U. Glaeser

and
© 2002 by CRC Press LLC
Rno 1 ( ) R = no( – 1)
= – sd P−1 P−1
2 2
sn ∑∑
p=0 m=0
p−m=2
⎧
⎨
⎩
h( m)h(
p)
(34.26)
Performance Comparison of Symbol Rate Timing Loops
So far, the properties of the SLT and MM timing gradients or phase detectors have been examined. If
the noise at the phase detector output for both systems were white we could directly compare their
performance by comparing their respective KPD to sno ratio as a kind of signal-to-noise ratio (SNR) of
the phase detector. The ratio would measure a signal gain (experienced by sampling phase errors) to noise
gain across the entire bandwidth. If the noise had been white for both systems this ratio would scale
similarly for both systems when measured over the effective noise bandwidth determined by the loop
filter; however, for the MM loop we observed that the noise at the phase detector output was not white.
Therefore, we must examine the timing loop performance at the output of the loop filter not just at the
output of the phase detector. Before continuing our analysis let us make some qualitative comments
about the loop filter.
Qualitative Loop Filter Description
A timing loop is a feedback control loop. Therefore, the stability/loop dynamics are determined by the
“gain” (in converting observed amplitude error to a timing update) of the phase detector and the details
of the loop filter. If the timing loop were needed to remove the effect of a sampling phase error, a first
order DPLL would be sufficient; however, the timing loop must also recover the proper frequency with
which to sample the signal. Therefore, the use of a second order DPLL loop filter is needed. This allows
the timing loop to continually generate small phase updates to produce a clock, which not only has the
correct sampling phase within a symbol interval T but which also has the correct value for the symbol
interval i.e., the correct clock frequency. DPLL here refers to the portion of the overall loop filter transfer
function T(z) without the fixed delay term z −L . In addition, important to the performance of the loop is
its noise performance, i.e., for a given level of input noise, the effect on the jitter in sampling phase
updates. The jitter properties are determined by the noise gain of the phase detector as well as the loop
filter properties. The loop filters out noise beyond the bandwidth of interest, this bandwidth being
determined by how rapidly the loop is designed to react to timing changes. As mentioned earlier, the
DPLL loop filter is a second order filter with an additional latency term. Its transfer function is given by:
T( z)
z −L
fgz −1
1 z −1
z
⎛------------- –
+ p ⎞
⎝ g⎠
−1
1 z −1 --------------
=
⎛ ⎞
⎝ – ⎠
(34.27)
where f g and p g are frequency and phase update gains for the second order and first order sections,
respectively, while L is the loop latency. A block diagram of T(z) is also shown in Fig. 34.27(a).
Noise Jitter Analysis of Timing Loop
Linearized Z domain analysis of the DPLL is now performed by replacing the phase detector with its
KPD (denoted by K p in the equations for readability). In evaluating the SLT and MM DPLLs three sets
or combinations of p g and f g will be used: “LOW”, “MED”, and “HGH” where the LOW gains, are relatively
low update gains, which would be used in tracking mode, MED gains are moderate gains, and HGH
gains, are high gains, which might be used during acquisition. For the SLT and MM DPLLs the p g and
f g are scaled so that the same settings result in the about same transient response for a given sized phase
or frequency disturbance.