Scope bandwidth and rise time, what do they mean in practice?

[Galaxyrise]

Prepping to by my first oscilloscope after years of talking about it.  I initally decided on the Rigol DS2072, but now it turns out they're backordered, and I have to choose again...

(Background on me: I took some basic vocational courses in electronics.  I've had college physics. I put together one simple project using a Teensy.  So I'm definitely a beginner.  I'm looking to do more hobbyist stuff, probably mostly digital at first.  I want to buy good stuff that can grow to a number of applications as I get better.)

They do have a DS2102 in stock.  Looking at the data sheet, the differences between the 2072 and the 2102 are
Analog Bandwidth (-3dB): 70MHz vs 100MHz
Rise Time: 5ns vs 3.5ns

I've read https://www.eevblog.com/forum/testgear/frequency-response-of-your-dso/ and get the impression that the 2072 scope would be fine for viewing the shape of signals with much higher frequency than 70MHz; you just have to be aware to compensate for the attenuation.  But how much higher?  For example, could I meaningfully look at regular FM radio signals (87-108MHz)?  What kind of work would actually require a 100MHz bandwidth instead of 70MHz?

Both scopes have a sampling rate of 2GSa/s single-channel, 1GSa/s dual-channel.  Naively, I would think a 1GSa/s could notice a voltage jump in 1ns. That the 70MHz version specs 5ns makes me think there's some input filtering (like an inductor?) to attenuate higher frequency signals.  If this is the case, I would expect all the DS2000 series scopes to see the same spikes in a signal, but for the spike to be taller on the more expensive variants.  Do I understand rightly? What does 5ns translate into practically?  What kind of work would actually require a 3.5ns rise time instead of 5ns?

The 200MHz version adds a couple more things, but it still seems to boil down to the same thing.  Now a 200MHz bandwidth and a 1.8ns rise time.  Those do seem more obviously different, but that scope is twice as expensive!  Still, I'm curious what work would require the jump in capability.

(Sorry if this kind of question has been answered a zillion times already!  I did see a ton of "what blah should I buy?" posts.)

[alm]

I've read https://www.eevblog.com/forum/testgear/frequency-response-of-your-dso/ and get the impression that the 2072 scope would be fine for viewing the shape of signals with much higher frequency than 70MHz; you just have to be aware to compensate for the attenuation. 

This is wrong. It's often possible to show the presence of the signal at frequencies beyond the bandwidth. Viewing the shape requires bandwidth well beyond the fundamental frequency. Take for example a square wave. You might remember the Fourier transform from college physics. The Fourier transform allows you to represent any repetitive signal as a set of sinusoidal signals. Each of the sinusoidal signals will be attenuated differently by the scope. - 3 dB at 70 MHz (for a 70 MHz scope), and much more (eg. -9 dB) at for example 140 MHz. A square wave consists of odd harmonics, so a 70 MHz square wave will have frequency components of 70 MHz, 210 MHz, 350 MHz. The 70 MHz will be attenuated by - 3 dB, the 210 MHz by -12 dB or so (for a Gaussian roll-off, real life performance will often be worse), and the 350 MHz by even more. The bottom line is that the 70 MHz square wave will pretty much look like a sine.

So how do you tell if the supposedly 108 MHz FM signal is not a square wave? The rule of thumb is that you need a scope with about 3-5x more bandwidth than the frequency of the signal you want to study. This dates back to analog scopes where all you required was a qualitative estimate of the signal.

Both scopes have a sampling rate of 2GSa/s single-channel, 1GSa/s dual-channel.  Naively, I would think a 1GSa/s could notice a voltage jump in 1ns. That the 70MHz version specs 5ns makes me think there's some input filtering (like an inductor?) to attenuate higher frequency signals.

Yes, a one-pole RC filter is a good way to think about the front-end. This is the so called Gaussian response.

  If this is the case, I would expect all the DS2000 series scopes to see the same spikes in a signal, but for the spike to be taller on the more expensive variants.  Do I understand rightly?

Yes, the spike will be attenuated less in the higher bandwidth models. Of course attenuation can make the spike invisible.

What does 5ns translate into practically?  What kind of work would actually require a 3.5ns rise time instead of 5ns?

If you measure an extremely fast square wave that goes from 0V to 1V in 100 ps, the scope will show a square wave that takes 5 ns to go from 0V to 1V. If there is ringing or other crap in that 100 ps, the scope will be unable to show it, but the DUT might respond to it. Rise time is often a better way to think about digital signals. The clock rate may be very low, but the fast rise time might still require a fast scope. Going from 3.5 ns to 5 ns is of course a small difference, not sure if this is really worth worrying about.

[45Overload]

I think a simpler explanation would be to refer to the analog concept of "slew rate".  One usually finds this number in the op-amp spec sheets and indicates how fast the amp can ramp up in volts/sec.  Apply the same concept to an A/D converter while considering the sampling rates necessary to faithfully reproduce the input signal.

[Galaxyrise]

The bottom line is that the 70 MHz square wave will pretty much look like a sine.

Ah... AHhhh... Thank you!  Now I have a pretty good feel for how those interact with the input signal.

I opted for the discounted 100MHz.  I am still curious for actual examples where the 70MHz scope wouldn't be sufficient but the 100MHz would be.