Noise analysis and reduction for ppm level measurements - Page 1
Forum section: electronics / general

author: rhb
author_rank: Super Contributor
timestamp: April 02, 2018, 07:12:28 pm
content: I spent some time yesterday looking at some of TiN's data. I've very grateful to him for making those available. Otherwise I should have nothing with which to work. I cannot justify expending the amount of money he has on lab equipment and I have no way to arrange access to such equipment. I just bought an HP 8560A w/ TG and eagerly await its arrival. And I just finished cleaning my 3478A. So my lab is quite modest.One striking aspect of the data is the amount of noise present in the measurements using a 3458A. It is my understanding that the instrument will average measurements over a user selected period, commonly a number of power line cycles. Thus I expected far less noise in the data.In looking at the 3458A operator's manual, the discussion of the setting of bandwidth and integration time is rather vague about the window edges. In particular, if one integrates all samples over a number of power line cycles without applying a weighting function to the first and last few samples, it corresponds to a rectangular window in the time domain which is a sinc function with significant sidelobes in the frequency domain. This allows a considerable amount of noise leakage, far more than one might expect. Moreover, such noise will be aliased quite severely.Does anyone know of professional papers on the topic of the analysis and reduction of noise in high resolution DC voltage measurements? While a simplistic treatment in an operator's manual would not surprise me, I should be quite surprised if the actual implementation is not more sophisticated.

author: zhtoor
author_rank: Frequent Contributor
timestamp: April 02, 2018, 07:21:33 pm
content: see this document.best regards.-zia

author: TiN
author_rank: Super Contributor
timestamp: April 02, 2018, 07:22:39 pm
content: You might want to check my noise-related comparisonarticle with some dataand related threadhere at EEVBlog.Noise performance of top end DMMs usually limited by reference. Own LTZ1000A noise is in ballpark of 1-1.5 uV/peak-peak, unless you use multiple of refs together or cryocool them.

author: zhtoor
author_rank: Frequent Contributor
timestamp: April 02, 2018, 07:43:32 pm
content: also see this hp3458a design article beginning at page 13.https://expirebox.com/download/de878fad2a2f4f97f660eaedec47c02e.html-zia

author: Magnificent Bastard
author_rank: Regular Contributor
timestamp: April 02, 2018, 07:56:41 pm
content: Quote from: rhb on April 02, 2018, 07:12:28 pmWhite noise (above 1Hz) can be filtered out, LF ("1/f") noise (aka: "pink noise") is extremely difficult to filter out. There is no lower frequency limit-- as LF noise can have periods that exceed 1 month or even more. So, the total system noise is the RSS of the noise of the device under test, and the measurement instrumentation noise-- and strangely, longer integration times can actually spoil the measurements. For any given measurement system and device under test, there is an optimum integration time that can only be found by experiment, and then the Allan variance can be plotted-- which will indicate where the "sweet spot" is for integration time.Sometimes a simple gathering of a small (and odd) number of measurements, followed by a median filter will yield the best results.The BEST way to filter out 1/f noise is to not generate it in the first place. So, you select a reference source and device under test that has the smallest amount of 1/f noise that you can find (and/or afford), and go with that. You have to be realistic and understand that unless you have quantum based intrinsic standards, you are going to have to accept some level of noise in your measurements, and the final uncertainty will not be zero.That said, as an example, you can put a 100mHz filter on the output of a voltage reference like an LM399, and this will reduce the apparent noise by about 6X (1uVpp)-- but you will NOT be able to filter out changes in the LM399 that happen over minutes (about 1ppm jumps in the reference voltage). So, because of this, the LM399 cannot be relied upon for anything better than about 1ppm. If left on continuously, the LM399 will exhibit a temporal drift (of typically 4ppm/a, but some are better than that). If you only turn it on for a very short period to take a measurement, then turn it off for a very long period, the long term temporal drift can be negligible, but you are still limited to the 1ppm uncertainty due to the 1ppm "jumps" in the output (due to low Zener current, which you can do nothing about). If you are looking for better than 1ppm uncertainty, then an LTZ1000 is the only commercially available reference that has a long track record of providing sub-ppm uncertainties and annual drift rates. (Obviously, some LM399s and LTZ1000s are better than others, and typically 1 out of 100 will be exceptionally good).The same goes for resistors-- there are many known drift mechanisms and ways of dealing with those drifts. A hermetic package eliminate a whole set of problems. After that, artificial aging can significantly reduce temporal aging effects. After that, placing the resistor in a thermally lagged enclosure can improve temporal drift, and short term temperature drift. Keeping the resistor in a thermally stable environment (oil or oil bath) can further reduce temporal drift. Different resistance wire materials can have very good temporal stability-- some better than others. Zeranin-30 and Evanohm alloys are probably the most stable.So, this was a very long and complex answer to a simple question about a very complex problem. The short answer is that you CAN help some with sophisticated filtering, but at the end of the day there is a limit to what you can do with this, and I think you will find that your money and labor would be much better spent on better standards and measuring tools.

