Estimation of the Percentile Maximum Time Interval Error of Gaussian White Phase Noise

2. Definition of MTIE The MTIE is historically one of the main time-domain quantities considered for the specification of clock stability requirements in telecommunications standards. In this paper, MTIE is first introduced according to its classical definition and as a percentile quantity. Then, the percentile MTIE is estimated, under the assumption of Time Error (TE) affected by Gaussian White Phase Modulation noise, by deriving the probability distribution of the TE spanned range as a function of the noise standard deviation σ. The formulas herein derived may allow to interpret common Allan-variance factory specifications in terms of percentile MTIE as well. In order to support the theory with sound experimental evidence, some results measured on state-of-the-art telecommunications clocks are eventually provided. A thorough treatment of MTIE and of its properties can be found in [16]. Here, solely the main definitions are summarized for the sake of understanding and to provide the reader with the background concepts. A general expression describing a pseudo-periodic waveform which models the timing signal s(t) at the output of clocks is given by [12][13] s(t) = A sin Φ(t) (1) where A is the peak amplitude and Φ(t) is the total instantaneous phase, expressing the ideal linear phase increasing with t and any frequency drift or random phase fluctuation. The generated Time function T(t) of a clock is defined, in terms of its total instantaneous phase, as