Will Keysight upgrade the 2000, 3000T X-Series Oscilloscopes within a few months

[heavenfish]

fs/2 only works well if you want to reconstruct a sine wave. If you measure a 50 MHz square wave, 100 MS/s would reconstruct a sine wave on the screen. Of course whether it matters depends your applications. If you're dealing with digital signal and doing serial decoding, it still gives you all the information you need. If you cares about the shape not only timing then you probably want 500 MS/s.

[KE5FX]

It all depends on how good the reconstruction algorithm is. The thing is that according to Nyquist all information of the signal is there up to (but not including) fs/2. However if you LOOK at a sine wave which is close to fs/2 you'll only see a few seemingly random sample points. So in order to SEE the signal it has to be reconstructed and that is where reconstruction algorithms come into play. Still a higher than necessary samplerate doesn't add any extra information.

What some people may be overlooking is that the mathematics behind sampling describe how to reconstruct a continuous function.  An oscilloscope display isn't continuous, it's a stream of discrete, discontinuous frames displayed in time.  You can reconstruct what's on the screen accurately as long as Nyquist is satisfied, but that doesn't mean it will be particularly pleasant to look at a moving or changing signal near Nyquist, or even a repetitive one.



This is a 10 GS/s scope displaying a 3 GHz signal.  It's "correct" according to Nyquist, and no further information will be added by sampling at a higher rate, but you'd still prefer more oversampling margin if you could get it. 

[Wuerstchenhund]

What some people may be overlooking is that the mathematics behind sampling describe how to reconstruct a continuous function.  An oscilloscope display isn't continuous, it's a stream of discrete, discontinuous frames displayed in time.

Yes, but that does not matter. You can get a valid reconstruction even if you only had two sampling points.

You can reconstruct what's on the screen accurately as long as Nyquist is satisfied, but that doesn't mean it will be particularly pleasant to look at a moving or changing signal near Nyquist, or even a repetitive one.



This is a 10 GS/s scope displaying a 3 GHz signal.  It's "correct" according to Nyquist, and no further information will be added by sampling at a higher rate, but you'd still prefer more oversampling margin if you could get it. 

Yes, but that only looks so poor because you've enabled linear interpolation which never produces a true waveform. It's only there because it needs a lot less processing power so it will produce higher update rates on older/slower scopes and at very high oversampling rations the irregularities get so small that they can no longer be seen.

You should leave the scope on sin(x)/x which as we see produces a true waveform and which is the only interpolation function that produces true results as long as Nyquist-Shannon is satisfied.

[KE5FX]

Yes, but that only looks so poor because you've enabled linear interpolation which never produces a true waveform. It's only there because it needs a lot less processing power so it will produce higher update rates on older/slower scopes and at very high oversampling rations the irregularities get so small that they can no longer be seen.

You should leave the scope on sin(x)/x which as we see produces a true waveform and which is the only interpolation function that produces true results as long as Nyquist-Shannon is satisfied.

Point being, it looks shaky and twitchy even with sin(x)/x turned on.  I turned it off briefly to show how few points the scope has to work with. 

It would probably look quite a bit better if the firmware could map the trigger level back onto the sin(x)/x-interpolated waveform and adjust the horizontal position accordingly.  It doesn't look like they're attempting to do anything like that here, but I imagine more modern scopes can.  Of course, then you end up looking at trigger jitter...

[KE5FX]

With only two data points on a complete cycle of a waveform, you have no idea if it's a sine, or square or even a triangle, or maybe something else entirely.  Saying that "the 'scope can reconstruct an accurate rendition of the original signal with only two data points per full cycle" is not only naive, it's bordering on ridiculous.  Please stop, and THINK before you run on () about this...

If you only have two points per fundamental cycle to work with, you have no choice but to show a sine.  The signal has to be band-limited prior to sampling, with its content rolled off almost entirely before half the sample rate is reached.  From the point of view of the ADCs in the scope, it is a sine.

[testmode]

With only two data points on a complete cycle of a waveform, you have no idea if it's a sine, or square or even a triangle, or maybe something else entirely. 

I think this is the primary point of contention here.  "Reconstructing" a signal where one already has an idea of what to expect is entirely different than trying to "view" as much of an unknown signal as possible.  But of course one has to have some rough idea on the expected range of frequencies you have to care about else you'll just be throwing as many darts as you could with your eyes closed hoping somehow you'll hit the bull's eye.

