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Acquiring Waveforms
CSA7000 Series, TDS7000 Series, & TDS6000 Series Instruments User Manual
3-69
For electrical bandwidths the reference of a system is commonly the response of
the system to a sinusoidal frequency at or near DC. The point at which the
system response is one half would therefore be:
dB = 10 log
Ꮛ
0.5
response at DC
Ꮠ
=−3dB
In terms of frequency, voltage, and resistance the bandwidth is expressed as:
–3dB = 10 log
Ꮛ
V
(
f
)
2
R
÷
V
(
DC
)
2
R
Ꮠ
where V(f) is the RMS of the voltage swing response at the bandwidth frequency
and V(
DC) is the RMS voltage swing response at a frequency approaching DC.
Further math yields V(
f) = 0.707¢V(DC).
The expression is simplified by cancelling the R and moving the squared term
inside the log expression to a multiple outside the log expression:
10 log
Ꮛ
V
(
f
)
2
R
÷
V
(
DC
)
2
R
Ꮠ
= 2 × 10 log
Ꮛ
V
(
f
)
V
(
DC
)
Ꮠ
= 20 log
Ꮛ
V
(
f
)
V
(
DC
)
Ꮠ
In CSA7000 S eries instruments, the vertical units displayed for an optical
module are not in voltage, but watts; this is a unit of power. The optical-to-elec-
trical converter inside the instrument outputs a voltage whose amplitude is
linearly dependent on the incoming optical power; in this condition the voltage
applied at the electrical input already represents optical power in its linear form
(as opposed to having to square the voltage and divide by R). For the optical
input then, the bandwidth where the displayed optical power is one half that
approaching DC is:
dB = 10 log
Ꮛ
0.5
response at DC
Ꮠ
=−3dB