# Bandwith and time resolution

1. Aug 6, 2012

### fedeb1

Hi,

What is the smallest pulse i can see using an oscilloscope with 1GHz bandwidth?

Im interested in the formula that links bandwith and smallest time resolution. Also it would be nice if you could include the reference of where i could read and learn about this things.

Thanks and sorry for my english.

2. Aug 6, 2012

### milesyoung

There isn't any such general formula. If by pulse you mean square wave, it will depend on the frequency of the waveform.

The oscilloscope is effectively a filter. If you measure a square wave of low frequency relative to the bandwidth of the oscilloscope, you'll pass through the fundamental and plenty of it's harmonics, so you'll get to view a nice representation of the waveform. If the frequency of the square wave is close to the bandwidth of the oscilloscope, you'll probably just see the fundamental, as shown here:

Square wave frequency spectrum animation

This will make more sense if you read up a bit on 'Fourier series'. You can find plenty of good intuitive tutorials on it with a Google search.

3. Aug 6, 2012

### DragonPetter

A pulse in the time domain is a sinc function in the frequency domain. The spacing between sinc peaks and the amount of energy in each sinc peaks is related to the pulse width. A shorter pulse width will mean more energy in higher frequencies. A sinc spectrum is infinite, so a pulse requires infinite bandwidth to perfectly recreate, and so you will get a more distorted pulse measurement as you apply shorter pulses to the scope.

You need to define how much distortion you will accept in your pulse (how much energy you want under the sinc curve), then use that limit at 1GHz (but if digital scope take into account aliasing) and inverse fourier transform to get the pulse width.

Last edited: Aug 6, 2012
4. Aug 6, 2012

5. Aug 6, 2012

### the_emi_guy

"Smallest pulse I can see" is not a good way to link bandwidth with time resolution. For example, if the pulse amplitude is actually 1V, but it shows up as a 1uV bump on the oscilloscope would this count?

Instead, we connect the risetime with the oscilloscope bandwidth, and the most common formula is:

$$t_{rise} = 0.35/f_{bw}$$

Do Internet search for "risetime and bandwidth and oscilloscope" and you will find many dozens of papers on this.

6. Aug 6, 2012

### fedeb1

I was looking for that last formula. Trise and bandwith and i dont know why i thought it was pulse width and bandwith.

Thanks for all the replies!

7. Aug 7, 2012

### milesyoung

Just keep in mind, that relationship only applies if your oscilloscope exhibits a Gaussian-like response, which is common for analog scopes:

Relating wideband DSO rise time to bandwidth

If you're pushing the limits of your scope, DragonPetter suggested a better way to evaluate signal distortion.