddert’s presentation is a Software implementation, with combines the phase-detector and loop-…lter functions into a single …lter. 2 PLL Review A phase locked loop (PLL) has three functional elements, namely a phase detector, a loop …lter, and a voltage controlled oscillator (VCO). Figure (1) shows these functional elements and their interconnections. The index k identi…es a time sample. Software de…ned PLLs processes pre-recorded critically sampled complex data sequences. 1http://www.arachnoid.com/phase_locked_loop/index.html 2http://liquidsdr.org/blog/pll-simple-howto/