[Wuerstchenhund]

With only two data points on a complete cycle of a waveform, you have no idea if it's a sine, or square or even a triangle, or maybe something else entirely.  Saying that "the 'scope can reconstruct an accurate rendition of the original signal with only two data points per full cycle" is not only naive, it's bordering on ridiculous.  Please stop, and THINK before you run on () about this...

You really can't make that up...

Maybe you should take your own advice and next time read & think twice before writing silly nonsense. Because for a start I said *nothing* about a complete cycle (which would be silly, as Nyquist-Shannon states that the sample rate needs to be higher than 2x f₀, so 2 points per period are clearly not sufficient to get a true reconstruction of a true sine wave)

That however doesn't change the fact that with a BW-limited signal, sampled at >2xf₀, two sample points are sufficient to truly reconstruct the segment between these two points with sin(x)/x interpolation.

It also doesn't matter what waveform it is, as long as it's BW limited (i.e. the highest frequency components are sampled at a rate that satisfies Nyquist-Shannon).

Point being, it looks shaky and twitchy even with sin(x)/x turned on.  I turned it off briefly to show how few points the scope has to work with.

It looks shaky and twitchy very likely because of irregularities in the signal (i.e. phase noise, quantization noise), which means you don't get a true sine but something else.

What's your signal source?

[EEVblog]

That however doesn't change the fact that with a BW-limited signal, sampled at >2xf₀, two sample points are sufficient to truly reconstruct the segment between these two points with sin(x)/x interpolation.

For a gaussian response scope front end you should be using at least 4xf sample rate is the typical figure quoted.
A minimum of 2.5xf if you have a sharp flat response front end.
http://cp.literature.agilent.com/litweb/pdf/5988-8008EN.pdf

[nctnico]

With only two data points on a complete cycle of a waveform, you have no idea if it's a sine, or square or even a triangle, or maybe something else entirely.  Saying that "the 'scope can reconstruct an accurate rendition of the original signal with only two data points per full cycle" is not only naive, it's bordering on ridiculous.  Please stop, and THINK before you run on () about this...

I'd strongly suggest to read up about Fourier and sampling theory before typing more nonsense. When people use an oscilloscope they expect it to show the actual signal at the tip of the probe. Unfortunately it never works that way. An oscilloscope and the probe will always have limits and you have to be aware of those limits. When you look at a 50MHz square wave with any oscilloscope which has a 100MHz bandwidth you'll see a sine wave. There just isn't enough bandwidth to show the higher harmonics.

I have done quite a bit of research on signal reconstruction algorithms and managed to come up with one which can reconstruct up to 0.45fs (while including the original samples) so I do know what I'm talking about and what is/isn't possible.

[nctnico]

It all depends on how good the reconstruction algorithm is. The thing is that according to Nyquist all information of the signal is there up to (but not including) fs/2. However if you LOOK at a sine wave which is close to fs/2 you'll only see a few seemingly random sample points. So in order to SEE the signal it has to be reconstructed and that is where reconstruction algorithms come into play. Still a higher than necessary samplerate doesn't add any extra information.

What some people may be overlooking is that the mathematics behind sampling describe how to reconstruct a continuous function.  An oscilloscope display isn't continuous, it's a stream of discrete, discontinuous frames displayed in time.  You can reconstruct what's on the screen accurately as long as Nyquist is satisfied, but that doesn't mean it will be particularly pleasant to look at a moving or changing signal near Nyquist, or even a repetitive one.

This is a 10 GS/s scope displaying a 3 GHz signal.  It's "correct" according to Nyquist, and no further information will be added by sampling at a higher rate, but you'd still prefer more oversampling margin if you could get it.

Again: there is a difference between sampling enough points to reconstruct the signal (with a DAC for example) and getting enough points to SEE a signal. However getting enough points to SEE a signal is a matter of using a signal reconstruction algorithm. You don't need a higher samplerate for that because all the information needed for the signal reconstruction algorithm to work is there. Our brains are the problem here, not the scope or the sampling frequency!

[omgfire]

And to elaborate, while Nyquist theorem is all about 1's and 0's, it is in fact about the digital representation of the underlying analog signal.

Last time I checked Nyquist–Shannon–Kotelnikov sampling theorem, it was defined in the field of real numbers (possibly infinite length decimal representation). How do you digitally represent real (specifically irrational) numbers? Scopes work with quantized samples (8 bit ADC, 16 bit ADC, ..). It is possible to mathematically analyze how quantization butchers signal: http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pdf
But Nyquist–Shannon–Kotelnikov sampling theorem do not touch quantization and I am not sure where you find "all about 1's and 0's" in this theorem.

