Estimation of total jitter and jitter probability density function from the signal spectrum

Abstract

The total jitter of a signal can be found directly by integrating the sideband spectrum as it appears on a spectrum analyser. If there are any significant spur components, these can be included in the calculation of total RMS jitter if they are identified and corrected in power level according to the spectrum analyser resolution bandwidth. The jitter amplitude PDF (probability density function) can be calculated on the assumption that the jitter amplitude has a Gaussian PDF provided that there are no sufficiently strong spurs. In the limiting case of a single dominant sine wave spur with a power that exceeds the rest of the sideband noise the PDF is the central +pi region of the 1/cos x =sec x function. This has a well-defined width equal to the sine-wave peak-to-peak amplitude. When Gaussian noise is added to a single spur the PDF becomes 'Rician' representing a convolution of the PDFs of the spur and the Gaussian noise. The convolution process may be extended to include further spur components (of unrelated frequencies) to give the final PDF. To find such total jitter measures as 'time interval error jitter', 'period jitter', 'cycle-to-cycle jitter' or any other total jitter definition, the appropriate frequency weighting functions should be applied before the spectrum is integrated and then it can be converted to a PDF. It is the 'tails' of a jitter PDF that mainly determine the bit error rate (BER); in general these can be reasonably well estimated from spectrum analyser measurements, even though the exact shape of the main central part of the PDF is not easily computable. A simple approximation is proposed.