you should use a limited number of samples
so that the slow variation does not become no
-
ticeable or alternatively use the dedicated sta
-
tistic measure for this kind of measurement,
the Allan deviation.
To measure the slower variation you calculate
Max, Min or Mean on a long series of aver
-
aged samples. Here averaging eliminates the
jitter in each sample and the long measuring
time and large number of samples means that
the measurement can record very slow varia
-
tions. The maximum pacing time equals the
maximum measuring time for each sample
and is 1000 s, and the maximum number of
samplesis2
*
10
9
, which in effect means that a
single data capture could theoretically span up
to 2
*
10
12
s or more than 60000 years.
Statistics and Mathematics
The counter allows you to perform mathemat-
ical operations on the measured value before it
is presented to the display or to the bus. See
Page 6-2to get an overview of the four avail-
able equations.
Any systematic measurement uncertainty can
be measured for a particular measurement
setup, and the needed correction constants can
be entered into these equations. Statistics will
then be applied to the corrected measured
value.
Confidence Limits
The standard deviation can be used to calcu
-
late the confidence limits of a measurement.
Confidence limits = ± ks
x
Where:
s
x
= standard deviation
k = 1 for a confidence level of 68.3%
(1s - limits)
k = 2 for a confidence level of 95.5%
(2s - limits)
k = 3 for a confidence level of 99.7%
(3s - limits)
n
Example
A measurement of a time interval of 100 msis
used to illustrate how the confidence limits are
calculated from the measurement result.
Use the statistics to determine the mean value
and standard deviation of the time interval.
Take sufficient samples to get a stable reading.
Assume further that the start and stop trigger
transitions are fast and do not contribute to the
measurement uncertainties. The counter dis
-
plays:
MEAN value = 100.020 msandaSTDDEV=
50 ns, then the 95.5% confidence limits =
±2s
x
=±2
*
50 ns = ±100 ns.
The 3s - limit will then be ±3
*
50 ns =
±150 ns
Jitter Measurements
Statistics provides an easy method of deter-
mining the short term timing instability, (jit-
ter) of pulse parameters. The jitter is usually
specified with its rms value, which is equal to
the standard deviation based on single mea
-
surements. The counter can then directly mea
-
sure and display the rms jitter.
Otherwise, the standard deviation of mean
values can be measured. The rms value is a
good measure to quantify the jitter, but it
gives no information about the distribution of
the measurement values.
To improve a design, it might be necessary to
analyze the distribution. Such measurements
as well as trend analysis can be performed by
means of the built in graphic capability - tog
-
gle the STAT/PLOT key to see the two
graphic presentation modes.
Statistics 6-5
Process
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