
where: S
y
(f) = ^S*(/)
This equation is numerically integrated in the HP 3048A software. The
lower limit of integration, 0, is replaced by the minimum offset frequency
for which there is data in memory
(f
m
i
n
).
Because arbitrarily low frequency
data is not available, the maximum possible r for which
<T(T,
//,) can be
computed is
r
max
= ^J—.
The upper limit of integration (fh) is specified by the user based on the
actual bandwidth of the system in which he tests or uses the particular
device for which (7y{r) is being calculated.
Depending on the dominant slope of the phase noise at offsets 1 decade
above and below -k-, the maximum value of r for which an accurate
computation of a can be made and can be chosen as shown in Table 4-2.
Table 4-2. Slope versus Maximum Tau
Slope of £(/)
—50 dB/decade
—40 dB/decade
-30 dB/decade
-20 dB/decade
— 10
dB/decade
0 dB/decade
Maximum r for
data to
f
min
*
lu
/mm
'JJmin
"Jmm
dJmin
°Jmin
fh
*
10
T
10
r
1Q
r
As appropriate
As appropriate
Calculation not recommended. Will not be accurate unless there is a
region of shallower slope below the 50 dB/decade region.
System Default.
4-12 Sigma vs. Tau
rev.05SEP89
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