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Flicker noise voltage distribution.

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Paul

Jan 1, 1970
0
Does anyone have an idea what the distribution (e.g. voltage
distribution) equation is for flicker noise? You know, the
probability of the voltage being at a specific level. I have looked
high and low for it, without success.

An example is Gaussian distribution, which is used for Johnson noise,

http://en.wikipedia.org/wiki/Gaussian_distribution


Thanks,
Paul
 
P

Paul

Jan 1, 1970
0
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


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
 
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
 
P

Paul

Jan 1, 1970
0
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


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
 
E

EE123

Jan 1, 1970
0
Paul:
There is an old HP app note on flicker noise - AN 963

Good luck,
Dave
 
E

EE123

Jan 1, 1970
0
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
 
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- Hide quoted text -

- Show quoted text -

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
 
P

Phil Allison

Jan 1, 1970
0
"Paul"

BTW, why is it called "flicker" noise?


** In optical devices it causes visible flicker.

A flick should have spikes,no.


** Does a flickering candle have spikes ?




...... Phil
 
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Paul

Jan 1, 1970
0
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


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

PL
 
P

Paul

Jan 1, 1970
0
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


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
 
P

Paul G.

Jan 1, 1970
0
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.

Check this site: http://www.firstpr.com.au/dsp/pink-noise/ .
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

http://stason.org/TULARC/entertainm...4-What-is-white-noise-What-is-pink-noise.html
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:
http://en.wikipedia.org/wiki/White_noise
Similarily, white noise doesn't need to be gaussian!

This reference
http://books.google.ca/books?id=PIm...g=PA163&ots=bycjmSQ4Qd&dq=pink+noise+gaussian
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%
http://en.wikipedia.org/wiki/Normal_distribution)?

Paul G.
 
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- Hide quoted text -

- Show quoted text -

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=1 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
 
P

Paul

Jan 1, 1970
0
   Check this site:http://www.firstpr.com.au/dsp/pink-noise/.
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

http://stason.org/TULARC/entertainment/audio/general/13-4-What-is-whi...
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:http://en.wikipedia.org/wiki/White_noise
Similarily, white noise doesn't need to be gaussian!

This referencehttp://books.google.ca/books?id=PImqHW34Bt0C&pg=PA163&lpg=PA163&ots=b...
 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%http://en.wikipedia.org/wiki/Normal_distribution)?

Paul G.


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.

PL
 
P

Phil Allison

Jan 1, 1970
0
"John Larkin"
George Herold

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


** Wrong as usual........


I did a test a few days ago using 0.5 watt MF, 2 watt MF & finally some old
0.5 watt carbon film resistors - using two similar resistors in series
with a (well filtered) variable DC supply.

The mid point was cap coupled to a high input Z JFET pre-amp followed by a
1000 times gain stage ( a balanced mic pre ) and finally an audio band
filter with gain of 10. This set-up showed only a dB or two more residual
noise than predicted from thermal calculations when using a pair of 100k
resistors ( of whatever type).

I found no trouble identifying lots of "excess noise" as soon as DC bias was
applied with 20 to 40 volts bringing the excess noise up to a level matching
the previous thermal (ie a 3dB increase).

The oft published figure for MF types of " 0.1uV/V " per decade of
frequency was found to be about right.

The old carbon film types I tried gave about 2.5 times more excess noise
than the MF ones at similar DC bias voltages.

The 2 watt MF power resistors showed about 50% more noise than their lower
powered cousins, plus exhibited a sharp crackling noise as well as pink
noise. I did not try cermet types but from experience would expect them to
be much noisier than the others.

Also, resistor excess noise is largely independent of value - so using
lower values than 100kohms will shift the DC bias level *downwards* for
similar results re the ratio of thermal to excess noise.

Eg: for 1 kohms, thermal noise is lower by a factor of 10 (compared to
100kohms ) so he DC bias needed will be 1/10 for the same ratio.

Certainly not a trivial issue nor something one can afford to ignore.



...... Phil
 
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- Hide quoted text -

- Show quoted text -


Hmmm, The metal films I looked at showed a bit of bias noise. This
could have been the batteries. I'll have to try this again with a
bettre filter on the battery. I think I saw about a factor of two
increase in noise at 100 Hz and 27 Volt bias. At what frequency/ bias
did you make your measurements?

George Herold
 
"John Larkin"








**   Wrong as usual........

I did a test a few days ago using 0.5 watt MF, 2 watt MF & finally some old
0.5 watt carbon film resistors  -  using two similar resistors in series
with a (well filtered) variable DC supply.

