A Better Method than Tail-fitting Algorithm for Jitter Separation Based on Gaussian Mixture Model

Abstract

Jitter is roughly defined as the timing shaking of the square waveforms output from phase locked loops. It consists of two parts: deterministic jitter and random jitter. Separating and identifying each jitter component are important in understanding the root cause of jitter and further in improving on phase locked loop design. A popular method for jitter separation is so-called Tail-fitting Algorithm. A better method than Tail-fitting Algorithm for separating deterministic jitter (DJ) and random jitter (RJ) from total jitter (TJ) is presented in this Letter. The new method targets directly on the original total jitter series, instead of the histogram. Histogram is dependent on bin number and is uncertain, but is inappropriately selected as the starting point of Tail-Fitting algorithm. Our method is based on Gaussian mixture model (GMM). The mathematical relationship between this model and the quantities of DJ and RJ is established. The concept of kurtosis is used to determine the order of GMM, thereby rendering our method fully automatic, highly efficient. Our method circumvents the most cumbersome difficulty in tail identification of Tail-Fitting Algorithm, because tails and peaks of the histogram, even after being filtered, are fundamentally ambiguously defined, both theoretically and practically. Our method also bypasses the problem of initial value selection.