Rise times with 2Ghz scopes at 5GS/s

[burkat]

So I'm getting back into electronics after a 20 year detour of software and have been looking for some new gear.  I'm looking in the range of a tek MSO4 or r+s MXO4 or 5 in the 1.5/2 Ghz range.  Looks like I have to trade a nice car for it but I'm ok with that.
The thing is I dug out my old TDS3012, and "upgraded" it (thanks to this community, so it's now 500Mhz, 5GS/s) and as I'm testing it's limits, something jumped out at me.   I'm looking at doing primarily some signal integrity experiments and I was trying to look at the rise times of some microcontrollers.  In this case ESP32c6.  I have been told that I need a much faster scope than 500Mhz and active probes to determine accurate rise times/noise content of today's fast logic, but here is what makes no sense to me..
So right now I can measure the rise time, to about 650ps with this 25 year old scope.

( See attached image of rise time )

In order to see a quick rise like this the frequency content of this 650ps square edge should be around 550Mhz, which is probably hitting the limit of the probes and this scope. So a 1.5Ghz scope should be better.

( See attached image of rise time as dots )

But at 5GS/s these scopes would be doing just 5 samples in a 1ns division, so with this 650ps rise time at best ADC is only reading 2 or 3 samples.  The MXO4l/5 scopes that I have been leaning to are still only 5GS/s so even though they have higher BW I'm not sure I would be seeing that much of a different signal since that scope is only doing a couple of ADC samples in that rise time.  Even with active probes I might have higher frequency content but at the 5GS/s ADC rate that would just get averaged/extrapolated out.

Am I on crack in thinking that 5GS/s is pretty slow for these fancy scopes, or am I missing something obvious here?

[benj38]

There are a lot of articles available on the web that you can read about the Nyquist frequency, and the assumptions one makes, so I will not try to summarize that theory here.

That said, I think you are confusing the rise time of the scope and the rise time of the signal being measured. To accurately measure a 650ps rise-time signal, a 650ps rise-time scope is definitely not good enough, as the measured rise-time will be a combination of the rise time of the scope and of the signal. The usual formula used (for scopes with Gaussian frequency response) is that the displayed rise time is the square root of the sums of the squares of the signal's rise time and the scope's rise time. Thus, a 650ps rise time signal on a 650ps rise time scope will measure as 919ps --- hardly an "accurate" measurement. If, however, the signal's rise time is double that of the scope's, the measured value will be only about 12% off.

In case the TDS3052 does not have a Gaussian response, but more of a flat one, the formula above does not hold, but the measurement accuracy should be actually a bit better than what this formula gives.

Finally, keep in mind that while 6 or 7 samples during the rise time (as would be the case for a signal rising at 1.3 ns) are not sufficient to see the shape of the rising portion (and indeed that is being heavily interpolated), it is quite enough to find out the time it takes for the signal to rise from 10% to 90% to within the accuracy stated above.

[G0HZU]

For repetitive waveforms, some scopes offer equivalent time sampling to combat the sample rate issue but this might not be suitable for your needs. I'm no scope guru by any means but I do have quite a few scopes here (mostly old) and I generally try and ensure the rise time of the scope is at least three times faster than the rise time of the waveform being measured. This gives good accuracy and (usually!) avoids ringing artefacts in the scope front end that can cause confusion and disappointment.

So I would agree that you need a fast scope to do this properly.  I've noticed that it's best to choose a cope with a dedicated (relay switched) 50 ohm path rather than a scope that switches in an internal 50R termination on the 1 Meg path. Otherwise, the scope artefacts tend to be worse than expected. But for the stuff you are doing at 650ps I'd expect the scope to have a dedicated 50R path anyway.

