MODELING AND BUDGETING OF TIMING JITTER AND NOISE - Advanced Signal Integrity for High-Speed Digital Design - page 560

Intersymbol Interference As we have seen, ISI is caused by losses, dispersion,
and reflections on the transmission lines that make up the interconnect channel.
We show examples of probability density functions for channels with and without
equalization in Figure 13-11c and d. In general, the ISI PDF for a nonequalized
channel has multiple peaks, whereas that for an equalization channel looks like
a truncated Gaussian distribution.

Bounded Uncorrelated Jitter BUJ is deterministic jitter that is not aligned in
time to the data stream. The most common source of BUJ is crosstalk. Recall that
we have shown that crosstalk affects signal delay and amplitude through coupling
of signals between neighboring transmission lines. As a result, crosstalk can be
a significant source of jitter in high-speed systems. Crosstalk-induced jitter is
correlated to the data on neighboring signal, but is not correlated to the data
pattern on the signal itself. Hence, it is uncorrelated. The key characteristics of
deterministic and random jitter types are described in Figure 13-10.

Example 13-1 Jitter Distributions for a 10-Gb/s Interface We now present an
example running at 10 Gb/s to demonstrate multiple aspects of system jitter and
bit error rate calculations. We start by showing how the various jitter sources
combine to give the total system jitter. We then develop the dual Dirac model
parameters and show how the model provides a suitable approximation of the
system jitter at low error rates.
Our system contains sources for periodic jitter, duty cycle distortion (DCD)
jitter, ISI jitter, and random jitter. The amplitude of the periodic jitter is 20 ps,
and it has the PDF in Figure 13-11a. The DCD jitter is caused by a 10% duty
cycle variation ( α DCD 0 . 1), and the resulting PDF is shown in Figure 13-11b.

The ISI jitter in our example is obtained from a signaling system that is based
on the design that is presented in Section 14.2. This particular case is an 84-
differential pair that is driven by a 5-mA current source with 40- termination
at each end. The system uses a single tap equalizer with a coefficient value of
−

=

0 . 27. The resulting ISI PDFs for the nonequalized and equalized cases are
shown in Figure 13-11c and d, respectively. For this analysis we focus on the
equalized case, which has a distribution that lies between 6 ps.

The random jitter has an RMS value of 2.5 ps, resulting in the Gaussian jitter
PDF shown in Figure 13-11e. We calculate the PDFs for the system-level DJ and
total jitter via convolution using equations (13-13) and (13-14). The resulting
distributions are shown in Figure 13-11f and g.

±

PDF DJ (t) = PDF PJ (t) ∗ PDF DCD (t) ∗ PDF ISI (t) (13-13)

PDF TJ (t) = PDF DJ (t) ∗ PDF RJ (t) (13-14)

Our next step is to use the distribution in Figure 13-11f to find the maximum
(peak-to-peak) deterministic jitter. By plotting the PDF on a log scale, as shown
in Figure 13-12, we see that distribution shows a steep slope at the lower and
upper jitter extremes. This indicates that we have reached the bounds of the