Digital Signal Processing Reference
In-Depth Information
comprise the
peak distortion analysis
(PDA) method.
∞
WC
1
(t)
=
y(t)
+
y(t
−
kT )
|
y(t
−
kT )<v
ss
0
(13-41)
k
=−∞
k
=
0
∞
WC
0
(t)
=
v
ss0
+
y(t
−
kT )
|
y(t
−
kT )
v
ss
0
(13-42)
k
=−∞
k
=
0
where
WC
1
(t)
=
signal waveform representing the worst-case logical 1
WC
0
(t)
=
signal waveform representing the worst-caselogical zero
y(t)
=
received pulse response
T
=
symbol period
v
ss0
=
steady-state system response when driving low
In equations (13-41) and (13-42),
k
is an index into the data stream that
represents the number of bit positions away from the cursor position (
k
=
0 rep-
resents the cursor position). The PDA equations operate by conditionally adding
the ISI at multiples of the unit interval to the value of the waveform at the
current sample point. For a worst-case 1, the samples that contain negative ISI,
y(t
−
kT ) < v
ss0
, are added to the pulse response. For the worst-case zero cal-
culation, the samples containing positive ISI,
y(t
−
kT ) > v
ss0
, are added to the
steady-state low response. Note that although the bit position index
k
extends
from minus infinity to plus infinity, in a real system the length of the analysis
must be limited. There is no need to carry out the analysis beyond the point
at which the system reaches the steady-state value (either before or after the
cursor).
By applying the equations at each sample in the received pulse response,
we can deterministically calculate the worst waveforms. The repetitive nature of
the calculation clearly suggests that we can use a computer program to automate
the process. In Figure 13-27 we show the worst-case eye calculated by apply-
ing the PDA approach to the pulse response of Figure 13-26. The figure also
depicts the received eye for a 200-bit pseudorandom data sequence. The figure
shows clearly that the PDA approach yields a smaller eye than does the random
sequence, thus providing a better estimate of the worst-case noise and jitter from
a single simulation!
13.5.3 Peak Distortion Analysis Including Crosstalk
In Chapter 4 we showed that crosstalk also affects the behavior of signals in
a coupled channel. As a consequence, our methodology must include potential
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