The only reasonably modern/fast scope I have here is an oldish Tek MSO4104 (1GHz BW 5GSa/s) and it would struggle a bit with the stuff you are doing if the aim was to see an accurate representation of the waveform of something like a 650ps rising edge. It would do a reasonable job, but a faster scope with a decent front end would be better. The Tek MSO4104 is really just a mid range (big!) portable scope with a fairly low tech PCB design for the front end. It does have a dedicated 50R path though. It has some nice features but being Tek, it is also a bit clunky and restrictive in terms of what the user can do with it.

[tggzzz]

In general the samples/s figure is marketing wank. What matters is the bandwidth in Hz. Examples: I have a <140ps risetime scope with <<100kS/s, and a 200ps risetime scope which has BC107s (f_T=300MHz) in the signal path. The latter was designed for signal integrity measurements c1970, and is not general purpose!

For signal integrity measurements, the eye diagram is king, since that captures the worst cases. The sampling rate is not very important for those diagrams.

G0HZU makes sensible points. I will add that probes and probing technique are vitally important at these frequencies.

[David Hess]

For repetitive waveforms, some scopes offer equivalent time sampling to combat the sample rate issue but this might not be suitable for your needs.

For DSOs which lack a time delay counter to support equivalent time sampling, which is most modern ones, a sort of averaging produces almost the same result.

During acquisition, the digital trigger uses interpolation to find the trigger point, much as a time delay counter does so for an old DSO which supports equivalent time sampling.  Then the acquired waveform is merged into the processing record just as it would be with equivalent time sampling, so the processing record has a higher sample rate, limited only by record length.

The difference between this and old style equivalent time sampling with an analog trigger is that the digitally reconstructed trigger point is subject to aliasing because it is based on the digitizer's sample rate.

So as a practical matter for repetitive signals, only bandwidth matters.

[benj38]

But for the stuff you are doing at 650ps I'd expect the scope to have a dedicated 50R path anyway.

The TDS3000 family scopes indeed have a dedicated relay-switched 50Ohm input path.

[tautech]

2GHz SDS6204A with 30ps Bodnar pulser:
https://www.eevblog.com/forum/testgear/show-us-your-square-wave/msg4032745/#msg4032745

[burkat]

Oh, so let me see if I understand this.... so even if the scope ADC at 5GS/s is taking very few samples on a fast signal rise time, it's merging samples from multiple conversions/triggers of say a clock signal.  I imagine it offsets randomly? or in some manner the start of the trigger so it can get ADC samples at slightly different parts/time of a repetitive signal, and then it smushes 100s ?  of these samples to produce a representation of the signal on the screen.

So looking at the datasheet for say a r+s mxo4 it says 5GS/s as well as "effective sampling rate" of 5 TB/s.  So the 5TB/s is that interpolated spec. 

Is there spec that tells you how many interpolations a scope is doing to represent the signal.  I imagine that would require the input signal to have enough pulses as well as the display rate of the generated waveform on the screen.

   

[tggzzz]

There are various mechanisms.

If you set a digitising scope to infinite persistence, then all you have to do is wait.

Have a look at the explanations and diagrams in https://en.wikipedia.org/wiki/Eye_pattern which contains this example of poor signal  integrity is

[David Hess]

Oh, so let me see if I understand this.... so even if the scope ADC at 5GS/s is taking very few samples on a fast signal rise time, it's merging samples from multiple conversions/triggers of say a clock signal.  I imagine it offsets randomly? or in some manner the start of the trigger so it can get ADC samples at slightly different parts/time of a repetitive signal, and then it smushes 100s ?  of these samples to produce a representation of the signal on the screen.

Alignment is usually random, so it is possible for the sample clock to align with signal, but some DSOs deliberately randomize things to prevent this.

So looking at the datasheet for say a r+s mxo4 it says 5GS/s as well as "effective sampling rate" of 5 TB/s.  So the 5TB/s is that interpolated spec.

That is correct.  Sometimes the limit depends on the number of points available in the record, and sometimes it depends on the resolution of a counter or math.

