U. Glaeser

where B = B 1 + B 2 + 1 is the size of the slope table input i.e., the number of data bits used in calculating
the slope. The SLT-based gradient is then,
© 2002 by CRC Press LLC
(34.12)
where the factor of −2 in Eq. (34.8) can be absorbed in the lookup table. In our analysis we need the
slope generating filter coefficients ψ(c). These coefficients ψ(c)s are obtained in the process of numerically
generating the signal slopes, which are correlated with the data.
Phase Detector Properties
Before computing the output noise jitter of the entire timing loop, the properties of the phase detector
must be analyzed. Quantities important for the performance of the phase detector are its KPD and output
noise standard deviation ratio KPD/ sno. The KPD is the ratio of the mean phase detector output to a
constant sampling phase error, τ. The KPD can thus be thought of as the signal gain of the timing loop
where the signal is the sampling phase error. The output noise no(k) is the equivalent noise at the output
of the phase detector for a given input noise n(k) at the phase detector input. The error, e(k), at the
equalizer output is a combination of contributions from the sampling phase error, τ(k) and noise. Let
n(k) represent the noise at the equalizer output (intersymbol interference + filtered equalized noise). We
then have,
The phase detector output, ∆(k), is then
(34.13)
(34.14)
Figure 34.25 shows in detail the timing loop of Fig. 34.22 with the details of the SLT phase detector and
the composition of the error signal from the sampling phase and noise per Eq. (34.13).
Now find the statistical properties of KPD and n o using E as the expectation operator. For a tractable
analysis we assume n(k) is AWG. To easily relate σ n to the error event rate (EER) at the output of the
Viterbi detector, we assume that channel errors are dominated by a minimum distance error event (with
distance d min).
τin
τout
τ (k)
(T)
FIGURE 34.25 Timing loop with SLT phase detector.
∆( k)
= e( k)sˆ(
k)
e( k)
= t( k)s(
k)
+ n( k)
∆( k)
= [ t( k)s(
k)
+ n( k)
]sˆ( k)
= t( k)s(
k)sˆ(
k)
+ no( k)
n(k) (LSB)
(LSB)
s(k)(LSB/T)
d(k)
e(k) (LSB)
s n
=
d min/2
Q −1 -----------------------
( EER)
Phase Detector
Slope Lookup
Table (SLT)
s(k)
∆(k)
(LSB)
DPLL
Filter
T(z)
KV
(T/LSB)
(34.15)