MODELING AND BUDGETING OF TIMING JITTER AND NOISE - Advanced Signal Integrity for High-Speed Digital Design - page 551

0.40

0.35

s = 10 ps

0.30

0.25

0.20

0.15 34.1%34.1%

0.10

0.1% 2.1% 2.1% 0.1%

0.05

13.6% 13.6%

0.00

Timing uncertainty (ps)

(a)

1.E-02

1.E-06

1.E-10

1.E-14

1.E-18

1.E-22

1.E-26

1.E-30

1.E-34

1.E-38

1.E-42

1.E-46

1.E-50

Timing uncertainty (ps)

(b)

Figure 13-6 Gaussian distribution of timing uncertainties with σ = 10 ps: (a) linear

plot; (b) semilog plot.

links are moving to a BER-based budgeting approach. Our discussion proceeds
with the premise that future high-speed signaling links will be designed to achieve
a finite bit error rate. As such, we need to develop a method for calculating the
BER from the timing distributions. We start by formulating an expression for the
bit error rate as a function of the distribution of timing jitter:

BER (t) = ρ T ∞
−∞

J(t)dt (13-5)