Is there spec that tells you how many interpolations a scope is doing to represent the signal.  I imagine that would require the input signal to have enough pulses as well as the display rate of the generated waveform on the screen.

It depends on the number of samples acquired per trigger, and the alignment between the trigger and sample clock.  Since the DSO does not know the alignment, or even whether the signal is repetitive, it cannot know how many triggers will be required ahead of time or how long it will take.

[smaultre]

In oscilloscope and digital signal processing contexts, having
5 samples in a 1ns division (1 nanosecond per horizontal grid division) defines several key technical parameters for the system:

    Sampling Rate: The system samples data every 0.2 ns (200 picoseconds), resulting in a real-time sampling rate of 5 GSa/s (Giga-samples per second).
    Sample Interval: The time between each individual sample point is 200 ps.
    Nyquist Frequency: The maximum theoretical signal frequency that can be accurately represented (without aliasing) is 2.5 GHz (half the sampling rate).

Step 1: Calculate the Sample Interval The sample interval (\(T_{s}\)) is the time elapsed between two consecutive samples. Given there are 5 samples in a 1 nanosecond (ns) division:\(T_{s}=\frac{1\text{\ ns}}{5}=0.2\text{\ ns}=200\text{\ ps}\)
Step 2: Determine the Sampling Rate The sampling rate (\(f_{s}\)) is the reciprocal of the sample interval:\(f_{s}=\frac{1}{T_{s}}=\frac{1}{200\times 10^{-12}\text{\ s}}=5\text{\ GSa/s}\)
Step 3: Calculate the Minimum Rise Time In digital sampling, the rule of thumb to accurately capture and reconstruct a rise time (\(10\%\) to \(90\%\)) requires approximately 1.6 to 2 samples on the rising edge to avoid significant interpolation errors. Using the standard coefficient of \(1.6\):

[tggzzz]

In oscilloscope and digital signal processing contexts, having
5 samples in a 1ns division (1 nanosecond per horizontal grid division) defines several key technical parameters for the system:

    Sampling Rate: The system samples data every 0.2 ns (200 picoseconds), resulting in a real-time sampling rate of 5 GSa/s (Giga-samples per second).
    Sample Interval: The time between each individual sample point is 200 ps.
    Nyquist Frequency: The maximum theoretical signal frequency that can be accurately represented (without aliasing) is 2.5 GHz (half the sampling rate).

You have to be very careful how you define "maximum signal frequency" in that context.

Standard interview question: you have an audio signal amplitude modulated onto a 10MHz carrier. What is the minimum sampling frequency? A candidate who mentions MS/s is asked to think again

[smaultre]

We are taking about  maximum theoretical signal frequency. And

thinking that 5GS/s is pretty slow for these fancy scopes

, Yes PRO models have 16-20Gs/s on these frequency ranges! All of that

tek MSO4 or r+s MXO4.

... are middle grade scopes.

[tautech]

……….

Am I on crack in thinking that 5GS/s is pretty slow for these fancy scopes, or am I missing something obvious here?

Those coming from entry level DSO’s expect the sampling rate to be divided down by the # of active channels yet in middle and high class scopes each channel has its own ADC but will sometimes divide down the memory available.
ETS is another feature sometimes offered in the better scopes and can provide double or more sampling rate.

One must do their homework or know what they’re looking for or what questions to ask.

[David Hess]

There is something to watch out for.  When they dropped equivalent time sampling, HP/Agilent/Keysight published an application note discussing how averaging was just as good.  Their newer models average the results of after sin(x)/x interpolation, preserving all of the aliasing, so not the same thing we are discussing here.  This however does not add much error to rise and fall time measurements.

ETS is another feature sometimes offered in the better scopes and can provide double or more sampling rate.

Double?  I would be disappointed if equivalent time sampling did not increase the sample rate by at least a order of magnitude.

My 20 MS/s and 100 MS/s DSOs increase to 2 GS/s.  My 500 MS/s real time DSO increases to 20 GS/s.