SYSTEM ANALYSIS USING RESPONSE SURFACE MODELING - Advanced Signal Integrity for High-Speed Digital Design - page 624

10

5

0

35 40 45 50 55 60 65

R TT ( Ω )

(c)

Figure 14-7 ( Continued )

Next, we apply the RSM fit equations to the input variables that we generated
for each of the 500,000 cases with length set at the worst case (0.508m) and
equalization at the optimum (

0 . 26). The resulting eye height and eye width
distributions are shown in Figure 14-8. Each appears to be normally distributed.
As expected, the eye width distribution shows significantly more margin in the
spec than that for the eye height distribution. Distribution statistics for the three
input variables and two responses are summarized in Table 14-9.
Our defect rate is the number of parts that fall below the lower spec limit. We
estimate it in parts per million:

−

− µ)/ √ 2 σ ]
1 , 000 , 000

1
2

1 + erf[ ( LSL

D ppm = (14-35)

where erf( x ) is the error function, LSL the lower spec limit, µ the distribution
mean, and σ the standard deviation of the distribution. Table 14-9 includes both
the actual defect rate from the Monte Carlo simulation and the estimated defect
rate, showing that we meet the 1000-ppm target for an equalizer.
Repeating the analysis at multiple values for the equalization coefficient allows
us to plot the defect rate as a function of the equalization setting, which we show
in Figure 14-9. The figure shows that our design has sub-1000 ppm fallout for a
range of equalization values from approximately

0.245. As a result,
we conclude that it will meet our defect rate targets for an equalization setting
of

− 0 . 285 to −

0.26, including the error in the equalization.
As a final step, we repeat the analysis without the impedance screening to
assess our ability to eliminate the PCB impedance screen. Figure 14-10 shows
that although the defect rates increase slightly, we can still meet the target without

−