HP 54710A, User'S Reference Manual

Page: 42 / 412

System Bandwidth
The bandwidth of the combined oscilloscope and probe system must be
sufficient to accurately reproduce the input signal. Otherwise, time-interval
measurements are inaccurate. For example, if the oscilloscope and probe
have a combined rise time of 1 ns, and the signal also has a 1-ns rise time, the
measured rise time is:
√
(
1
ns
) 2 +
(
1
ns
) 2
=
1.41 ns
The answer is in error by 41 percent.
If the oscilloscope and probe have a combined rise time of 330 ps, and the
signal has a 1-ns rise time, the measured rise time is:
√
(
1 ns
)
2
+
(
330 ps
)
2
=
1.05 ns
Now the error is only 5 percent.
There are three rules worth memorizing. First, the combined system rise
time (oscilloscope and probe) should be less than 1/3 the rise time of the
measured signal for an error of less than 5 percent, or less than 1/7 of the rise
time of the measure signal for an error of less than 1 percent. Second, rise
time and bandwidth are inversely related as shown in equations 5 and 6.
Third, rise times add approximately as the square root of the sum of the
squares.
For example, if the oscilloscope and the probe each have 1-GHz bandwidths,
the combined bandwidth is approximately 707 MHz and the combined rise
time is approximately 495 ps. Therefore this combination could be used
confidently to measure actual signal rise times of 1.5 ns with less than 5
percent error, or 3.5 ns with less than 1 percent error.
How the Oscilloscope Works
System Bandwidth
1–25