Digital Signal Processing Reference
In-Depth Information
The RMS thermal noise is
4
1
.
38
J
/
K
(
300 K
)(
50
)(
5
σ
therm
=
×
10
−
23
×
10
9
Hz
)
10
−
5
V
=
6
.
43
×
The RMS shot noise is
2
(
1
.
6
10
−
4
V
10
−
19
C
)(
0
.
025 A
)(
5
10
9
Hz
)(
50
)
=
σ
shot
=
×
×
3
.
16
×
The two noise sources combine in an RMS relationship:
(
6
.
43
10
−
4
V
σ
total
=
×
10
−
5
V
)
2
+
(
3
.
16
×
10
−
4
V
)
2
=
3
.
23
×
From equation (13-34) we find that the probability that the noise from thermal
and shot sources at any instant is less than 1 mV:
−
e
−
(
1
mV
)
2
/
2
(
0
.
323
mV
)
2
=
=
P(v
noise
<v)<
1
0
.
992
99
.
2%
The small value suggests that thermal noise and shot noise are generally not sig-
nificant sources of noise for single-ended signaling systems, which have relatively
large signal swings.
13.4.2 Noise Budgets
The existence of so many noise sources in a high-speed signaling system demands
that they be managed to ensure proper operation. The method for managing noise
is to construct a noise budget and use it to design sufficient noise margin into the
system. Most of the sources that we have discussed are bounded, and in construct-
ing a budget we assume that each of them is at the worst-case value. In practice,
this is a conservative approach, since the probability of all noise sources being
at their worst-case extremes is remote. The benefit of the worst-case approach
is that by satisfying such a conservative budget, we minimize the probability of
having a noise problem in our system, and noise issues can be exceeding difficult
to diagnose.
Thermal noise and shot noise, which are Gaussian sources, do not directly
fit the worst-case noise method. However, we can calculate an approximate
worst-case value for Gaussian sources by choosing a maximum probability of
exceeding the worst-case value that we are willing to tolerate. We then use the
probability curve shown in Figure 13-18 to determine how many standard devia-
tions we must take into account. This is similar in concept to the BER calculation
from the preceding section. (Of course, BER applies to signal amplitudes as well
as timing. Noise-based BER calculation is left as a problem at the end of the
chapter.) For example, if we choose a maximum probability of exceeding the
worst-case noise of 1 in 1 trillion (10
−
12
), we set the noise to a minimum of
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