8413S12I-100 Datasheet, PDF (15/33 Pages) Integrated Device Technology – Ten 100MHz clocks for PCI Express

8413S12I-100 DATA SHEET
Peak-to-Peak Jitter Calculations
A standard deviation of a statistical population or data set is the
square root of its variance. A standard deviation is used to calculate
the probability of an anomaly or to predict a failure. Many times, the
term "root mean square" (RMS) is used synonymously for standard
deviation. This is accurate when referring to the square root of the
mean squared deviation of a signal from a given baseline and when
the data set contains a Gaussian distribution with no deterministic
components. A low standard deviation indicates that the data set is
close to the mean with little variation. A large standard deviation
indicates that the data set is spread out and has a large variation
from the mean.
A standard deviation is required when calculating peak-to-peak jitter.
Since true peak-to-peak jitter is random and unbounded, it is import-
ant to always associate a bit error ratio (BER) when specifying a
peak-to-peak jitter limit. Without it, the specification does not have a
boundary and will continue get larger with sample size. Given that a
BER is application specific, many frequency timing devices specify
jitter as an RMS. This allows the peak-to-peak jitter to be calculated
for the specific application and BER requirement. Because a stan-
dard deviation is the variation from the mean of the data set, it is
important to always calculate the peak-to-peak jitter using the typical
RMS value.
The table shows the BER with its appropriate RMS Multiplier. There
are two columns for the RMS multiplier, one should be used if your
signal is data and the other should be used if the signal is a repeti-
tive clock signal. The difference between the two is the data transi-
tion density (DTD). The DTD is the number of rising or falling
transitions divided by the total number of bits. For a clock signal,
they are equal, hence the DTD is 1. For Data, on average, most
common encoding standards have a.5 DTD.
Once the BER is chosen, there are two circumstances to consider.
Is the data set purely Gaussian or does it contains any deterministic
component? If it is Gaussian, then the peak to peak jitter can be cal-
culated by simply multiplying the RMS multiplier with the typical
RMS specification. For example, if a 10^-12 BER is required for a
clock signal, multiply 14.260 times the typical jitter specification.
Jitter (Peak to Peak) = RMS Multiplier x RMS (typical)
If the data set contains deterministic components, then the Random
Jitter (R_J) and Deterministic Jitter (D_J) must be separated and ana-
lyzed separately. RJ, also know as Gaussian Jitter, is not bounded
and the peak-to-peak will continue to get larger as the sample size
increases. Alternatively, peak-to-peak value of D_J is bounded an can
easily be observed and predicted. Therefore, the peak-to-peak jitter
for the random component must be added to the deterministic com-
ponent. this is call Total Jitter (T_J).
Total Jitter (Peak to Peak) = [RMS Multiplier x Random Jitter
(R_J)] + Deterministic Jitter (D_J)
This calculation is not specific to one type of jitter classification. It
can be used to calculate BER on various types of RMS jitter. It is
important that the user understands their jitter requirement to ensure
they are calculating the correct BER for their jitter requirement.
Table 8. BER Table
BER
10^-3
10^-4
10^-5
10^-6
10^-7
10^-8
10^-9
10^-10
10^-11
10^-12
10^-13
10^-14
10^-15
RMS Multiplier Data,
“DTD = 0.5”
6.180
7.438
8.530
9.507
10.399
11.224
11.996
12.723
13.412
14.069
14.698
15.301
15.883
RMS Multiplier Clock,
“DTD = 1”
6.582
7.782
8.834
9.784
10.654
11.462
12.218
12.934
13.614
14.260
14.882
15.478
16.028
NOTE: Use R_J and D_J values for AC Characteristics Tables 7C to
calculate T_J.
REVISION B 2/03/2015
15
CLOCK GENERATOR FOR CAVIUM PROCESSORS