8V41N010 DATA SHEET
Applications Information
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.
Table 8. BER Table
RMS Multiplier Data,
RMS Multiplier Clock,
“DTD = 1”
BER
“DTD = 0.ꢀ”
10-3
6.180
6.582
7.782
10-4
7.438
10-5
8.530
8.834
10-6
9.507
9.784
10-7
10.399
11.224
11.996
12.723
13.412
14.069
14.698
15.301
15.883
10.654
11.462
12.218
12.934
13.614
14.260
14.882
15.478
16.028
10-8
A standard deviation is required when calculating peak-to-peak jitter.
Since true peak-to-peak jitter is random and unbounded, it is
important 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
standard 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.
10-9
10-10
10-11
10-12
10-13
10-14
10-15
Table 8 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 repetitive clock
signal. The difference between the two is the data transition 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 0.5 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
calculated 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 * RMS (typical)
If the datasheet contains deterministic components, then the random
jitter (RJ) and deterministic jitter (DJ) must be separated and
analyzed separately. RJ, also known 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 DJ is
bounded and can easily be observed and predicted. Therefore, the
peak to peak jitter for the random component must be added to the
deterministic component. This is called total jitter (TJ).
Total Jitter (peak-to-peak) = [RMS Multiplier * Random Jitter
(RJ)] + Deterministic Jitter (DJ)
The total jitter equation 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.
NOTE: Use RJ and DJ values from AC Characteristics Tables 7B and
7C to calculate TJ.
CLOCK GENERATOR FOR CAVIUM PROCESSORS
12
REVISION 1 06/30/15