[omgfire]

fs/2 only works well if you want to reconstruct a sine wave.

Yes, but scopes frontend bandwidth is also specified for sine wave and signal can be decomposed into Fourier series.

If you measure a 50 MHz square wave, 100 MS/s would reconstruct a sine wave on the screen. If you cares about the shape not only timing then you probably want 500 MS/s.

50 MHz square wave is NOT bandwidth limited to 50 MHz. 70 MHz limited frontend will filter 50 MHz square wave into sine wave, after that you can sample it at 500 MS/s or 5 GS/s, but it still would be sine wave.

To see fifth harmonic you would need over 250 MHz of bandwidth and consequently over 500 MS/s. But sample rate of 500 MS/s alone would not help to see 50 MHz square wave on 70 MHz bandwidth limited scope.

[omgfire]

With only two data points on a complete cycle of a waveform, you have no idea if it's a sine, or square or even a triangle, or maybe something else entirely.  Saying that "the 'scope can reconstruct an accurate rendition of the original signal with only two data points per full cycle" is not only naive, it's bordering on ridiculous.  Please stop, and THINK before you run on () about this...

indeed.

If signal is bandwidth limited to X MHz, I am pretty sure signal is NOT X MHz square wave or X MHz triangle wave. Because X MHz square wave is not bandwidth limited to X MHz.

[Wuerstchenhund]

Last time I checked Nyquist–Shannon–Kotelnikov

Don't forget Whittaker

sampling theorem, it was defined in the field of real numbers (possibly infinite decimal). How do you digitally represent infinite decimal? Scopes work with quantized samples (8 bit ADC, 16 bit ADC, ..).

Indeed, which is why even if you'd manage to feed a pure, perfect sine wave to a scope with sufficient bandwidth and an excessive sample rate, the acquired waveform would still not be a perfect sine wave but a (very close) approximation.

It is possible to mathematically analyze how quantization butchers signal: http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pdf
But Nyquist–Shannon–Kotelnikov sampling theorem do not touch quantization and I am not sure where you find "all about 1's and 0's" in this theorem.

You won't, because as you stated the theorem is a mathematical product in the real domain, actually considering analog sampling.

As to quantization errors, the only way out is increased (true) vertical resolution, which won't eliminate the errors (which are inherent in ADCs) but at least minimize them.

[nctnico]

If you are going to argue about quantization errors then you'd also need to include the number of pixels on the screen! At some point all of this is pretty moot because the frequency response of a scope isn't prefect, the analogue input stage will have some distortion, noise (ofcourse), frequency dependant phase shift and there are probably some other factors I didn't mention.

edit: typo

[testmode]

And to elaborate, while Nyquist theorem is all about 1's and 0's, it is in fact about the digital representation of the underlying analog signal.

Last time I checked Nyquist–Shannon–Kotelnikov sampling theorem, it was defined in the field of real numbers (possibly infinite length decimal representation). ...
...
...
... But Nyquist–Shannon–Kotelnikov sampling theorem do not touch quantization and I am not sure where you find "all about 1's and 0's" in this theorem.

The 1's and 0's are in the context of our discussion. Although technically your argument is correct, we don't need to go into such level of depth of that subject here I suppose.  It is already a given that we are discussing the theorem in the context of how it applies to quantization.

[lukier]

If you have a digital camera, more pixels is better-- especially if you want to zoom in on a particular section of the photo to see more detail.  Everyone that has actually done this has noticed that the photos becomes "pixelated" as you continue to zoom in. 

Nope. Like in the oscilloscopes, the full optical path matters. In the digital camera case the lens itself will be the limiting factor due to the Airy Disk and the manufacturing quality. More on that here:
http://www.edmundoptics.co.uk/resources/application-notes/imaging/limitations-on-resolution-and-contrast-the-airy-disk/

That's why there are so called "megapixel" lenses in machine vision and more expensive too. So many MPix camera with a crappy piece of plastic for the lens will not give you any more detail if you zoom in. It won't be pixelated, it will be just blurred over many pixels, all containing redundant data (no extra information) - just a waste of sensor's silicon, ADC power consumption and data bus bandwith to transmit them. Instead a sensor with less pixels, but bigger to fit the Airy Disk would be better for different reasons (bigger pixels are more light sensitive and less noisy). In the analogy, think of the lens as probe + front end, and instead of a bigger sensor (faster GPSPS ADC) the smaller sensor with bigger pixels = slower ADC but with 16 bits for example.