The mid point was cap coupled to a high input Z  JFET pre-amp followed by a
1000 times gain stage ( a balanced mic pre ) and finally an audio band
filter with gain of 10.   This set-up showed only a dB or two more residual
noise than predicted from thermal calculations when using a pair of 100k
resistors ( of  whatever type).

I found no trouble identifying lots of "excess noise" as soon as DC bias was
applied with 20 to 40 volts bringing the excess noise up to a level matching
the previous thermal (ie a 3dB increase).

The oft published figure for MF types of  " 0.1uV/V " per decade of
frequency was found to be about right.

The old carbon film types I tried gave about 2.5 times more excess noise
than the MF ones at similar DC bias voltages.

The 2 watt MF power resistors showed about 50% more noise than their lower
powered cousins, plus exhibited a sharp crackling noise as well as pink
noise. I did not try cermet types but from experience would expect them to
be much noisier than the others.

Also, resistor excess noise is largely independent of value  -   so using
lower values than 100kohms will shift the DC bias level *downwards*  for
similar results re the ratio of thermal to excess noise.

Eg:  for 1 kohms, thermal noise is lower by a factor of 10 (compared to
100kohms ) so he DC bias needed will be 1/10 for the same ratio.

Certainly not a trivial issue nor something one can afford to ignore.

..... Phil- Hide quoted text -

- Show quoted text -

Phil, You're great! Have you ever tried putting an old carbon
composite resistor in your setup?

George Herold
 
P

Phil Allison

Jan 1, 1970
0
<[email protected]>
"Phil Allison" :
"John Larkin"
George Herold
** Wrong as usual........

I did a test a few days ago using 0.5 watt MF, 2 watt MF & finally some
old
0.5 watt carbon film resistors - using two similar resistors in series
with a (well filtered) variable DC supply.

The mid point was cap coupled to a high input Z JFET pre-amp followed by a
1000 times gain stage ( a balanced mic pre ) and finally an audio band
filter with gain of 10. This set-up showed only a dB or two more residual
noise than predicted from thermal calculations when using a pair of 100k
resistors ( of whatever type).

I found no trouble identifying lots of "excess noise" as soon as DC bias
was
applied with 20 to 40 volts bringing the excess noise up to a level
matching
the previous thermal (ie a 3dB increase).

The oft published figure for MF types of " 0.1uV/V " per decade of
frequency was found to be about right.

The old carbon film types I tried gave about 2.5 times more excess noise
than the MF ones at similar DC bias voltages.

The 2 watt MF power resistors showed about 50% more noise than their lower
powered cousins, plus exhibited a sharp crackling noise as well as pink
noise. I did not try cermet types but from experience would expect them to
be much noisier than the others.

Also, resistor excess noise is largely independent of value - so using
lower values than 100kohms will shift the DC bias level *downwards* for
similar results re the ratio of thermal to excess noise.

Eg: for 1 kohms, thermal noise is lower by a factor of 10 (compared to
100kohms ) so he DC bias needed will be 1/10 for the same ratio.

Certainly not a trivial issue nor something one can afford to ignore.


Phil, You're great!


** What a nice man George is ....

Have you ever tried putting an old carbon composite resistor in your
setup?

** As luck would have it - I just located a pair of 1 watt, 100kohm
"carbon comp" resistors taken from a Fender tube guitar amp during
refurbishing.

Plus, I also have a pair of unused 0.5 watt, 150 kohm " Metal Glaze"
resistors ( aka "Cermet" ) - so the test rig will get another go soon as I
cook dinner and watch my favourite TV shows.

It's about 6pm Saturday, here in Sydney.

Weather is mild and overcast (23C), could be a thunder storm on its
way.....



..... rgds, Phil
 
P

Phil Allison

Jan 1, 1970
0
"Phil Allison"
George Herold
** As luck would have it - I just located a pair of 1 watt, 100kohm
"carbon comp" resistors taken from a Fender tube guitar amp during
refurbishing.

Plus, I also have a pair of unused 0.5 watt, 150 kohm " Metal Glaze"
resistors ( aka "Cermet" ) - so the test rig will get another go soon as
I cook dinner and watch my favourite TV shows.


** OK - I did a couple more resistor noise tests.

Results as follows:

1 watt carbon composition = 0.22 uV/V ( per decade of frequency)

0.5 watt *Metal Glaze (cermet) = 1.7uV/V ( !!!!!!!! )

------------------------------------------------------------


From earlier testing:

0.5 watt MF = 0.09 uV/V

2 watt MF = 0.12 uV/V

0.5 watt carbon film = 0.22 uV/V

( * leaded resistors made by IRH about 20 years back. )

See ABSE for pic of the stars of the show.




..... Phil
 
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