# Oscilloscope: How are Bandwidth specification and Sampling Rate related?

I had thought that a (digital) Oscilloscope with higher Sampling Rate, would automatically have higher Bandwidth. That seems intuitive because of Nyquist Sampling Theorem. But I've read in several places that in an Oscilloscope "sampling rate is not directly related to the bandwidth specification" (see here for example). That doesn't make any sense to me. Could you explain the logic?

• Have you read this article: cp.literature.agilent.com/litweb/pdf/5989-5732EN.pdf ? Sampling rate (SR) and BW are not directly related although the SR does set a maximum for the usable BW. You'll notice how on "better"scopes the ratio SR/BW ratio increases meaning more samples per period at the highest frequency. Commented Nov 20, 2016 at 21:58
• @FakeMoustache, Except that the fastest scopes, until a few years ago, were repetitive sampling types that might have 50 GHz analog bandwidth but only 40 kSa/s sampling. Commented Nov 20, 2016 at 22:25
• @ThePhoton, true, but I don't believe they call this as "sampling". I believe they call it "repetition rate". Commented Nov 20, 2016 at 22:43
• Actually, Agilent does call it as "sampling", keysight.com/upload/cmc_upload/All/… Commented Nov 20, 2016 at 22:52
• @Ali, in my corner of the world we call the repetitive sampling ones "sampling scopes" and the more usual ones "real time scopes". But that's mainly because 80% of the scopes in our lab are repetitive sampling ones. Commented Nov 20, 2016 at 23:46

The bandwidth is related to the analog part of an oscilloscope; the attenuator, amplifier and trigger modules. It specifies the frequency where the signal is attenuated by 3dB.

Simply put the sample rate determines how "fast" the ADC probes the analog signal to gather discrete readings. According to the Nyquist theorem it should be at least twice the maximum signal frequency (bandwidth). If the bandwidth would be only half the sample rate, the resulting reading would then be lower that it actually is.

On the other hand, frequencies higher than the sample rate (given twice or thrice the bandwidth is available), can not be read without "loosing information" (that's called aliasing).

See this Keysight document on Scope fundamentals for EE Students. On page 17 you find a typical block diagram of an oscilloscope, page 18 and 19 mention the relationship between bandwidth and sample rate.

From page 17, part of the block diagram (the blueish part is determines the analog bandwidth):

From page 18:

• All oscilloscopes exhibit a low-pass frequency response.
• The frequency where an input sine wave is attenuated by 3 dB defines the scope’s bandwidth.

From page 19:

• Required BW for analog applications: ≥ 3X highest sine wave frequency.
• Required BW for digital applications: ≥ 5X highest digital clock rate.
• More accurate BW determination based on signal edge speeds (refer to “Bandwidth” application note listed at end of presentation)

In my experience, the specced analog bandwidth tends to be 20 to 30 % of the real-time sampling rate (the Nyquist limit is 50%).

To avoid aliasing during sampling, the signal chain should better contain an analog low-pass filter, preventing any input from reaching the Nyquist limit... not sure if this is what the scopes actually do :-) as it would hamper repetitive sampling.

A possible different angle: at the Nyquist limit, the digital approximation of the original analog signal is already pretty coarse, so it doesn't make much sense to stretch it. And, fast analog circuitry is expensive and power-hungry. So if you give up repetitive sampling, you don't even need to reach the Nyquist limit.

Next: beware of the probes! The cheap variety with just a passive 1:10 divider only make it to about 200 MHz. Anything faster costs an arm and a leg.

As for the ADC's alone, I've noticed that TI make integrated ADC's with sampling rates in the lower GSps range. You can reach higher sampling rates by interleaving several ADC channels (including their Sample and Hold front ends).

As someone already mentioned, having 20 to 30 percent of analog bandwidth of real-time sampling rate is okay. This is done to sample signal in a way interpolation or other techniques could do better job recreating signal. And I'm pretty sure all of the electronics should have anti-aliasing low pass filter.

However, you could sometimes see oscilloscopes where sampling rate is relatively low but maximum frequency is high, higher than limitations claimed by Nyquist. Well, there's no magic really - signal is at first saved to some analog memory and later processed. That means that by looking at the same signal, just changing phase there is a good possibility to see voltage of really high speed signal. What is the downside of this? You have to save your signal and use some precision electronics to achieve this

DSO's serve many many functions as measurement devices in both Time and frequency domain. Factors which affect the quality of the signal capture are not just the fundmantal but even for a pure sinewave, the spectral SNR is important for many applications/

One method is defining a signal is the FFT defined by span and resolution. This is where a high ratio of Sampling rate to Signal Bandwidth is useful. This higher rato reduces the Resolution bandwidth in an FFT.

Effects of higher Sampling Rate and lower Resolution Bandwidth improved resolution is lower Noise per Root Hz Bandwidth. The more samples per bin, the lower the noise floor as shown below.