MODELING AND BUDGETING OF TIMING JITTER AND NOISE - Advanced Signal Integrity for High-Speed Digital Design - page 555

of the leading and trailing edges of the eye are given by

0 . 5 erfc t − erfc t +

DJ δδ / 2
√ 2 σ RJ

DJ δδ / 2
√ 2 σ RJ

BER lead (t) = + (13-8)

0 . 5 erfc UI erfc UI

− t − DJ δδ / 2

√ 2 σ RJ

− t + DJ δδ / 2

√ 2 σ RJ BER trail (t) = +

(13-9)

where erfc( t ) is the complementary error function, which is defined as

∞

2
√ π

e − x 2 dx erfc (t) =

t

Note that in developing the equation for the leading-edge BER, we calculate the
cumulative density function (CDF) moving from right to left (toward decreasing
time values), while we move in the positive time direction when calculating the
trailing-edge CDF. This explains the difference in the sign of the time argument
in the two equations.
Using the equations, we can plot the bit error rate as a function of the horizontal
position in the data eye. We call this plot a BER “bathtub plot” and show an
example in Figure 13-9 using the AGP 8X timing distributions that we just
developed. The plot has flat regions near the edges of the eye in which the BER
is dominated by deterministic jitter and sections with steep slope near the center
of the eye that are dominated by random jitter. We can use the plot to assess the
ability of a given design to meet the BER requirements by finding the rate at
which the two curves intersect. For the example in the figure, the crossing point
is 10 − 18 , which represents the minimum BER that the design can meet.

13.3 JITTER SOURCES AND BUDGETS

In this section we expand our discussion of jitter to provide a fuller understand-
ing of the various sources of jitter and how they propagate through a signaling
system so that we can budget for their effects. To start with, we define jitter as
the deviation of a signal timing event from its ideal position. This is what causes
the “smearing” of a data eye along the time axis. Any component that trans-
mits, propagates, or receives a signal can contribute to jitter. As such, we first
categorize the types of jitter and their origins, followed by an analysis of how
the different components combine to produce the jitter signature for the entire
system.