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Relationship Between Bandwidth and Rise Time



Hardware: Modular Instruments>>High-Speed Digitizers (Scopes)

Problem:
I would like to digitize a square signal with a specific rise time, but I am not sure what the recommended bandwidth would be and what devices could achieve it.

Solution:
To satisfy the Nyquist theorem, we need to sample at least twice as fast as the maximum bandwidth of the signal (or about 10 times to have a proper shape). This statement has been seen in other documents (see related links for more information), but square signals have sharp edges and therefore the total bandwidth of the signal is not straight-forward to calculate.

The following is a general equation relating bandwidth and rise time:

BW = 0.35 / Tr

Where BW is bandwidth and Tr is the rise time of the signal.

For example, if you need to measure a square signal with 100 ns rise time, your bandwidth will be about 3.5 MHz (0.35 / 100E-9). Therefore, you should choose a digitizer that can sample at least twice as fast or, for shape purposes, 10 times faster: ~35 MS/s (Samples per second). For example, the NI 5112 or NI 5122 is a good choice because they have a sampling rate of 100 MS/s. Additionally, be sure that the anti-alias and noise filters on your digitizer are not enabled, as these can reduce the measurable bandwidth.

For more information about the products, please refer to the High-Speed Digitizers product page in the Related Links section below.

Related Links:
Developer Zone Tutorial: Sampling/Digitizer Basics - General Analog Concept
Products and Services: Digitizers/Oscilloscopes
KnowledgeBase 2D39R50A: How Do the High Speed Digitizer (Scope) Boards Calculate the Rising Time of a Signal?

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Report Date: 02/14/2007
Last Updated: 04/19/2009
Document ID: 46DA70JX

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