Comments on oscilloscope sampling, #13, 1 of 2

[jahonen]

Hi,

I made some tests using HP (now Agilent) 54645 scope which has only 200 MS/s sampling rate with 100 MHz analog bandwidth. What is special that it seems to use sin x/x reconstruction of the waveform, which results much better results than just "join-the-dots"-method.

I agree that there should be enough sampling rate, but the used reconstruction method is also important. Remember that your sampling rate will decrease quite quickly anyway when time/div is increased as the record length is finite, whatever the maximum is.

Used measurement setup is a Tektronix AFG-series 100 MHz function generator, set to 5-cycle burst of 50 MHz sine with 1 Vpp amplitude. Burst mode is used here so that scope can't use equivalent time sampling tricks. The generator was connected using BNC cable, terminated at the scope end with 50? inline BNC terminator (54645 doesn't have internal terminator), to get rid of any probe artifacts. The scope was set to single sweep. And here are the results:

Pre-trigger display:



And after single sweep:



I think that 200 MS/s is quite enough for reconstructing the 50 MHz sine burst quite nicely. The first sine peak is somewhat low but otherwise it looks pretty much ok. Unfortunately the Tek function generator doesn't allow higher than 50 MHz frequency on the burst mode so I can't test the actual practical limit. Sin x/x-reconstruction is by the way, mathematically only correct way to reconstruct the analog waveform from the samples, assuming the sampling was done correctly and Nyquist rule was obeyed. It is not a guessing in that sense. However, it is difficult to guarantee Nyquist criterion, so it is easier to oversample.

Another gotcha where I and several of my colleagues have been stumbled on with the DSO's is the aliasing. It is too easy to set the scope to relatively long time per division and then connect relatively high frequency signal to scope and then start wondering why the scope doesn't want to trigger on the signal. The signal is often looking just correct, but too low frequency. This seems to work also on the cases where input waveform is not sinusoidal! Finally when you start decreasing the time/div then you'll figure out what is "wrong" Tektronix scopes (at least up to 3000-series) seem to suffer from this effect, my Agilent 6000 series does not to be affected, it properly shows just "bar", like on an analog oscilloscope (although on heavy zooming the waveform breaks down in such case).

Anybody else have opinions or experiences on this?

Regards,
Janne

[EEVblog]

It can be argued (mathematically) that SinX/X interpolation can reconstruct any complex input waveform provided you have (from memory) 4 times the sample rate (not 2 times).
But that of course misses the point that the limited analog bandwidth is distorting your signal, so it's kinda moot.
Yes, Sin/X interpolation is nice to have, but it's not magic.

People still like to rant on about aliasing as being the biggest problem with digital scopes, but the fact is modern (real time) scopes are pretty good at dealing with it, and it's indeed impossible to get aliasing on many good digital scopes.

Dave.

[qno]

You have found one of the problems of the digital scope.
That is why I save my combiscope (analog and digital).

One solution is switching on the Peak Detect option.
I do not remember how the option is called with HP scopes but the Tek a.o. call it peak detect.

This displays the min and max measured value of the input signal and will mimic analog behavior.

[jahonen]

Today I took some examples of the aliasing, the first one is a Tektronix TDS3034A, 300 MHz, 4-channel, 2.5 Gs/s DSO. I used a 10 MHz sine wave input. I don't know if that qualifies as "modern scope". But as you'll see, it does have alias problems.

First, a quick look at 20 ns/div horizontal setting:



increase horizontal to 10µs/div:



increase horizontal to 40µs/div:



Now the "bar" starts to break up, let's bump the time/div to 4 ms/div:



Wait a minute, measurement says now that our 10 MHz signal has turned into 57 Hz one! What if you wanted to measure some kind of an amplitude modulation from 10 MHz carrier? The amplitude and waveshape are quite correct. The only artifact seems to be that the scope seems not to trigger on the sinewave even if the settings are appropriate. Let's do a single sweep:



Perfectly nice "57 Hz" sine Now, let's try more complex waveforms. First, a 10 MHz square wave @ 20ns/div:



And then with 4 ms/div single sweep:



Quite amazing undersampling from Tek, even the very small reflection bumps get nicely undersampled

And how about 1 MHz sinc-function, certainly that can't be undersampled? Think again.





