Theory, model, and applications of non-Gaussian probability density functions for random jitter/noise with non-white power spectral densities

In high speed data communications, timing jitter and voltage noise analyses often depend on mathematical models to predict long-term reliability of the system, typically merited by a low bit error ratio (BER). Many methods involve the extrapolation of random jitter (RJ) and random noise (RN) to very low BER, assuming that RJ is white Gaussian noise. In reality, RJ spectra are not always white. Thus, RJ statistical distributions can deviate from an ideal Gaussian, affecting the accuracy of extrapolations. This paper presents a theory and model for relating RJ distributions with colored spectra. We apply this model to various filtered RJ spectra, including the extreme case of Brownian (1/f²) noise, and show correlation between simulation and measurement.