Noise spectral density measurement calibration - Page 1
Forum section: electronics / projects

author: Martinn
author_rank: Frequent Contributor
timestamp: August 22, 2023, 06:17:55 pm
content: I'd like to replicate the noise plots in voltage regulator or opamp datasheets. The plan is to measure the signal (amplified with a LNA), calculate the FFT and scale it to V/rtHz.As measurement devices I have a 6.5 digit DMM (DMM6500) and a RTB2004 scope. After I had purchased the DMM6500 I discovered I got two instruments for the price of one: It is not only a 6.5 digit DMM, but also a 1 MS/s 16 bit digitizer with a bandwidth of up to 440 kHz and a max sample buffer of 7 MS! So for up to 500 kHz the DMM certainly has lower noise than the scope.For the FFT I'd use the Welsh method with piecewise linear detrending in order to eliminate drift effects. But I have worked with FFTs enough to know that regardless how much thought you put into the scaling, there will be a bug somewhere. You always have to verify the scaling with a given calibration signal.Just how do you do this for analog sources? Calibrating a spectrum analyzer is easy - you generate single tone signals and see if the amplitude is correct, be it FFT or receiver based. But what about noise spectral density? Best I could think of would be to generate some bandwidth limited wideband noise, measure its RMS value and compare that with the integrated spectral density values.Assuming DMM or scope would measure correctly, one could simply generate a random number vector, maybe filter it (probably not necessary), feed it into the FFT and compare variance/RMS value with sum of spectral density scaled FFT bins.What do you think?

author: Kleinstein
author_rank: Super Contributor
timestamp: August 22, 2023, 06:59:41 pm
content: If the input amplifier is low noise (and low current noise), one can use the johnsone white noise of resistors as the basis. With current noise things get quite a bit more tricky.There is the option to use a noise generator and if needed a attenutor to bring the level down the needed level. A few arb genrator include a kind of pseudo-random noise that may be suitable and include a known scale.Computer generated numbers are a good idea for the FFT / math part. This however still leaves the input / ADC part.AFAIK the DMM6500 has a fast ADC in the digitizer mode, but the actual BW of the input stage is limited and not all ranges have a flat response (e.g. accurately compensated dividers / gain stages). So the actual useful BW may be quite a bit lower, especially in some ranges (espeically 100 mV or 100 V). I would not be so sure that the DMM is actually lower noise than a good scope, at least not in the higher frequency range.

author: zrq
author_rank: Frequent Contributor
timestamp: August 22, 2023, 08:19:52 pm
content: I don't think one would need to calibrate a digitizer in a way different from a spectrum analyzer, if you do the Fourier transform, it's basically measuring the same thing. For use with Welch's method for noise measurement, I think one would simply need to characterize the (of course) DC precision, the flatness of frequency response and (more tricky if needed) possibly the input impedance.

author: MasterT
author_rank: Frequent Contributor
timestamp: August 23, 2023, 01:31:16 am
content: Some noise test on LDO regulators

author: rf-fil
author_rank: Regular Contributor
timestamp: August 23, 2023, 05:58:03 am
content: You can calibrate the FFT with a CW (tone). That takes care of any unknowns / bugs in the scale, the "y" direction. In the "x" direction, the Effective Noise Bandwidth per FFT bin can be reliably calculated. It only depends on the sample rate, FFT size, and the chosen window. I've done this with success a number of times.

author: magic
author_rank: Super Contributor
timestamp: August 23, 2023, 06:23:19 am
content: You said nothing about bandwidth and tolerance.When I tried measuring voltage noise of some opamps, I checked frequency response flatness of my FFT maths by simply testing a few chips.Precision opamps are fairly flat for a few decades from 10Hz up. You would have to trust the datasheet wrt exact amplitude, though.

author: Martinn
author_rank: Frequent Contributor
timestamp: August 23, 2023, 11:05:31 am
content: Here's my LNA assortment:AM 502 (JFET, probably not ideal for low impedance sources)LT AN83 "The silence of the amps"my own HP461A interpretationhttps://www.eevblog.com/forum/projects/measuring-switch-mode-supply-noise-hp461a-replacement-ada4895/msg4652395/#msg4652395Quote from: magic on August 23, 2023, 06:23:19 amNo requirements, just for fun, bandwith <1 MHz for power supplies, much more for a scope frontend. But as I said I have very limited RF equipment, so I'd stick to the kHz region first.Quote from: rf-fil on August 23, 2023, 05:58:03 amI have done those calculations before, but I am looking for a means of verification. Like a 100 nV/rtHz wideband source.Quote from: MasterT on August 23, 2023, 01:31:16 amCould you explain what analyzer you used? What LDOs? Measure is in dBc - which is decibel relative to the carrier - how does this relate to the spectral density in nV/rtHz?Quote from: Kleinstein on August 22, 2023, 06:59:41 pmNeither the AN83 nor my HP461A clone are low impedance, so if I wanted to use the Johnson noise of a resistor as a source, I'd probably have to use the AM-502 (not sure about that though). It has precise bandwith limiters so at least that would be handy.The DMM6500 I guess uses its digitizer for AC measurements, so I assume that the digitizer is accurate as stated in the AC accuracy specs, 0.6% 50-100 kHz for example.

