Zero Crossing Statistics of Chaos-Based FM Clock Signals

We investigate the statistical features of both random- and chaos-based FM timing signals to ascertain their applicability to digital circuits and systems. To achieve such a goal, we consider both the case of single- and two-phase logic and characterize the random variable representing, respectively, the time lag between two subsequent rising edges or between two consecutive zero-crossing points of the modulated timing signal. In particular, we determine its probability density and compute its mean value and variance for cases which are relevant for reducing Electromagnetic emissions. Finally, we address the possible problems of performance degradation in a digital system driven by a modulated timing signal and to cope with this we give some guidelines for the proper choice of the statistical properties of the modulating signals.