Improved Jitter Distribution Tail-Fitting Algorithm for Decomposition of Random and Deterministic Jitter

Abstract

An improved method for decomposition of random and deterministic jitter measurements using tail fitting of the probability density function of total jitter is proposed. The currently employed techniques assume that the tails of the probability density function tend to a Gaussian function. We show that to be inaccurate by deriving analytical expressions for the accurate asymptotic form of the probability density and cumulative distribution functions. In doing so, we prove that the tails approach a Gaussian function multiplied by a term that is inversely proportional to the total jitter. Monte Carlo simulations of jitter consisting of a combination of random and deterministic components are performed and nonlinear least squares fits to the derived asymptotic forms are used to estimate the root mean square of the random component and the bounds of the deterministic component for a few examples.