author: magic
author_rank: Super Contributor
timestamp: August 23, 2023, 12:10:51 pm
content: I thought about making a white noise "standard" out of a resistor and off the shelf opamp.You may want to do your own math (it's not too hard), but I recall concluding that BJT inputs have too much current noise (particularly at low frequencies, dunno how low you care about) and the optimal choice seemed to be 0.1~10MΩ and JFET input. (OPA164x looks like good bang for the buck, ADA4625 for top specs).However, there are problems with that too, namely RC time constants. I considered a few topologies:1. Rnoise to IN+, noninverting gain. Here Rnoise and Cin of the chip make a lowpass, so it won't go to 1MHz, not even 100kHz IIRC.2. Rnoise feeding a transimpedance amplifier - BW problem eliminated, but low gain unless Rfeedback is high. But then see 3.3. Grounded IN+, Rnoise feedback. Same RC problem as 1, but rolloff is replaced by gain peaking, so maybe worse actually.4. Rnoise/2 to IN+, Rnoise/2 feedback. Perhaps the best / least bad.Another thing to watch out for is current noise of JFET opamps. It's rarely documented, but OPA604 and OPA2134 datasheets suggest a possibility of a surprising raise at high frequencies. I figure it may be caused by capacitive coupling of internal voltage noises.So maybe BJT would be better, after all. But flicker noise must be considered. At least its documented.

author: MasterT
author_rank: Frequent Contributor
timestamp: August 23, 2023, 12:52:10 pm
content: Quote from: Martinn on August 23, 2023, 11:05:31 amLDO part number is file name (look below image .jpg).Analyzer DYI - mcp3562 + nucleo-H743zi2. No LNA preamp, just adc buffer G = -1, lme49721(prototype)dBc is directly proportional to Vref, so -120dBc is 3.3 uV/sqrt(Hz)More interesting LDO, ultra-low noise:

author: jonpaul
author_rank: Super Contributor
timestamp: August 23, 2023, 05:53:05 pm
content: see old General Radio "Handbook of Noise Measurement" book1963..1980https://www.ietlabs.com/pdf/Manuals/Handbook_Noise_Measurement.pdfj

author: David Hess
author_rank: Super Contributor
timestamp: August 24, 2023, 09:25:51 am
content: Quote from: Martinn on August 22, 2023, 06:17:55 pmI do not understand why a single tone test signal is not completely adequate for calibration of both.I have done what you suggest with a spot noise measurement of a bandwidth limited noise source to convert from RMS to nV/SqrtHz, but this was only to confirm calibration using a tone.Note that the results from your FFT need to be adjusted by the RBW (resolution bandwidth) which depends on the FFT bin width and window type.

author: jonpaul
author_rank: Super Contributor
timestamp: August 24, 2023, 10:55:42 am
content: Noise is characterized by the peak to RMS ratio, PSD, BW, etc.Thus response to a single or multi tone cal will differ from a tru (TRN) or pseudo (PRN) signal.General Radio noise gens are calibrqated and some adjust output, BW and peak to RMS. All have a meter for the noise RMS.1380/1380A use an arc tube in a magnet.https://worldradiohistory.com/Archive-Company-Publications/Archive-General-Radio/GR%20Exp%201951_12.pdfGenRad/IET 1381, 1382, (Noise Zener)Audio testing eg loudspeakers, theatre EQ use white or pink noise for equal bins in 1/3 octave RTA.Nationa Semi and others made a shift reg noise gen in 8 pin DIP circa 1970s..1980s.Use of maximum legnth sequence for analysis was pioneers by our old freinds Vanderkoy and Liptschutz at U. Waterloo, Guelph, Canada in 1980s.Cheers,Jon

author: Martinn
author_rank: Frequent Contributor
timestamp: August 24, 2023, 06:01:21 pm
content: Quote from: David Hess on August 24, 2023, 09:25:51 amWell, if you have digitizers you know that they are accurate (like the DMM or oscilloscope), then calibration would be unnecessary. Just do the calculation right and everything is fine.However, from my personal experience I know that it is very easy to mess up FFT scaling. Of course you can check this numerically (white noise with known RMS voltage), but still I was wondering what analog signal I could use for verification. Using a single tone would require that I trust my RBW calculation, which is something I am not yet not familiar with.Anyway I don't think it's very critical - if you introduce a scaling error, most likely the result will be off by an order of magnitude or a factor of 2, which should be easy enough to spot.

author: gf
author_rank: Super Contributor
timestamp: August 24, 2023, 06:37:26 pm
content: I suggest to read this paper:https://holometer.fnal.gov/GH_FFT.pdf

author: zrq
author_rank: Frequent Contributor
timestamp: August 24, 2023, 06:54:01 pm
content: An off by 2 problem is indeed common when working with FFT, and it indeed make sense to have a analog check source. However, if one can verify the result against an reputable numerical package that can do Welch's method by itself (scipy.signal.welch or Matlab pwelch), and be careful of the error of wrong by a square root (pretty easy to spot), I would say the risk of messing up the FFT math is not so high. Also the paper in reply #13 is a very good read.I would say the biggest caveat may be with the source and meter impedances, which may make separation of current and voltage noise difficult.

author: TimFox
author_rank: Super Contributor
timestamp: August 24, 2023, 07:03:13 pm
content: Note that for noise generation and amplification measurements, the "RBW" (resolution bandwidth) and "ENBW" (equivalent noise bandwidth) differ.The latter is defined as the bandwidth of a brickwall filter which produce same integrated noisepoweras that of an actual filter. This is also referred to as noise bandwidth or effective noise bandwidth.The important word there is "power", and relates to the statistical properties of thevariance, which relates in turn to the square of the rms value.A good spectrum analyzer manual gives the ENBW for its available RBWs, which depends on the shape of the filter used to limit the bandwidth.