Bandwidth vs Sample Rate

Bandwidth is not how many measurements are taken per second, that is the sample rate and they are different!   Bandwidth is maximum frequency of an input signal which can pass through the analog front end of the scope with minimal amplitude loss (from the tip of the probe to the input of the oscilloscope ADC). It is specified as the frequency at which a sinusoidal input signal is attenuated to 70.7% of its original amplitude (the -3 dB point).  That may come as a surprise as designers often assume a scope gives an exact picture of the signal at the probe tip, but its not actually the case. If you are measuring analog signals at anywhere remotely near the scopes bandwidth specification you have to bear this issue in mind as 70% is a long way from 100%!  For digital signals its worse – read on…

Sample rate is the maximum number of samples the scope can take per second and will usually be across all of the channels (e.g. a 4Gsp/s 4 channel scope won't necessarily be able to do more than 1Gsa/s on each individual channel – check the specs).  This wasn't a specification for analog scopes, but is of course for digital scopes. Also take care with the exact wording of a scopes sample rate as there are various tricks a scope manufacturer can play to make the spec sound better – generally you are interested in the "real time" sample rate and not a repetitive signal sample rate.

So sample rate is all that's really important if you are working with digital signals?  You might think that if a scope has, say, a 1Gsa/s sample rate but only 70MHz bandwidth that you can happily measure a 200MHz digital square wave signal on it as its 5nS per division setting and sample rate will cope fine.  Well yes and no, because the other effect of the bandwidth specification is that square wave signals not only get reduced in amplitude as sinusoidal input signals do, but they will also appear rounded off (ultimately into a sin wave looking signal) and also loose any fast peeks, ringing etc within the signal displayed by the scope.  This can lead you to look at a signal that not only isn't at all square like you expect but also doesn't appear to have any noise problems at all whereas in fact may have terrible ringing occurring on it!

Some general recommendations for scope bandwidth based on these issues:

For general analog signals use a scope with a bandwidth specification at least 2x the highest frequency component in the signal.

For digital signals where you care about seeing what noise is occurring – determine the fastest signal rise/fall time you are interested in and work out the bandwidth using the formula Bandwidth = 0.35 / Rise time.  Yes, rise time is what is important here not the frequency of the signal.  How the signal changes state is what you need to be able to see in this case, not how often it changes state which will be a lower specification.  To capture the true shape of the signal, you need a scope with a bandwidth large enough to capture several of the signals harmonics, so ideally use a scope with 3x to 5x the bandwidth you calculated for your signal.   For example the typical IO pin output rise and fall time for a PIC32MX7xx microcontroller is 5nS.  0.35 / 5nS (0.000000005) = 70000000 = 70MHz.  So a 200MHz scope would do very well at showing the real noise present at this switching speed and a 350MHz or faster scope would be fantastic.

For digital signals where you only care about seeing what states the signal is changing between – apply the general analog approach or just accept your signals will be getting rounded off corners and reduced amplitude as you reach or exceed the scopes bandwidth spec.  If this is OK then you can happily exceed the bandwidth spec and care more about the scopes sample rate spec. Just remember when you find yourself looking at a signal of some clocked bus which looks fine but which isn't working properly it will be because there is more happening in the signals than you can see, a typical example being ringing / bounce on a CLK signal causing extra clock events to be seen by a device being clocked.

Annoying huh as higher bandwidth adds a lot of cost to a scope, but there you go.  As with all things in electronic design you are often working with balancing compromises, in this case what you can afford vs how accurate what you see is.  If you have less than ideal bandwidth then your scope is still fine for lots of electronics tasks but just remember that you will not necessarily be seeing all of the true peeks of your signals and the sharpness of the edges.

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  1. chamzz

    8 years ago

    how to measure the bandwidth of a signal using no of samples

  2. Kbop

    3 years ago

    Straight to the point, love it! Very helpful, thanks.

  3. Bogdan Chakis

    3 years ago

    Useful article. Thanks.

  4. Abdullah Saba

    3 years ago

    can an oscilloscope have bandwidth higher than its sample rate? i mean, say, can an oscilloscope have 150Mhz bandwidth with 20Ms/s sample rate? how is it possible, please explain.

    1. Mike Mazzantini

      3 years ago

      My thoughts on this are…Yes. You’ll want a high bandwidth that won’t attenuate signals, but you may not need to sample that quickly.

  5. Anonymous

    2 years ago

    There are a couple ways that the sample rate can be less than the bandwidth.

    (1) using aliasing as a down conversion mechanism. It is possible to recover the entire FM broadcast band (88 — 108 MHz) by sampling at 56 MSamp/sec. Of course the bandwidth of the whole FM band is 20 MHz (< 56 MSamp/s)

    (2) More subtly, if you can sample the signals as well as some of its derivatives, you can reconstruct a signal with bandwidth greater than the sample rate. Nyquist's s Sampling Theorem is more general than most people are aware of.

    In phase/quadrature receivers approach this, using the "cosine" and "sine" channels to produce two samples per sample instance.

  6. Anonymous

    2 years ago

    I’m learning here too, and if someone reading this is like me, I think it may be useful to think of the scope as 2 parts, just as a clarification abstraction.

    Think of the “analog block,” which receives an analog signal (whatever you’re measuring) and outputs to the next block. This analog block can represent any changes the signal might undergo due to the impedance of components or other influences of the analog signal’s frequencies.

    The “ADC block” which receives analog signal, converts it to digital signal, and outputs that signal. During conversion, more loss may occur on the analog signal. Everything up to this point of conversion can be considered to be affected by the BANDWIDTH parameter of the scope. Think of the bandwidth as a low pass analog filter, defined by the constraints of your measurement system.

    The ADC will sample this analog signal at the desired SAMPLE RATE, and that data can be processed, stored, and displayed on to the screen. To get a good idea of what your signal looks like, and because its not so expensive to do so, the sample rate is multiples larger than your bandwidth. This is why we get to see nice, smooth continuous curves on the screen.

    I think what can be confusing is that older scopes didn’t have so many digital features. What you saw on the scope was fully defined by a “bandwidth” spec, and sample rate was not as relevant on a CRT display.

    Bandwidth is generally the more important spec to look at either way when deciding if the scope is appropriate for your measurement. For general use, sample rate is not as important.

    Hope this will be helpful for someone and happy for people to correct or add


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