Oscilloscope Sampling Rate vs Bandwidth

[jmole]

So I was wondering to myself, after recently purchasing an MSOX2024A, why in the world you need 2 Gigasamples/second, if the bandwidth of the scope is only 200 MHz?

I ran across this Agilent Application Note that talks about the issues behind it in detail: http://cp.literature.agilent.com/litweb/pdf/5989-5732EN.pdf

The general idea is that unless you can effectively attenuate frequencies above the Nyquist limit (i.e. sampling freq / 2), you will see aliasing in the reconstructed waveform.

So I'm wondering, why not just heavily low-pass filter the input of the scope, and use a slower ADC?  Seems to me like you could just chain a few op-amps together in unity gain follower configuration, and as long as the GBW of the op amp was close to your scope bandwidth, you could get rid of most of the aliasing frequencies.

[jmole]

Here's an example of what I'm thinking, crazy as it looks. It's 8 cascaded LMH6642 op-amps, all in unity gain follower configuration. Some of the feedback resistors have been tuned to add a bit of peaking to balance out the attenuation at the GBW product frequency.

The peak you see in the Bode plot is about +2dB, the -3db frequency is 95MHz, and at 175MHz, we're down to -52dB. Don't pay attention to the phase plot, it's a bit misleading, since what you're really seeing is signal delay. It's not like I'm feeding back that signal into the first stage or something. Although it would be interesting to see what that would do.

Anyway, with 175MHz at -52dB, you could use this cheap (for it's class) 350MSPS ADC, and get ~100 MHz bandwidth with fairly limited aliasing.

http://www.intersil.com/content/dam/Intersil/documents/fn68/fn6813.pdf

[jpb]

A few points. (Sorry if this sounds a bit hectoring - it is not meant to be.)

Firstly, scopes are used to look at digital signal such as pulses, the rise time of a 200MHz scope is 1.75 nsecs. You probably want to have at least one point on the slope and one on each end say so it would be nice to have a sample every 0.9nsecs but every 1nsec is probably ok but you don't want to go much below that. 2GS/s would give a sample every 0.5 nsec which gives you two or three on the slope.

Secondly, manufacturers tend to develop families of scopes so it makes sense to develop or use ADCs across the range which generally for these low end scopes goes up to around 500MHz for which at least 1GS/s is needed. The savings from using a different/slower ADC for the 100MHz model are probably not great compared to the savings of ordering/using a large number of the same part across the family. Often on the higher end models interleaving is used with the same speed ADCs e.g. 2GS/s is available if only one channel out of two is used by interleaving two 1GS/s ADCs. (I know that the 2000X only goes up to 200MHz but if you count the 3000X series in as well this can go up to 1GHz.)

Thirdly, scopes are used for measurements so adding additional filters just to enable lower speed ADCs would save little money whilst producing a scope that had a worse specification than rival products - analogue filters with a sharp and accurate frequency cut off without ripple in the pass band are not the easiest things to develop and mass produce and all for the purpose of a net saving that might be only a few pence. 

Another, more minor point is that having more sample points enables you to avoid having to do interpolation. A screen worth of points is 500 typically (though some of the wide-screen scopes have more). At 2GS/s 500 points is 250 nsecs or 25 nsec/div. With a 200MHz scope you can accurately look at signals up to about a third of this as a rule of thumb which is around 70MHz for which the period is around 15 nsecs only so you'd probably want to set a time base of 2 nsec/div when even at 2GS/s you will only have 40 points in the wave form.

With a sharp filter and sinc(x) interpolation you may be able to fill in the points but it would be doing a lot of work (and expense) for what can more easily be done with a faster ADC and a simpler filter.

[jmole]

So I totally understand your points in the context of a "real" test equipment provider not needing to water down their ADC, since they can more diversify their product line with a high-end ADC, and essentially have the people who need the extra bandwidth pay more to "unlock" it.

But, here:

all for the purpose of a net saving that might be only a few pence.

The price difference between a ~250 MSPS ADC, and a 1 GSPS ADC is pretty considerable, at least from the vendors I'm familiar with. Agilent probably develops their own. I'm just tossing around some ideas here, because I've always been interested in building a cheap scope, just to learn about the analog signal chain.

[jmole]

Also, while doing some more simulations, I noticed one potential pitfall: The S/N drops below 46db (same as the ADC spec) at about 88 MHz.

[jpb]

So I totally understand your points in the context of a "real" test equipment provider not needing to water down their ADC, since they can more diversify their product line with a high-end ADC, and essentially have the people who need the extra bandwidth pay more to "unlock" it.

But, here:

all for the purpose of a net saving that might be only a few pence.

The price difference between a ~250 MSPS ADC, and a 1 GSPS ADC is pretty considerable, at least from the vendors I'm familiar with. Agilent probably develops their own. I'm just tossing around some ideas here, because I've always been interested in building a cheap scope, just to learn about the analog signal chain.

I must own up to ignorance here as I don't know the prices. If you're building your own scope so that labour costs and tuning a filter are fun rather than an expense then you have a different economic model and what you say makes a bit more sense.

If you're producing something to sell then a multi-stage filter with components that vary I would have thought would be a nightmare to get consistent where as an ADC is a chip that you don't need to adjust (or adjustment is done in software).

Generally the cost in scopes comes down to the front end, a 350MHz scope costs a lot more than a 200MHz scope even though they probably share the same circuitry from the ADCs back. Adding extra filters to the front end for a manufacturer doesn't make sense. For a hobbyist building their own it might make perfect sense.

[jmole]

I must own up to ignorance here as I don't know the prices. If you're building your own scope so that labour costs and tuning a filter are fun rather than an expense then you have a different economic model and what you say makes a bit more sense.

If you're producing something to sell then a multi-stage filter with components that vary I would have thought would be a nightmare to get consistent where as an ADC is a chip that you don't need to adjust (or adjustment is done in software).

Hard to say if you can consider the "filter" complex or not. It's really pretty straightforward, although I will say that reality and simulation rarely go hand-in-hand, especially with high speed analog stuff. Not exactly something you can breadboard thanks to parasitics. May be a good candidate for BatchPCB, next time I have some spare time to try it out.

But yes, no company who can develop a multi gigasample ADC is going to try such a stupid method as this