Analysis of Peak and Statistical Spectrum of Random Nonreturn-to-Zero Digital Signals

It is important to understand the spectral profile of the noise sources in electromagnetic compatibility (EMC) design. One of the various noise sources in modern electronics is the nonreturn-to-zero (NRZ) signal, a common digital signal format. Although conventionally the power spectral density of NRZ signal can be calculated based on Wiener-Khinchin theorem, which gives the average power per unit bandwidth, some specific properties are still unstudied. This paper analyzes 1) the maximum (peak) level, and 2) the probability density function (PDF) of the spectrum of NRZ signals. The importance of the peak level is that it represents the worst-case interference that may be produced by an NRZ trace, while the PDF is a more complete description of the spectral characteristics. The peak power is obtained through an algorithm and then well fitted, for most frequencies, by a formula, whereas the PDFs are represented in closed-form by using the central limit theorem. Based on the analysis, the peak level is found to have the same sinc shape but roughly 30-dB larger than the average power, in a 1-MHz bandwidth channel. The PDF is found to have the circular normal distribution at most frequencies, but is degenerated at frequencies of integer multiples of half-bit-rate. Measurement and simulation results verify the correctness of the proposed theory.