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Measuring Distortions with the Scope:What you see is not what you really have..
mawyatt:
--- Quote from: mawyatt on January 07, 2023, 05:24:00 am ---To evaluate the DSOs ability to properly represent the THD of a waveform, rather than use a waveform of unknown low THD (sine-wave for example), use a waveform with known THD such as a square-wave or triangle-wave. Altho these waveforms may have an uncertainty in creation from the generator like the sine-wave they have a THD that can be computed theoretically and not ideally zero, so the results from a DSO FFT evaluation can be compared to the theoretical THD of the applied waveform.
Because these waveforms naturally possess higher levels of controlled THD compared to a uncontrolled abet low THD sine-wave, they can be measured by the DSO with the lower resolution ADCs & performance Input amplifiers/attenuators within their span of limited performance.
Here's a few THD for common waveforms derived from this IEEE paper:
https://www.researchgate.net/publication/260672713_Analytic_Method_for_the_Computation_of_the_Total_Harmonic_Distortion_by_the_Cauchy_Method_of_Residues
Square-wave THD = Sqrt[(pi^2)/8 -1] ~ 48.3%
Triangle-wave THD = Sqrt[(pi^4)/96 -1] ~ 12.1%
Sawtooth-wave THD = Sqrt[((pi^2)/6 -1} ~ 80.3%
Pulse-wave THD = Sqrt[((D(1-D)*(pi^2))/2(sin^2(pi*D))) -1] which varies from 48.3% to 191% as D (Duty Cycle) varies from 0.5 to 0.9, or 0.1 as THD function is symmetrical about D = 0.5 (Square-wave).
We are unable to verify our DSO FFT against these theoretical waveform THD readings at this time, so others may want to utilize this information and report results. Hopefully we'll be able to perform these measurements ourselves and report the results soon.
Of course this introduces another "uncertainty" with the waveform "quality", some of the modern AWGs likely are good sources at lower frequencies (as shown with sine-waves), and we do have an accurate by design custom low frequency squarewave source with precise duty cycle and amplitude available.
Anyway, hopes this helps with the FFT evaluations regarding THD.
As always, YMMV.
Best,
--- End quote ---
Got a chance for a quick measurement. This is with SDS2000X+ in 10-bit mode using SDG2042X for waveforms.
Triangle-wave at 5VPP, THD 12.0% (12.09%) using first 19 harmonics (Theoretical 12.1%), using 50 harmonics 12.10%
Square-wave at 5VPP, THD 46.5% (46.64%) using first 29 harmonics (Theoretical 48.3%), using 50 harmonics 47.42%, 100 harmonics 48.14%
Sawtooth-wave at 5VPP 100 harmonics 80.05% (Theoretical 80.3%)
Pulse-wave 25% Duty Cycle at 5VPP, 100 harmonics, THD 91.99% (Theoretical 92.23%)
We could see the results converging towards a slightly higher THD as we added more harmonics in the measurements, which is to be expected as the higher order harmonics are being truncated (not included) which yields a lower overall THD rendering. We also confirmed the Square-wave result with the mentioned precision custom source. The squarewave error is more susceptible to harmonic truncation because the harmonics fall of as 1/f, whereas the triangle wave falls off as 1/f^2.
Anyway, this gives us a little more confidence in the DSO FFT ability to render a reasonable THD result for waveforms with higher THD, curious what others find utilizing these waveforms.
Best,
Edit: Added results from (PicoScope 4262) with 16-bit core ADC.
mawyatt:
--- Quote from: _Wim_ on January 07, 2023, 03:39:11 pm ---
Many high resolutions ADCs use oversampling to achieve their high resolution, and for me oversampling and HIRES/ERES are essentially the same. Bandwidth reduction and bit-enhancement can be seen from the attached tables (copied from the Lecroy explanation)
So for a 10 bit scope a 3 bit enhancement is certainly possible for these low frequency ranges in the posts above, giving around 78db of dynamic range. Anything below that must indeed be taking with a grain of salt, but I just wanted to point out that an 8-bit scope has more that 48db of dynamic range...
--- End quote ---
Having been involved in ADC chip developments in the past, it's funny when folks think an ADC chip is the single conversion type one often refers to as a "Flash" single step conversion, when they really are an oversampled multi-step conversion type. The prior mentioned 24-bit resolution types are massively oversampled Delta-Sigma types, which are very CMOS friendly and yield nicely to CMOS advanced technologies, and why they are so reasonably priced (small chip size). However, no free lunch as they tend to operate at lower frequencies, but with CMOS process advancements are moving up in frequency and soon maybe into the lower RF bands. Hopefully we'll soon see some new CMOS friendly ADC architectures appear and trade off massive oversampling with waveform quantization in both amplitude and time, and support post Analog to Digital conversion Anti-Aliasing filtering dictated by the actual input waveform metrics!!