author: Kleinstein
author_rank: Super Contributor
timestamp: April 02, 2018, 07:59:58 pm
content: The rectangular aperture is not that bad: there is some noise aliasing from higher frequencies, but also less coming in from the lower frequencies. As there usually is some 1/f noise, this is a good trade in. The problem with possible line frequency connected signal is lowered by having the integration times linked to the mains frequency. So just around 50/60 Hz there is not much aliasing. Here a slightly (e.g. over maybe 100 µs) rounded aperture would give a slight advantage, but the 3458 HW does not allow for this.For longer integration times it is a repeated 10 PLC mode, usually alternating with a zero measurement. Thus the input aperture is like 166 ms active and 166,2 ms off repeated many times. This gives aliasing of noise in the 3 Hz range, but is still close to the best option.As TiN already noted, at a higher input voltage the reference noise is a significant contribution. At 7 V input it is higher than the raw ADC noise about below 0.5 Hz and even more the lower the frequency. The reference has 1/f noise in the low frequency range, while the ADC itself in AZ mode is kind of chopped and thus has no or low 1/f noise. There is some from reference scaling to 12 V that acts much like reference noise, but still lower than the ref. itself. The noise specs in the 3458 and with many other DMMs usually use kind of sweet spots where this 1/f noise is not that high. One of the often shown curves is also ignoring 1/f noise inside the ADC that cause the noise to go down slower from 0.1 PLC to 10 PLC.

author: rhb
author_rank: Super Contributor
timestamp: April 02, 2018, 09:45:48 pm
content: Thanks to all. It's very hard to do searches on such a narrow topic without having to wade through an immense number of bad hits. The article Zia linked was an excellent introduction and the references should help me find a lot of other material.TiN's cryogenic data was the thing that really surprised me and got me thinking about measurement noise. I very much hope he will have time to write it up soon. That was a very long run at constant temperature. The temperature data during the long cold section before warm up are bimodal, but I don't believe that is valid unless it reflects a phase transition effect. However, I did nothing more than make a mental note to investigate. There were far too many other things to examine. I'm rather rusty at Octave, so it will take me a bit of time to come back up to speed. Lots of time spent reading the help to find out what the function names and arguments are.I plan to make plots of the DMM noise measurements at xdevs.com. I have a program that will generate 2D histograms which I then plot in color. It allows comparing a lot of data in the form of distribution functions. In this instance error distribution vs instrument. I have used it to do 3D distributions by making slices in the 3rd dimension and then playing them as a movie loop.I'm interested in mathematical techniques that can be applied to data from instruments of any quality. I can't afford and have no need of high end measurement equipment other than as a means of calibrating my other instruments. For general use, the DMMCheck Plus I ordered is probably more than sufficient.After some 30 years of following the gospel according to Norbert Wiener, Candes and Donoho really blew me away with sparse L1 pursuits. Having invested 3 years making the hammer, I've been looking for a suitable nail. I want to hit something with it ;-)On an individual device level, aging looks quite tractable based on my experience with solving the exponential decline of fluid flow from a porous medium under load. On the other hand, I know nothing about 1/f noise beyond what it is. So I shall need to learn a good deal more about that. If there are statistical properties which relate the noise at one or a group of frequencies to the noise at other frequencies I may be able to derive error bars from that. If it can be modeled as a/f for some constant a, then I should be able to do a very good job of separating that from aging. That should greatly improve my estimates of the aging function and provide tight bounds on error.Edit: I just found "1/f noise: a pedagogical review" by Edoardo Milotti. Treating the variation of a voltage reference over time as 1/(f**a) + b*ln(g(c)) should work quite nicely, albeit, it might take the computer a bit of time to solve. Most of that being calculating a large number of possible answers from which to choose a, b & g(c) and then generating a ridiculously large input file to feed glpsol from GLPK.

