New jitter decomposition diagram and new jitter separation method

   As signal rates continue to increase and the requirements for accuracy become higher and higher, it is necessary to separate jitter components to further characterize jitter characteristics and find the root cause of the problem. In modern times (after 2012), jitter components are mostly decomposed as shown below.

Figure 1  Jitter component decomposition diagram

Random Jitter RJ

   Random jitter is timing noise that is unpredictable because it has no discernible pattern. A classic example of random noise is the sound you hear when a radio receiver is tuned to a carrier frequency with no activity. Although in theory random processes have arbitrary probability distributions, we assume that random jitter has a Gaussian distribution to model jitter. One reason for this assumption is that in many circuits the main source of random noise is thermal noise (also called Johnson noise or shot noise), which has a Gaussian distribution. Another more basic reason is that the central limit theorem states that the combined effect of many uncorrelated noise sources should approximate a Gaussian distribution, regardless of the distribution of the individual noise sources. The Gaussian distribution is also called the normal distribution, but one of its most important characteristics is that for a Gaussian variable, the peak value it can reach is infinite. Although most samples of this random variable will be clustered around the median value, in theory, any single sample can deviate from the median value by an arbitrarily large amount. Therefore, a Gaussian distribution has no peak-to-peak boundary values, and the more samples you take from this distribution, the larger the peak-to-peak value you will measure. So, we use stdev or RMS (mean square deviation) value to measure random jitter RJ.

Deterministic Jitter DJ

Deterministic jitter is repeatable and predictable timing jitter. As such, the peak-to-peak value of this jitter has upper and lower bounds, and based on a relatively small number of observations, its boundaries can usually be observed or predicted with high confidence. DDJ and PJ further subdivide this type of jitter based on its characteristics and root causes. Deterministic jitter and random jitter can be visualized graphically on statistical graphs.
 

RJ and DJ spectrum separation method

   The traditional method of separating RJ and DJ is the spectrum separation method, which is to obtain RJ and PJ in the frequency domain, then obtain DJ in the time domain, and then calculate ISI and DCD. The key to the spectrum separation method is to select the PJ threshold, which is generally derived from experimental data. The separated spectrum lines are filtered out through the PJ threshold, and the remaining is the RJ spectrum, which is then integrated to obtain RJrms.

Figure 2   RJ and PJ separation by spectrum separation method
 
   If the spectrum is similar to white noise, the RJ separation effect is better, but if the measurement data is insufficient, another situation may occur, as shown in the figure below, then RJ separation needs to be carefully considered. At this time, in the jitter analysis software, there are two RJ bandwidths to choose from: Wide and Narrow.
   When to choose wide or narrow?
   If the amount of measured data is large enough, just choose Wide. But if the amount of measured data is small, choosing Narrow can better ensure the measurement accuracy.

Figure 3  Selection of RJ separation bandwidth

ABUJ and Gaussian tail fitting separation method

        When crosstalk occurs, we will find that the measured data in the bathtub curve and the data simulated using the dual Dirac model do not intersect smoothly or have no intersection, which means that jitter separation is inaccurate. Therefore, the jitter separation method has been improved recently, and non-periodic jitter ABUJ has been added to measure crosstalk or ground bounce.

Figure 4  The difference between the traditional spectrum separation method and the latest Gaussian tail fitting method in separating crosstalk The changes in
 
   waveforms and statistical graphs caused by crosstalk or ground bounce are shown below. It can be seen that the traditional spectrum separation measurement method cannot accurately perform jitter separation in the presence of crosstalk or ground bounce, and the latest Gaussian tail fitting method solves this problem well.


Figure 5  The change in the signal caused by crosstalk or ground bounce is the change in the statistical graph
 
   The Gaussian tail fitting jitter separation method is performed in the time domain to obtain the jitter statistical graph, and Gaussian fitting is performed on the left and right edge distributions to obtain RJ. In fact, this is not easy to operate in practice, and it is very critical to properly select the fitting window.
 

Figure 6   Gaussian tail fitting principle

Figure 7  Gaussian tail fitting method error consideration