Flicker noise voltage distribution.

Flicker noise (or anything else where the variance is bigger than the mean) is nonstationary, so you can't uniquely define a PDF.

Cheers,

Phil Hobbs

Flicker noise is filtered white noise, with a 1/f frequency distribution. Since white noise doesn't necessarily have a unique PDF (e.g, could be Gaussian or uniform), I would think that the same would be true of flicker noise.

--
John

Thanks Phil! Your answer is very clear. I read that flicker noise is correlated noise. Still, I'm left with an unsatisfactory understanding of flicker noise. What would say 5 days worth of flicker noise data logging look like? Pulses widely ranging in amplitude? Is there an upper crest limit to such pulses? I find flicker noise fascinating.

Paul

Paul if you have access to a low noise pre-amp (or maybe you can build one with an op-amp or two) you can make your own 1/f noise source. All you need is a old carbon reisistor and a battery to bias it with. A 10k resistor works nice. First observe the Johnson noise with zero bias. Then put several volts across it you will see lots more noise with a specturm that goes as 1/f. Which means there is equal power in each decade of frequency. ie if you look at the noise between 100Hz and 1kHz it will be the same as between 10 Hz and 100 Hz. It's really 'strange' if you are use to 'normal' white noise.

Ohh one trick to look at low frequencies is to put four carbon resistors in a bridge, then when you bias them you don't have to AC couple to get rid of the DC offset.

George Herold

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Hi George,

Thanks for the info. I'll take your advice, as it would be interesting. I'd like to put it on a data logger, shove it in the corner of the lab for a few months. Perhaps a 2nd logger recording temperature would be nice. Hey, some guys web page swears that the moon has a significant effect on flicker noise, lol. Perhaps a moon logger? ... Nah. Anyhow, I have an idea what you mean by the four R bridge.

BTW, why is it called "flicker" noise? A flick should have spikes, no. How could it be ultra low frequency if it has spikes? The main cause in semiconductors is the trapping and de-trapping of the carriers.

Regards, Paul

Paul: There is an old HP app note on flicker noise - AN 963

Good luck, Dave

OK, let me try this again!

"Flicker Noise in Schottky Diodes" HP App note 956

Agilent document number 5952-0487

Better luck this time! Dave

So zero-mean Gaussian noise is non-stationary?

I think you're confusing stationary with Gaussian, or your references are. Stationary noise means that if you know what time it is you know more about the noise than if you don't -- fer instance, the probability density of the average rainfall on any given day at any given point on the earth is highly dependent on the season, so average rainfall isn't stationary in that sense.

If you can point to a proof (that includes the definition of "stationary" that's used) I'd be willing to read it.

I suspect that someone made an assertion that isn't correct some time in the dim past that's been taken up, or that someone has found it convenient to _model_ certain types of non-Gaussian noise as non- stationary, and that useful approximation has been taken as truth.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

A lot of what looks like 1/f noise is actually temperature fluctuations changing something, with the thermal mass of the something integrating the waveform. Noise from a cheap (non-oven) crystal oscillator is generally like that: swaddle the gadget in foam, and the apparent 1/f noise drops radically.

John

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Paul, I'm not sure what your data logger is recording. If you want to record a time record of the noise at say a 1 Hz to 1kHz band width... you're going to record a lot of data in a month. Try a few seconds first. You'll also need a bunch of gain.

The problem with biasing a single resistor is that you're looking for this tiny noise voltage on top of several volts of bias. If you put four resistors in a bridge and bais with equal magnitude but opposite sign on two of the opposite nodes, ground the third and sense on the fourth node you should have a signal closer to gound. You still have to deal with the difference in the resistor values... there's several way to go there.....

have fun! George

ps I have no idea why it's called flicker noise. I call it 1/f noise, which at least describes the specturm.

Upon further reflection, you can't do this with a single resistor and battery you need at least two resistors. (Sorry, I did these measurements a few years ago and had forgotten the path that led me to the bridge idea.)

