Digital Signal Processing Reference
In-Depth Information
1
0.1
0.01
1
⋅
10
−
3
1
⋅
10
−
4
1
⋅
10
−
5
1
⋅
10
−
6
1
⋅
10
−
7
1
⋅
10
−
8
1
⋅
10
−
9
1
⋅
10
−
10
1
⋅
10
−
11
1
⋅
10
−
12
1
⋅
10
−
13
1
⋅
10
−
14
1
⋅
10
−
15
1
⋅
10
−
16
1
⋅
10
−
17
DJ
pp
= 62 ps
0 0 0 0 0 0
−
50
−
40
−
30
−
20
−
10
Jitter (ps)
Figure 13-12
Extraction of system-level deterministic jitter for Example 13-1.
DJ distribution, which allows us to estimate that the peak-to-peak deterministic
jitter is 62 ps. We can check the accuracy of the system DJ distribution by
comparing the peak-to-peak DJ against the sum of the peak-to-peak jitter for
the individual DJ components. The sum of PJ (
±
20 ps), ISI (
±
6 ps), and DCD
(
5 ps) components also equals 62 ps, indicating that our system DJ distribution
is accurate.
To estimate the DJ
δδ
terms we must look at the PDF for the total system jitter.
Recall that the dual Dirac model treats the DJ as being distributed as a pair of
delta functions. The model works by setting DJ
δδ
such that the tails of the total
jitter distribution model accurately reflect the tails of the actual distribution. We
start by converting the probability values from the total jitter PDF to
Q
-scale
values. The
Q
scale, denoted as
Q
BER
, specifies the amount of eye closure due
to random jitter that we must account for at a given BER and is described by
Q
BER
(
BER
)
=
√
2 erf
−
1
1
±
BER
ρ
T
−
(13-15)
Values of
Q
BER
over a wide range of error rates are listed in Table 13-1.
Figure 13-13 shows the
Q
BER
versus jitter plot. The utility of the plot is that it is
approximately linear at low error rates, with a slope equal to
±
σ
−
1
RJ
. We obtain
the deterministic jitter term for the dual Dirac model by extrapolating the linear
slope starting at very small BER. The DJ
δδ
is simply the jitter value obtained via
the linear extrapolation to a BER value of 1. From the figure we calculate that
the values are
−
28
.
5 ps and 27.7 ps for the left- and right-hand side of the plots,
so that DJ
δδ
=
56
.
2 ps.
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