34410A/11A User’s Guide 107
Measurement Tutorial 4
Estimating High–Frequency (Out–of–Band) Error
A common way to describe signal waveshapes is to refer to their “Crest
Factor”. Crest factor is the ratio of the peak value to RMS value of a
waveform. For a pulse train, for example, the crest factor is approximately
equal to the square root of the inverse of the duty cycle.
Notice that crest factor is a composite parameter, dependent upon the
pulse–width and repetition frequency; crest factor alone is not enough to
characterize the frequency content of a signal.
Traditionally, DMMs include a crest factor derating table that applies at all
frequencies. The measurement algorithm used in the 34410A/11A
multimeters is not inherently sensitive to crest factor, so no such derating
is necessary. With this multimeter, as discussed in the previous section,
the focal issue is high–frequency signal content which exceeds the
multimeter’s bandwidth.
For periodic signals, the combination of crest factor and repetition rate
can suggest the amount of high–frequency content and associated
measurement error. We know that the first zero crossing of a simple pulse
occurs at , so we can get an immediate impression of the
high–frequency content by identifying where this crossing occurs as a
function of crest factor:
The following table shows the typical error for various pulse waveforms as
a function of input pulse frequency:
Typical Error, for Sqare wave, Triangular wave, and a pulse train of CF=3, 5, or 10
prf square wave triangle wave CF=3 CF=5 CF=10
200
–0.02% 0.00% –0.04% –0.09% –0.34%
1000
–0.07% 0.00% –0.18% –0.44% –1.71%
2000
–0.14% 0.00% –0.34% –0.88% –3.52%
5000
–0.34% 0.00% –0.84% –2.29% –8.34%
10000
–0.68% 0.00% –1.75% –4.94% –26.00%
20000
–1.28% 0.00% –3.07% –8.20% –45.70%
50000
–3.41% –0.04% –6.75% –32.0% –65.30%
100000
–5.10% –0.12% –21.8% –50.6% –75.40%
pp
tprf
T
td
CF
*
111
===
p
t
f
1
=
prfCFf ⋅=
2
1
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