Geo

"Paul"

BTW, why is it called "flicker" noise?

** In optical devices it causes visible flicker.

** Does a flickering candle have spikes ?

..... Phil

AN 963 is "Impedance Matching Techniques for Mixers and Detectors"

AN 956-3 is "Flicker Noise in Schottky Diodes"

Maybe that is the one you were thinking of?

There is a list of old app notes at

Does it have the one you were looking for?

Regards,

Mike Monett

Dave,

I replied to your original, but it hasn't shown up yet.

Thanks for the update. You can find AN 956-3 here

Regards,

Mike Monett

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A lot of caps are also like that, such as ceramics. A mineral oil bath does amazing wonders to stop temp gradients.

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What I meant by data recording, is to convert the output to digital, ADC, and record the digital data. I would probably use a PC to record the data, just write to a file since it could be a considerable amount of data.

I know there are people who have done this kind of research. Studies have shown flicker noise to remain as 1/f spectrum for weeks on end. I believe the present record is well over a month, and the flicker noise remained 1/f frequency. One month would be 373 nHz. It's believed there must be an end to 1/f noise due to it's power spectrum, since there's not enough power in the universe to go for ever. :-)

PL

Check this site:

. Although the answer to your question isn't explicitly stated, the paper states that pink noise can be made from adding multiple white noise sources that have been low pass filtered, (Voss-McCartney algorithm of adding multiple white noise sources at lower and lower octaves). Filtering should not affect the amplitude distribution. You'd expect the summations would also not affect the probability distributions. All this assumes that your white noise sources have gaussian (normal) amplitude distribution.

Other articles

suggest pink noise is coloured by frequency distribution, and amplitude distribution is determined by the noise mechanism - it may or may not be gaussian. See also: Similarily, white noise doesn't need to be gaussian!

This reference

says that pink or bandwidth limited white noise is "pseudo gaussian", in that the integral of the noise doesn't work out to be exactly zero as true gaussian noise should (but its close).

There is a mention in the rec.audio.faq: "Another term you'll hear about is Gaussian noise - this is noise with a Gaussian amplitude probability density. Gaussian noise has the amazing property that linearly filtering it preserves its Gaussian amplitude density and that sums of Gaussian random variables are again Gaussian. The two terms shouldn't be confused. It is possible to have Gaussian white or pink noise."

Several hours of searching through papers really didn't provide much enlightenment, especially with the useful looking ones needing a payment before you could get at them! My best search results were using "pink noise gaussian" as a criteria. Some of the hits don't seem to be very authoritative! Why the need for probability distribution? Was it to determine probabilities of the multiples of rms levels (ie., prob that gausssian signal exceeds 3*rms is 0.37%

Paul G.

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Oh, are you saying you want to look at the noise from DC to some upper frequency? There are going to be all sorts of issues if you try to look at the noise at DC. First are simple things like the op-amp input offsets. (you are going to need a total gain of about 10^5 to

10^6) Then there are going to be all sorts of DC drifts. As John L. said earlier, how do you tell the difference between 1/f noise and a simple drift with temperature.

I went back and looked at my notes. I was using 10 k ohm resistors and biasing them in a bridge with three 9V transistor batteries in series (27 Volts of bias). With a Q=3D1 bandpass filter centered at 100 Hz I found the noise voltage went up about 16 times when the resistors were biased. That might give you some idea of what size signal levels to expect. Of course this might also change with the make of cabon composite resistor you use.

George Herold

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I appreciate all that info. I'm surprised to read that white noise is not always Gaussian! Isn't Johnson noise (that's caused by natural thermal energy) Gaussian? I wouldn't doubt that some forms of simulated white noise could be a different distribution.

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I did some tests a while back with metal-film and cermet (standard surface-mount) resistors, looking for shot and "excess" noise, noise that increases with dc bias. With a setup that about resolved the Johnson noise, I saw no evidence of increased noise with bias.

John