Best,
rf-loop:
Some may say that when the ADC is 8 or 10 or 12 bit then this and that dynamic range and below this and that level FFT displayed things are more like shit.
So or so. But in practical example this happens in real life with real instruments and not with student books.
Oscilloscope
SDS2504X HD
Generator SDG1000X
Input CH1, 50ohm AC, Full BW, 50mV/div (with this setup 4dBm signal is roughly full screen (thewre is stioll small overlap after screen 8div before ADC F.S.
Acquisition mode Normal,
FFT also normal and window Flat Top.
FFT span 300Hz (30Hz/div) and center 100020Hz
There are two signals. Marker 1 signal is 99930Hz from SDG CH1 and Marker 2 signal is 100070Hz from SDG CH2 but there is ~30dB attenuator before splitter.
SDG Ch2 signal is amplitude modulated using modulation depth 0.2% and modulating frequency 50Hz so sidebands are 60dBc
Now think that marker 1 signal is in practice maximum level (near ADC full scale. Screen height 400mVpp responds -3.98 dBm
In image (77), there can see modulation sidebands well and even levels are measured quite well. These mod. Peaks are around -90dB below marker 1 signal (maximum level) and -60dBc (carrier is 30dB below maximum level. )
As can also see there is still nice distance to noise floor.
Image (78), all same but FFT trace average 8 what lightly cleans random noise to more close its average.
nctnico:
--- Quote from: markone on January 07, 2023, 02:03:31 pm ---
--- Quote from: _Wim_ on January 07, 2023, 06:36:23 am ---
--- Quote from: JeremyC on January 07, 2023, 01:48:39 am ---- Don’t use any kind of averaging, ERES, highres, etc.
....
As good start I suggest to check THD + Scope published by W2AEW about 3 years ago:
--- End quote ---
I think you need to re-watch the referenced video by W2AEW (#65: Basics of using FFT on an oscilloscope), because it perfectly makes sense to use HI-RES or ERES to increase the effective number of bits. This way an 8-bit scope can have a larger effective number of bits at a much lower bandwidth.
A good comparison between ERES and HI-RES can be found here: https://teledynelecroy.com/doc/differences-between-eres-and-hires
--- End quote ---
The point is that any math process that extend dynamic range with ADC sampling add artifacts and alter BW, so what JeremyC is saying makes perfect sense if you want to be sure to no catch phantom FFT peaks or miss real ones with BW cut.
I personally agree with that, while I often use ERES equivalent functions in YT mode I have no interest to see FFT fake deep dynamic ranges in 8-12 bits scopes, I find all those small false frequency components quite distracting and when I see 100-120dB FFT screenshot taken from ordinary scopes I make a smile.
--- End quote ---
Agreed. For starters there has to be enough white / Gaussion noise for eres / high resolution to work well. Eres and high-res are nice tools to make a signal look cleaner but if you zoom in far enough, you can see all kinds of weird distortions. I recall doing some testing on my good old Tektronix TDS744A. Turning the 20MHz bandwidth limit on, made the high-res produce all kinds of fantasy signals. The same goes for FFT; you need to be really carefull with interpreting what you are seeing. Deep FFT is useful to look at closely spaced frequencies (as others have mentioned as well) but the extra dynamic range might not be there at all. Or put differently: the reliability / confidence level of the measurement results that are below the dynamic range of the ADC, is very low.
_Wim_:
--- Quote from: nctnico on January 07, 2023, 06:20:37 pm ---Agreed. For starters there has to be enough white / Gaussion noise for eres / high resolution to work well. Eres and high-res are nice tools to make a signal look cleaner but if you zoom in far enough, you can see all kinds of weird distortions. I recall doing some testing on my good old Tektronix TDS744A. Turning the 20MHz bandwidth limit on, made the high-res produce all kinds of fantasy signals. The same goes for FFT; you need to be really carefull with interpreting what you are seeing. Deep FFT is useful to look at closely spaced frequencies (as others have mentioned as well) but the extra dynamic range might not be there at all. Or put differently: the reliability of the measurement results that are below the dynamic range of the ADC, is very low.
--- End quote ---
I agree some fantasy signals can be shown, but this is in my (limited) experience always below the effective dynamic range (so not the dynamic range visualized, but the once calculated using the enhanced number of bits).
Is there in your opinion a difference between oversampling (https://www.analog.com/media/en/technical-documentation/tech-articles/Increase-Dynamic-Range-with-SAR-ADCs-Using-Oversampling.pdf) and HIRES? For me it seems this is exactly the same, but I could be missing something.
Maybe with my 12-bit pico I am closer the the actual noise floor and never had insufficient gaussian noise? I do not use the FFT on my 8-bit scope (DS1054Z) because it is a pain, but with the 12-bit Pico (and Analog discovery) I always have had quite trustworthy results by using averaging and/or ERES.
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