Nyquist Criteria to know Oscilloscope Sampling rate Criteria

hi we are making a new sensor hardware which can sample the data at 4Mhz or even lower ( in Khz) .What minimum Bandwidth specification for Oscilloscope is required to measure the samples correctly?
I have heard (or googled) that to measure the sample we need the instruments which has measure capability of at least twice the Bandwidth of the required hardware sampling.This is Nyquist Criteria?
I actually read this on some IRC while chatting some unknown scientist.Too curious now?

softy342 said:

... sample the data at 4Mhz or even lower ( in Khz) . What minimum Bandwidth specification for Oscilloscope is required to measure the samples correctly?
I have heard (or googled) that to measure the sample we need the instruments which has measure capability of at least twice the Bandwidth of the required hardware sampling.This is Nyquist Criteria?

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That's right. Still, one shouldn't forget that bandwidths add inversely quadratically. That means if you measure your 4MHz data rate with an 8MHz bandwidth oscilloscope, the bandwidth of the total measuring system is already about 18% less, i.e. just 3.3MHz. So if you want to see nearly the full original bandwidth, your measuring tool should have a considerably higher bandwidth than the signal to be measured.

Additionally one shouldn't forget that a 4MHz data rate consisting of rectangular pulses needs a much higher bandwidth than the data rate itself, if the rectangular form of the pulses shall be kept: harmonics!

erikl said:

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Additionally one shouldn't forget that a 4MHz data rate consisting of rectangular pulses needs a much higher bandwidth than the data rate itself, if the rectangular form of the pulses shall be kept: harmonics!

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Yes, to measure the sample pulses with reasonable fidelity you should have an oscilloscope bandwidth at least 3 times the inverse of the pulse width.

To measure digital pulses, you should know not only the frequency, but also the rise time. The oscilloscope must have bandwidth at least F = (0.35 ... 0.5)/Trise to catch the signal correctly. The wider the BW, the more accurate measures are.

erikl said:

That's right. Still, one shouldn't forget that bandwidths add inversely quadratically. That means if you measure your 4MHz data rate with an 8MHz bandwidth oscilloscope, the bandwidth of the total measuring system is already about 18% less, i.e. just 3.3MHz......

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How did you arrive at this 18% figure?

crutschow said:

Yes, to measure the sample pulses with reasonable fidelity you should have an oscilloscope bandwidth at least 3 times the inverse of the pulse width.

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Is this some law?Can you please put the reference..

How did you arrive at this 18% figure?

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Is this some law?Can you please put the reference..

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All these statements are based on assumptions, e.g. about the sampling function, about the frequency characteristic of an oscilloscope. But we don't know if they are actually valid for the problem which is only loosely sketched in the original post.

I don't see a chance for a clearer view without specifying the problem correctly.

softy342 said:

Is this some law?Can you please put the reference..

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No law. It's just a rough rule-of-thumb based upon measuring the rise-time with a resolution of about 1/10th of the pulse width. If you want a better resolution then you use a higher bandwidth oscilloscope.

softy342 said:

How did you arrive at this 18% figure?

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1/bw_tot = sqrt((1/bw₁)²+(1/bw₂)²))

For bw₁=4MHz and bw₂=8MHz you get bw_tot=3.58MHz , i.e. 10.6% less, not 18%, sorry.