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Keysight Technologies
Bandwidth and Rise Time Requirements for
Making Accurate Oscilloscope Measurements
Application Note
Introduction
How much oscilloscope bandwidth do you need and how fast does the rise time need to be to
measure your signals accurately? Oscilloscope users ask this question regularly, but getting a good
answer is typically dificult. The answer depends on the frequency response roll-off characteristics
of the signal under test (SUT); it must be down about 15 db or more at the scope bandwidth. Most
users don't know the roll-off characteristics of their signals, so this answer isn't likely to be useful.
The roll-off characteristics will largely determine the amount of overshoot present in the step
response of the SUT, so it may be more useful to have some "rules of thumb" for the bandwidth and
rise time margin you need, based on the amount of overshoot.
To that end, we ran simulations in ADS (Keysight Technologies, Inc. Advanced Design System) for
two different cases: a step with no signiicant overshoot (a ifth-order Bessel response) and a step
with about 10% overshoot (a fourth-order Butterworth response). The oscilloscope frequency
response used for these simulations is the lat phase and magnitude response used in Keysight high
performance oscilloscopes. These simulations were normalized to a 1-GHz bandwidth, but the
results apply for any bandwidth.
03 | Keysight | Bandwidth and Rise Time Requirements for Making Accurate Oscilloscope Measurements - Application Note
Signal under test with little or no overshoot in the step
response
Figure 1. 1-GHz scope step response and scope measuring a step with little overshoot
In Figure 1, the red trace is the step response of a 1-GHz scope channel, the blue trace
is the step response of a ifth-order Bessel ilter, and the magenta trace is the step
response of the scope measuring the ifth-order Bessel ilter step. The bandwidth of the
ifth-order Bessel ilter was adjusted as high as possible until the rise time of the scope
measurement of the Bessel step (magenta) was within 3% of the Bessel step rise time
(blue).
Measurement results
Scope rise time 434.7 pS
Fifth-order Bessel rise time 678.0 pS
Scope rise time measurement of ifth-order Bessel step 697.8 pS
Error in scope measurement 2.911%
Fifth-order Bessel rise time/scope rise time 1.560
The bandwidth of the Bessel ilter that limited the rise time error to 3% or less turned out
to be 520 MHz. The frequency response of the Bessel ilter and the scope are shown in
Figure 2. Note that the Bessel ilter is down -14.3 db at the scope bandwidth.
04 | Keysight | Bandwidth and Rise Time Requirements for Making Accurate Oscilloscope Measurements - Application Note
Signal under test with little or no overshoot in the step
response
Figure 2. Frequency response of 1-GHz scope channel and ifth-order Bessel ilter
05 | Keysight | Bandwidth and Rise Time Requirements for Making Accurate Oscilloscope Measurements - Application Note
Signal under test with ~10% overshoot in the step
response
Scope_Measure_Fourth_Order_Butterworth_Step
Fourth_Order_Butterworth_Step
Keysight Scope Step Response
Figure 3. 1-GHz scope step response and scope measuring a step with 10% overshoot
In Figure 3, the red trace is the step response of a 1-GHz scope channel, the blue trace is
the step response of a fourth-order Butterworth ilter, and the magenta trace is the step
response of the scope measuring the fourth-order Butterworth ilter step. The bandwidth
of the fourth-order Butterworth ilter was adjusted as high as possible until the rise time
of the scope measurement of the Butterworth step (magenta) was within 3% of the
Butterworth step rise time (blue). Tabular results of measurements on these steps are:
Measurement results
Scope rise time 434.7 pS
Fifth-order Bessel rise time 608.2 pS
Scope rise time measurement of ifth-order Bessel step 697.8 pS
Error in scope measurement 2.819%
Fifth-order Bessel rise time/scope rise time 1.399
The bandwidth of the Bessel ilter that limited the rise time error to 3% or less turned
out to be 640 MHz. The frequency response of the Butterworth ilter and the scope are
shown in Figure 4. Note that the Butterworth ilter is down -17.3 db at the scope
bandwidth.
06 | Keysight | Bandwidth and Rise Time Requirements for Making Accurate Oscilloscope Measurements - Application Note
Signal under test with ~10% overshoot in the step
response
Figure 4. Frequency response of 1 GHz scope channel and fourth order Butterworth ilter
07 | Keysight | Bandwidth and Rise Time Requirements for Making Accurate Oscilloscope Measurements - Application Note
Conclusions