I understand your point that when debugging extra bandwith and sampling might be helpful, because it might turn out the signal is a square wave (so much higher harmonics) etc. However, here we discuss  the specs, and these are specified for a pure sine and here the full signal path will dampen the signal long before it reaches ADC (probe, front end with roll off etc). Therefore (esp. with sinx/x) ADC will not reconstruct the sine wave much better than with just Nyquist. If the result with sinx/x and 2 samples is identical to the shape from 10x oversampled waveform then this oversampling didn't bring anything to the table (and it won't because any deviation from pure sine, noise spike for example, in these 10x samples would mean there is higher frequency component there and that would be gone in the probe and the front end).

[KE5FX]

It looks shaky and twitchy very likely because of irregularities in the signal (i.e. phase noise, quantization noise), which means you don't get a true sine but something else.

Nope, the signal is rock-stable, coming from an HP 8672A synthesizer.  It would take a helluva lot of phase noise to look like that.

Most of the apparent jitter is simply due to the inability of the scope to place the trigger point consistently from one acquisition to the next.  It would have looked better if the triggering system operated on the final reconstructed waveform, but that has some pretty severe drawbacks of its own (as I'm sure you're aware.)  A hybrid approach would be best.  I'm not sure if the TDS 694C was the first 10 GS/s realtime scope, but it was one of the first, and there are a few rough edges.

[nctnico]

It looks shaky and twitchy very likely because of irregularities in the signal (i.e. phase noise, quantization noise), which means you don't get a true sine but something else.

Nope, the signal is rock-stable, coming from an HP 8672A synthesizer.  It would take a helluva lot of phase noise to look like that.

Most of the apparent jitter is simply due to the inability of the scope to place the trigger point consistently from one acquisition to the next.  It would have looked better if the triggering system operated on the final reconstructed waveform, but that has some pretty severe drawbacks of its own (as I'm sure you're aware.)

It seems you (or the person who made the video) are feeding TDS694C a 3.1GHz sine wave. IMHO it should be able to trigger on it but it may take some fiddling with the trigger level to get it stable.

[KE5FX]

It looks shaky and twitchy very likely because of irregularities in the signal (i.e. phase noise, quantization noise), which means you don't get a true sine but something else.

Nope, the signal is rock-stable, coming from an HP 8672A synthesizer.  It would take a helluva lot of phase noise to look like that.

Most of the apparent jitter is simply due to the inability of the scope to place the trigger point consistently from one acquisition to the next.  It would have looked better if the triggering system operated on the final reconstructed waveform, but that has some pretty severe drawbacks of its own (as I'm sure you're aware.)

It seems you (or the person who made the video) are feeding TDS694C a 3.1GHz sine wave. IMHO it should be able to trigger on it but it may take some fiddling with the trigger level to get it stable.

It's at 3 GHz exactly, which is the spec limit. 

The trigger subsystem in these scopes works really well assuming you don't have a bad ASIC, about which plenty has been written elsewhere.  It can trigger on a 3 GHz signal at -30 dBm or lower.  But the triggering process runs independently of waveform acquisition, so when a trigger comes in, it could be anywhere between two of the three available sample points per cycle.  That ambiguity manifests itself as visible jitter.

If the scope were able to capture several points per cycle instead of just three, the asynchronous nature of the trigger and acquisition systems would be proportionally less noticeable.  The 694C is great for single-shot acquisition, but repetitive sweeps will never really look stable at higher frequencies. 

It would be interesting to feed a 6 GHz signal to a 20 GS/s DSO6000X-series scope -- to bring the thread back on-topic -- to see how stable it looks in comparison.  I'm guessing they reposition the reconstructed waveform slightly at each sweep to place the trigger point at its proper spot.

[nctnico]

It looks shaky and twitchy very likely because of irregularities in the signal (i.e. phase noise, quantization noise), which means you don't get a true sine but something else.

Nope, the signal is rock-stable, coming from an HP 8672A synthesizer.  It would take a helluva lot of phase noise to look like that.

Most of the apparent jitter is simply due to the inability of the scope to place the trigger point consistently from one acquisition to the next.  It would have looked better if the triggering system operated on the final reconstructed waveform, but that has some pretty severe drawbacks of its own (as I'm sure you're aware.)