Like I said previously I and my colleagues have been stumbled on this effect for several occasions, and it really sometimes takes a while to realize what is wrong. Next, an Agilent MSO6034A in next post...

Regards,
Janne

[jahonen]

Now some tests on my Agilent MSO6034A, 300 MHz, 4+16-channel, 2 GSa/s mixed-signal oscilloscope. I don't have a proper signal generator around, so I used an old color bar TV-generator tuned to VHF channel 12, which is about 230 MHz. Click on the pictures to get a larger one, I reduced the original XGA-sized images to fit more nicely here.

First, a sample of the RF-signal at 100 ms/div. Note the sample rate in bottom right, 4 MSa/s should result heavy aliasing, as the carrier is very much above Nyquist frequency.



The result is quite amazing. Not any sign of aliasing, very analog look, and using normal acquisition mode. What about when we zoom the acquisition:



One can actually find the 50 Hz frame synchronization regions from the zoom, not bad at all.. Let's look at the carrier so that we actually are measuring correct signal:



As expected, the carrier is around 230 MHz. Agilent seems to succeeded much better for alias suppression. I don't have pictures to show you, but the old 54645D HP seems also quite immune to the alias effect. So next time you get strange results from your DSO, try decreasing the time/div setting

Regards,
Janne

[armandas]

Wow! Thanks for sharing, Janne!

[qno]

Very nice.

Here you can see you can easily be fooled by a digital scope.

I do not see it in the display of the Tek or Agilent in your pictures but Tek use to display the sample rate in the screen.

Usually with slower y sweeps the sample rate goes down too. Here aliasing is prone to happen.
Do you have the same problem when peak detect is on??

This should lead you to the correct sample rate (y sweep speed) for the signal.

[jahonen]

Very nice.

Here you can see you can easily be fooled by a digital scope.

I do not see it in the display of the Tek or Agilent in your pictures but Tek use to display the sample rate in the screen.

Usually with slower y sweeps the sample rate goes down too. Here aliasing is prone to happen.
Do you have the same problem when peak detect is on??

This should lead you to the correct sample rate (y sweep speed) for the signal.

Personally I think that there shouldn't be any kind of aliasing so that user may possibly be fooled by it, regardless of the time/div setting. Ever. Of course, the peak detect gets rid of the problem (actually, I don't have a problem but just wanted to show this effect to you), but it turns the display somewhat not-so-nice so I don't often use it, unless I need to display very narrow pulse on a very long timescale.

I tested today also the Agilent 54855A and HP 54645D at work. 54855 showed aliasing when the input frequency equaled the displayed sampling rate but 54645 didn't (maybe very slightly in same situation but not anything like clear trace of TDS3034). Quite a surprise considering that 54855A is a higher end lab scope.

Actually, one can see the sampling rate on the Agilent when acquire or horizontal menu is displayed. All of the pictures I took from my MSO6034A display that information (4 MSa/s in the first two pictures, 2 GSa/s in the last one). Tek shows the sampling rate when acquire menu is displayed.

My point was that it is perfectly possible for a DSO to mitigate the alias effects, as the Agilent case shows. AFAIK, they have a patented method for the alias suppression. I suspect that they run the ADC at full rate all the time, and then use downsampling techniques to obtain desired sweep speed. During the process, one can better handle the situation. Agilent MegaZoom uses ASIC technology.

I don't have newer Teks (4000 etc.) around, so I can't say anything about them. Maybe they are better in this respect than TDS3000-series.

Of course, there are more oddities in the store, like trigger jitter or waveform capture rate limitation, but alias effect is quite easy to observe unless special care is taken during the product design.

Regards,
Janne