author: zhtoor
author_rank: Frequent Contributor
timestamp: April 03, 2018, 12:09:15 pm
content: discussion in this link is also relevant:-https://www.eevblog.com/forum/metrology/replacing-ltz1000-in-an-hp-3458a-with-a-lower-noise-()-reference/best regards.-zia

author: montemcguire
author_rank: Regular Contributor
timestamp: April 04, 2018, 01:49:59 pm
content: Quote from: rhb on April 02, 2018, 07:12:28 pmAren't noise and drift just similar processes on a different time scale? If so, then it's ideal to get un-retouched data, maybe with the hope that the noise and drift processes identify each other. You can always apply a power line cycle style rectangular filter to the data after the fact, but you certainly cannot undo such a filter.Overall, I think your idea of using modest parts to get better results is good, but the aspect of drift will be the big problem. However, it is possible to buy inaccurate parts that have inherently lower drift, and thus 'save money'. I put that in quotes because you're simply shifting money from parts cost to assembly cost. However, depending on the circuit, that can be a reasonable approach. I'm using something similar in a device I'm designing now. Rather than use a large number of tight tolerance components, I'm specifying looser tolerance components and spending money on post assembly calibration.I do remain skeptical that drift processes can be reliably modeled, simply because there are many processes that cause drift, and characterizing them could be expensive in terms of assembly time. My approach, at least with resistors, is to select relatively stable components, but save money by purchasing a looser tolerance specification. Post assembly calibration will be required regardless of the initial tolerance of these components, so overall, it results in a net savings and increase in accuracy. However, drift is something that I will not attempt to model. My feeling is that drift can be reduced by component and materials choice as well as assembly process, but it cannot be meaningfully characterized. I'd rather pay more for stable components than lengthy post assembly characterization of drift, but that's just me.

author: Echo88
author_rank: Frequent Contributor
timestamp: April 04, 2018, 02:03:44 pm
content: @rhb: I have no idea if its of interest to you, but heres a guy who theorizes about 1/f-noise:http://rubiola.org/pdf-static/Enrico's-chart-EFTS.pdfhttp://rubiola.org/

author: rhb
author_rank: Super Contributor
timestamp: April 04, 2018, 08:05:01 pm
content: This thread should be considered closed as it is subsumed by the thread on applications of sparse L1 pursuits which is a broader thread which includes noise analysis and reduction as a sub-problem within the larger context of mathematical models of system performance.

author: David Hess
author_rank: Super Contributor
timestamp: April 05, 2018, 01:17:39 am
content: Quote from: Kleinstein on April 02, 2018, 07:59:58 pmThis is a really big deal for external measurements. The sinc response produced by integration over a whole number of power line cycles notches not only the power line fundamental but also its harmonics.

author: rhb
author_rank: Super Contributor
timestamp: April 05, 2018, 01:08:41 pm
content: Yes, but it leaks badly at other frequencies. I am not suggesting not suppressing power line noise. I am asserting that there are very much more sophisticated ways of doing this. The powerline cycle averaging is a 1940's approach. But *please*, let this thread die and move to the 'applications of sparse L1 pursuits for precision reference" (sic).As TiN pointed out quite succinctly we do not need 3 threads on the same topic. So I want to separate the OSHW project from the sparse L1 pursuits topic. The first is engineering, the second it science. The L1 pursuits posts take an hour or two to write, so I can't really handle thee threads and do a proper job.Thank you for your interest in the topic.

author: David Hess
author_rank: Super Contributor
timestamp: April 05, 2018, 02:54:03 pm
content: Quote from: rhb on April 05, 2018, 01:08:41 pmI agree that the sinc response does not provide high performance filtering but the usual solution is to keep the sinc response provided by simple integration to notch power line interference and add analog filtering before the integrator. Multi-order integrated delta-sigma converters take this a step further to gain both so maybe some high sample rate DVMs do the same thing but if so, they are not advertising it.QuoteThere no link here to those discussion threads and based on the broken search facilities provided by this forum, they do not exist. Maybe you should provide a link if you want the discussion moved since you seem to know where they are.

author: rhb
author_rank: Super Contributor
timestamp: April 05, 2018, 03:34:03 pm
content: Sorry. Here they are:https://www.eevblog.com/forum/metrology/applications-of-sparse-l1-pursuits-to-precision-reference/https://www.eevblog.com/forum/metrology/a-low-cost-oshw-voltage-calibration-reference-project/I *really* wish we had a better search function.

author: precaud
author_rank: Frequent Contributor
timestamp: April 07, 2018, 02:43:51 pm
content: Quote from: rhb on April 05, 2018, 03:34:03 pmFor posts > ~24 hrs old, We do.https://www.google.com/advanced_searchPut eevblog.com in the "site or domain" and use the other conditionals to suit. Works great (for this or any other site).