It seems you (or the person who made the video) are feeding TDS694C a 3.1GHz sine wave. IMHO it should be able to trigger on it but it may take some fiddling with the trigger level to get it stable.

It's at 3 GHz exactly, which is the spec limit. 

The trigger subsystem in these scopes works really well assuming you don't have a bad ASIC, about which plenty has been written elsewhere.  It can trigger on a 3 GHz signal at -30 dBm or lower.  But the triggering process runs independently of waveform acquisition, so when a trigger comes in, it could be anywhere between two of the three available sample points per cycle.  That ambiguity manifests itself as visible jitter.

The triggering in a DSO doesn't work that way in general; they all have circuitry (a trigger time interpolator) to align subsequent acquisitions precisely on top of eachother. Otherwise triggering on high frequency signals would not work at all (especially in equavalent time sampling mode) and cause the jittery picture in the video.
From what I know specifically from the Tektronix TDS500 and TDS700 series is that they have a trigger time interpolator which measures the trigger point versus the sampling clock in order to put the trace at the right point on the screen. This leaves two possible causes for the effect shown in the video: the trigger level isn't adjusted properly or the scope is broken.

[KE5FX]

This leaves two possible causes for the effect shown in the video: the trigger level isn't adjusted properly or the scope is broken.

That's what I'm saying -- I'd expect this feature in newer scopes, but it's not universal by any means. 

Why, in your opinion, would anyone bother using a 20 GS/s sampler in a 6 GHz scope, if perfect, stable reconstruction is possible at 0.4 fs or even higher?

[nctnico]

This leaves two possible causes for the effect shown in the video: the trigger level isn't adjusted properly or the scope is broken.

That's what I'm saying -- I'd expect this feature in newer scopes, but it's not universal by any means. 

Why, in your opinion, would anyone bother using a 20 GS/s sampler in a 6 GHz scope, if perfect, stable reconstruction is possible at 0.4 fs or even higher?

I think jjoonathan summed it up nicely in an earlier post:

1. Full fs/2 bandwidth
2. Good step response
3. Good out-of-band signal rejection

Modern oscilloscopes sacrifice #1 to get #2 and #3. Last generation sacrificed #2 to get #1 and #3 ("brick-wall" front-end filters). Pick your poison.

[Wuerstchenhund]

It would be interesting to feed a 6 GHz signal to a 20 GS/s DSO6000X-series scope -- to bring the thread back on-topic -- to see how stable it looks in comparison.  I'm guessing they reposition the reconstructed waveform slightly at each sweep to place the trigger point at its proper spot.

I can't offer a 6Ghz signal on a 6GHz scope as I don't have the necessary equipment at home but if I find the time this evening anytime soon I'll get some video of a 3Ghz sine wave on a slightly more modern 20GSa/s scope (I got a new video gizmo to capture VGA output so that's a good opportunity to try it )

Why, in your opinion, would anyone bother using a 20 GS/s sampler in a 6 GHz scope, if perfect, stable reconstruction is possible at 0.4 fs or even higher?

I think jjoonathan summed it up nicely in an earlier post:

1. Full fs/2 bandwidth
2. Good step response
3. Good out-of-band signal rejection

Modern oscilloscopes sacrifice #1 to get #2 and #3. Last generation sacrificed #2 to get #1 and #3 ("brick-wall" front-end filters). Pick your poison.

This.

Also, Scope manufacturers develop their ADCs in certain steps (like 1-2-5-10-20-40-80-160-240 GSa/s), and for a 6GHz signal Nyquist-Shannon wants a sampling rate larger than 12GSa/s (plus some more for filter roll-off atc), so 20GSa/s isn't such a far off choice and using an existing ADC is cheaper than developing say a 15GSa/s just for that one scope.

Also, many scope series are offered with different BW ranges (some of them even BW upgradeable), and usually they come with the same acquisition system for all models as its cheaper than to give each BW step its own acquisition system variant with varying sample rates (which would also complicate BW upgrades).

[siggi]

It would probably look quite a bit better if the firmware could map the trigger level back onto the sin(x)/x-interpolated waveform and adjust the horizontal position accordingly.  It doesn't look like they're attempting to do anything like that here, but I imagine more modern scopes can.  Of course, then you end up looking at trigger jitter...

I know the 5/700-series TDS scopes have interpolators to measure the time from trigger to a sample clock edge, so they effectively do this in hardware. I've never seen schematics for a 600-series TDS scope, so I don't know whether they attempt the same thing, but your triggering looks pretty loosey-goosey for sure .