WHAT IS RANDOM JITTER (RJ)?

Jitter, defined as variation of a signal edge from its ideal position in time, is an important performance measure of a serial link, or clock signal. Jitter is generally divided into two types, deterministic and random. The deterministic jitter (DJ) is bounded and may be correlated to known sources. DJ has three main parts: periodic jitter (PJ), data-dependent jitter (DDJ), duty-cycle distortion jitter (DCD). Random jitter, on the other hand, is unbounded and is due to sources that can only be characterized statistically. For serial link qualification, jitter is decomposed to its various components because the impact of each one on bit-error-rate performance is different. The DJ contributes mainly to BER rate down to 5 10- , whereas random jitter determines BER performance for levels below 5 10- . Random jitter (RJ) is defined as jitter component that is non-deterministic, in other words, it is not periodic, dependent on the data pattern, or correlated to known deterministic sources. RJ often is modeled as a random process with normal or Gaussian probability distribution function (pdf).

However, in some applications, RJ may contain non-Gaussian components, e.g., due to coupling from other data links carrying uncorrelated data. Such random components are often called ‘bounded uncorrelated jitter (BUJ)’. This document discusses different existing RJ estimation methods, and describes the undersampled TIE frequency-domain technique, which uses TIA, such as GuideTech Femto3200. The method uses the time interval error (TIE) estimates that represent the displacement of an edge from its expected position. 2 RJ ESTIMATION METHODS RJ is often is characterized by its standard deviation RJ s , therefore, all RJ estimation methods try to provide an accurate estimate of RJ s . Different methods of estimating RJ s exist, including “pdf or histogram tail fit”, “BER bathtub curve”, “frequency domain”, “TIE frequency domain”, and “undersampled TIE frequency domain”. These techniques are described in next section. 2.1 PDF OR HISTOGRAM TAIL FIT METHOD Histogram provides an estimate of probability distribution function (pdf) of a signal or process. It is formed by dividing and range of the given sample set into a number of bins and plotting the number of samples occurring in each bin versus the center of that bin.

Figure 1 shows the histogram of 1Gbps serial link, which includes DDJ, PJ and RJ. DDJ and PJ dominate the middle portion of the histogram, while the tails exhibit a Gaussian behavior. Fitting Gaussian distributions to the left and right tails provide two estimates of the RJ standard deviation. The average of these estimates is used as RJ s . Although “pdf tail fitting” can produce fairly accurate estimates with reasonable number of TIE samples when DDJ and PJ are small, it requires very large sample sets and careful selection of histogram bins to provide reasonably accurate and precise (repeatable) results in the presence of DDJ and PJ. This is demonstrated in Figure 1, Figure 2, and Figure 3.

The plot in Figure 1 shows a histogram that only includes RJ, Figure 2 demonstrate the histogram when RJ and DDJ exist simultaneously, and Figure 3 shows histogram when significant PJ is also added. In all plots, the left and right fitting Gaussian distribution are also shown. In Figure 1, almost all the samples are used for RJ estimation, while in, Figure 2 approximately 20% of samples that fall in tail region can be used. Since the lack of sufficient samples in tail region deteriorates the RJ estimate precision, more samples will be needed to increase precision. Another issue with tail fitting is that PJ affects the curvature of the tail region. This causes a systematic error in estimating the real RJ. The plot in Figure 3 illustrates that the tail fit occurs only at the extreme ends of the tails, which deteriorates accuracy and precision further. Figure 4 shows the significant error that results from the impact of PJ for different peak-to-peak values of PJ.

RMS error (ps) 2.3 FREQUENCY DOMAIN Jitter is effectively unwanted phase modulation. This phase modulation can be estimated by observing the signal frequency components with a spectrum analyzer. RJ shows up as sidelobes around the main carrier decreasing with a slope of 20db/dec. The ratio of the power underneath the sidelobes to the main carrier provides an estimate of RJ power. Frequency domain method, however, is difficult to use for the test of digital serial links, because AM modulation may erroneously be accounted for as jitter, and also it is difficult to separate different jitter components. 2.4 TIE FREQUENCY DOMAIN High-speed real time sampling oscilloscopes are capable of estimating TIE for a record of consecutive edges of the signal. This record can be viewed in frequency domain using fast Fourier transform (FFT).

This is equivalent to observing phase modulation signal in frequency domain. The PJ and DDJ will appear as distinct spectral lines. If these spectral lines are eliminated, the remaining noise floor power provides an accurate estimate of RJ. For using this method special care has to be taken for selecting the record length, and frequency resolution. For long patterns, the DDJ spectral lines tend to distribute over a large number of frequencies and with amplitudes that decrease to the noise floor levels. Under such conditions, the DDJ contributions to the noise floor will introduce error in RJ estimation. 2.5 UNDERSAMPLED TIE FREQUENCY DOMAIN TIAs such as Femto3200 are capable of generating time interval error (TIE) data as well as absolute time tags (referenced to the first sample) for selected edges within a data stream. Since Femto3200 sampling rate is lower than the bit rate, the TIE data is effectively an undersampled sequence of total TIE.

The undersampled TIE, however, still can be used in conjunction with the time tags to provide accurate estimates of RJ. One method of doing so is to isolate RJ by eliminating the effect of DDJ+DCD and PJ. The method starts with taking a number of TIE samples for a number of edges in the pattern. The next step is to eliminate DDJ by computing DDJ for each pattern edge and subtracting it from the TIE data set for the relevant edges. Once DDJcompensated TIE sequence is obtained, the TIE for each pattern edge is passed through FFT operation to observe its frequency components. Subsequently, attenuating the distinct frequency peaks in FFT eliminates PJ. The remaining components in FFT are noise floor, whose power provides an excellent estimate of RJ. The RJ estimates from different FFT sequences are averaged to improve the overall estimation accuracy. Figure 5 and Figure 6 show the accuracy and precision of RJ estimate of this method for different values of DDJ and PJ.

As the plots illustrate, this method provides very accurate and consistent RJ estimates even in the presence of large DDJ and PJ. It also converges to a precise result with much less number of samples than algorithms such as tail fit, because it uses the RJ information embedded in all samples, rather than relying on a small subset of samples on the pdf tail. This method provides an estimate of total RJ, including non-Gaussian components, if there is any. Depending on the distribution of such RJ, their inclusion in total RJ will improve bit-error-rate estimates, and therefore, qualifies the link performance better.