Scope Math Bit Depth

[Zlotnik]

Hi all!

I have a project idea that will benefit from increased dynamic range in a DSO, and had the idea to try to circumvent some limitations with the scope's math channels:
- Use a log-amp, and then apply an exponential function in the scope's math channel
- Use an auto-ranging pre-scaler, with a parallel digital range-output, use MSO channels as input to math to scale the analog channel
- Same pre-scaler, but with analog range output (my current scope does not have MSO channels, and the MSOs I've looked at don't do math on logic channels)

All of these ideas only make sense though if the math channel result can have a higher bit-depth than the measured channels: eg ch1+ch2 has one bit more, ch1*ch2 has 2x bit depth etc.

However, in the case of my venerable DS1054Z, this is not the case. In fact, it looks like the math result is giving significantly reduced bit-depth...
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How is this with your scopes?
I'd be in particular interested in experience with the Siglent SDS2k+, R&S RTB 2k, and Keysight DSOX1k series scopes.

Cheers,
Alex

[David Hess]

The Rigol does all of its processing using an 8-bit record but that is not universal of all DSOs.  Many use a 16-bit processing record which is required to fully support high resolution and averaging modes anyway.

[mawyatt]

I'm working and waiting on delivery with some log amps now. These are based upon successive detection and can achieve very high DR. Back in ~2013 we did some IC designs in an advanced SiGe BiCMOS ~300GHz process that approached ~100dB DR.

They are highly temperature dependent tho, and must be carefully controlled, compensated and characterized for precision use, and a small error after the log compression expands to a large error after exponential expansion.

This was the ultimate limited factor in a new class of filters some years ago called Log Domain Filtering. The input signal was compressed into the log domain by a bipolar transistor and then filtering applied (the filtering is very complex mathematically). After filtering the compressed signal was expanded with a similar matched bipolar transistor. This worked beautifully and since the filtering was in the log domain this could easily be current controlled frequency scaled, which we did over 6 decades!! However the weak spot was the input noise was compressed, filtered and then expanded as expected, but the noise created in the log section was not prior compressed and when expanded became too high. The end result was a filter with good DR and amazing tuning range but very poor noise performance and never became widely used.

I think your approach might be useful on certain waveforms and expand the scopes apparent DR, but you are still limited by the scopes display. Maybe offload the log-amp captured data and process the signal on a PC may yield a better result. The thing to remember is that by log compressing, each scope ADC bit becomes a much larger representation of the signal, and any error represents a much larger signal error. Also look into the Hi-Resolution modes which expand the scope ADC with software, and the Eres function which is another software resolution expansion.

One clever thing that was done with the Bode Plots on certain Siglent scopes like SDS2000X Plus, was the scope input scale factor "gain" is scaled along with the DUT driving signal to "expand" the DR of the Bode Plot measurement as the frequency sweep was being applied. This allowed DUT devices with high attenuation like certain filters to be better measured by selective scaling the input scale gain and expand the input level for areas where the attenuation is high. I've played a little with this and it does work well, but slow. You can also create a "Profile" which allows the user to control the input signal level based upon expected DUT performance, nice features indeed!!! Others on here have much more experience with this than I, maybe they will comment.

Anyway, good luck with your project.

Best,

[Zlotnik]

Hmyah, seems the math result bit depth is insufficient to contain math results usually. At least found no reference for increased bit depth in math results in any datasheets or manuals.
Also, I agree with your caveats about log amplifiers.

In the application I’m thinking about, I’m after characterising energy estimates over wide dynamic range power consumption (i.a. on IoT gizmos etc), correlated with logic and analog channels on a scope.
I’m currently leaning towards making my life more simple by having separate measurement ranges output on separate channels, to be read on a scope with HiRes, integrated individually and then summed to get the total energy. That way each range channel has reduced dynamic range requirements, and the dynamic range of the integral is not tremendously large.
If range switching shorts the inactive range’s output, no hacky way to tell the scope which range we’re on is needed, and minimum noise from the unused channel is integrated up.

More wasteful of channels than I’d like though. And have to implement the range switching and channel shorting.
.. or I do what every other gizmo in that vein does, and digitise the high dynamic range on board with a wide ADC. Would prefer a solution without a PC though, don’t want to reinvent the wheel, scopes are good at correlation...

[radiolistener]

You can apply low pass filter to reduce noise floor in order to improve dynamic range.

DS1054Z has 1 GS sample rate and 12 megapoints.

if you reduce it to 48 kS sample rate, you will get:

process gain = 10*log(12M/48k) = 23.98 dB

this is about 4 bit. So, the total dynamic range for 8 bit ADC will be 6.02*8 + 1.76 + 23.98 = 73.9 dB

ENOB = (73.9-1.76)/6.02 = 11.98 bit

Almost 12 bit resolution for 24 kHz bandwidth 

[Zlotnik]

The thing is: if the math output is only 8bit wide, even a low-pass filtered signal that should give 12 ENOB will be only the 8MSB of the low-pass filtered signal.