For a single-pole low-pass response, the 10–90% rise time and −3 dB bandwidth are related approximately by rise time ≈ 0.35 ÷ bandwidth, or bandwidth ≈ 0.35 ÷ rise time. The rule estimates how much bandwidth is associated with an edge speed; it is not a universal identity for every digital waveform, oscilloscope, or measurement setup.
What rise time and bandwidth describe
Rise time describes an edge in the time domain: commonly, the interval for a signal to move from 10% to 90% of its final value. Bandwidth describes frequency response, often expressed for an oscilloscope as the frequency at which its response has fallen by 3 dB. The two are connected because a fast transition contains high-frequency components, and a system with limited bandwidth rounds and slows the edge.
The relationship depends on the response shape and threshold convention. It is useful to estimate requirements, but it does not reveal the full spectrum of an arbitrary digital waveform. National Instruments explains the estimation problem for digital signals in its rise-time bandwidth guidance.
How to use the 0.35 estimate
For a one-pole RC low-pass response, the step response is exponential. With a 10–90% rise-time definition, the approximate rise-time–bandwidth product is 0.35:
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- Bandwidth ≈ 0.35 ÷ rise time
- Rise time ≈ 0.35 ÷ bandwidth
Use compatible units: if rise time is in seconds, the result is in hertz; if it is in nanoseconds, the result is in gigahertz. For example, a 100 ns rise time gives 0.35 ÷ 100 ns, or approximately 3.5 MHz. This is an estimate under the stated convention, not a guarantee that a 3.5 MHz oscilloscope will measure that edge accurately. NI provides this worked example in its digital-signal bandwidth article.
Why 0.35 is not universal
The 0.35 factor suits a single-pole response and a 10–90% threshold definition. Change the system response or the threshold convention and the constant can change. Some oscilloscopes specify rise time using 20–80% crossings instead. Teledyne LeCroy describes 0.35 as a historical approximation most applicable to lower-bandwidth scopes with gradual rolloff; for some modern, higher-bandwidth or more complex responses, it notes values around 0.4–0.45 or higher. Consult the actual instrument specification rather than treating 0.35 as a universal conversion. See Teledyne LeCroy’s oscilloscope guidance and NI’s discussion of bandwidth and analog-signal acquisition.
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Ringing, overshoot, cascaded stages, and transmission-path loss can also affect the edge that reaches the instrument. The simple estimate does not prescribe a universal correction for these effects; the measurement chain and the relevant instrument specifications determine what is appropriate.
Do not confuse clock rate with edge bandwidth
A digital signal’s repetition rate or clock frequency is not, by itself, the bandwidth needed to represent its transitions. A square wave or other sharp edge includes frequency components above its fundamental repetition frequency. Restricting analog bandwidth removes or attenuates some of that content, making transitions appear slower and less sharp.
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When choosing an oscilloscope for digital work, consider the edge rise time as well as the clock rate. Tektronix discusses the need for multiple harmonics to reproduce waveform shape in its primer on oscilloscope bandwidth, sample rate, and performance specifications.
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Check both bandwidth and rise-time specifications
If the goal is to measure a signal’s rise time, the oscilloscope must be faster than the signal. Otherwise, the scope’s own response contributes to the observed rise time, making the edge appear slower. NI gives a general rule of thumb: the oscilloscope rise time should be about one-third to one-fifth of the signal rise time for minimal error. Treat that as a starting point; the permitted measurement error and the instrument’s response determine the actual requirement. Check the specified scope rise time as well as bandwidth, and note the threshold convention and response model used. See NI’s acquisition guidance.
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Account for sample rate separately
Analog bandwidth and sample rate are different constraints. A high sample rate cannot restore edge detail that the analog input path has already removed. NI’s digitizer guidance suggests at least twice the signal bandwidth for Nyquist sampling and about ten times for proper waveform shape; these are guidance values, not a substitute for checking the instrument’s specifications and acquisition mode. Anti-aliasing and noise filters can also reduce the bandwidth that can be measured. Consult NI’s explanation of bandwidth, Nyquist sampling, and aliasing.
Include the probe and circuit loading
The probe is part of the measurement chain. Its bandwidth and electrical loading can affect the observed edge; a probe can load the circuit and alter the signal being measured. Match probe bandwidth and loading characteristics to the circuit and confirm compatibility with the oscilloscope. Texas Instruments explains probe loading with an RC model in its article on accurately measuring power MOSFETs.
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Compare specifications, not a single conversion
For fast-edge measurements, compare candidate setups on the specifications that affect the result:
- Oscilloscope analog bandwidth and specified rise time
- The rise-time threshold convention and response model or constant
- Whether the scope rise time meets the measurement’s error target
- Sample rate and acquisition mode
- Probe bandwidth, loading, and scope compatibility
These factors are why a generic 0.35 calculation is useful for an initial estimate but insufficient as the sole basis for selecting an instrument.
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