# 1GHz digital oscilloscope with 50MS/s sample rate

Can someone please explain to me why can't I measure a non-periodic pulse signal $T_r=1ns$, with a digital oscilloscope $1GHz$ with a sample rate of $50MS/s$?

I may have to solve similar problems in an entrance exam for Faculty of Electrical Engineering, so I would like to really understand the problem and the calculations.

Any help or hints are welcomed and appreciated. Thank you.

• Have you actually tried dividing 1s by 50M? – Ignacio Vazquez-Abrams Aug 30 '17 at 14:52
• It can't. Simple answer. If it would be a periodic signal, then delaying each sample for one clock, then you reproduce the signal. But if it's non-periodic, then it can't because the sample rate is too small. – Marko Buršič Aug 30 '17 at 14:55
• To expand on Ignacio's comment: What is the separation between two successive samples taken at a 50 MHz rate? How does this affect acquisition of a single 1 nsec pulse? – WhatRoughBeast Aug 30 '17 at 14:57
• @IgnacioVazquez-Abrams I didn't because I don't understand why I need to do that. Can you explain? – mchingoska Aug 30 '17 at 15:00
• If you can't answer it, you're probably not ready for that course. Reading about Shannon's Sampling Theorem would help. – Brian Drummond Aug 30 '17 at 15:00

50 MS/s = 1/50,000,000 s between samples = 20 ns

If you are measuring one point ever 20 ns how could you tell the difference between a 1 ns rise time and a 19 ns rise time?

And to be honest if you can't answer that sort of question on your own then you need to do a lot more work before your exam. This isn't the sort of thing that you should need to memorize, it should be obvious to anyone who understands the underlying concepts. Learn the ideas rather than the answers to questions, that is the only way you can hope to answer questions you've not seen before.

• I haven't came across these type od questions until now, and just because I don't want to memorize answers is why I decided to ask here. Thank you for the answer, I understand it better now. – mchingoska Aug 30 '17 at 15:29

Nyquist Theory!

Here's a great app note on Nyquist Theory and Oscilloscope sample rates

Basically, to get an accurate depiction (and measurement) of your signal you have to have a high enough oscilloscope bandwidth and a high enough oscilloscope sample rate. I put together a quick 3m video a while back explaining the difference between oscilloscope bandwidth and sample rate.

In the case of your question, the oscilloscope bandwidth is fine, but the sample rate is so low the resolution wouldn't be accurate enough to give you a good idea of the signal's characteristics.

Like other comments mentioned 50 MSa/s = 1/50,000,000 = 20 ns/sample. To accurately sample a 1 ns rise-time signal, you'd theoretically need at least 500 ps resolution. In the real world, though, you'd still want faster than that.

• Thank you very much for your explanation, I will read the app note and watch your video. – mchingoska Aug 30 '17 at 16:25

Put a 49MHz square wave into a sampling scope running at 50MHz Fsample. Examine the scope display, and think about what does on.