Flicker noise voltage distribution.

[[email protected]]

  > Mike Monett wrote:

  >> Getting an  amplifier  with  flicker noise that  low  near  DC is
  >> pretty good. Any chance to post a schematic?

  >> Thanks,

  >> Mike Monett

  > That was  several  years  ago. I probably  still  have  it kicking
  > around in a drawer in my lab.

  > It used  iirc  3x  Toyo-Rohm  low  noise  transistors  (2SD786) in
  > parallel.

  > The 1/f  corner  was  around 1 Hz or a bit  below  (good  BJTs are
  > amazing).

  > Cheers,

  > Phil Hobbs

  Heh, I'm having problems finding a datasheet in Engish. There's some
  tantalizing fragments, such as

  en = 0.55nV / sqrt(Hz) (at 10Hz, 10mA)

 http://doc.chipfind.ru/pdf/rohm/2sd786.pdf

  There's also some discussions of the low noise at:

 http://sci.tech-archive.net/Archive/sci.electronics.design/2005-
12/msg02183.html

 http://sci.tech-archive.net/Archive/sci.electronics.design/2005-
12/msg02317.html

  There's probably more but I didn't take time to check.

  The 2SD786 seems to be available for $26.98, but there's no  date so
  it's not clear if that price is still valid:

 http://littlediode.com/components/2SD786_Transistor.html

  The Analog  Devices MAT02 and SSM-2210 are less  expensive  at about
  $6.00/1k:

 http://www.analog.com/en/other/matched-
transistors/MAT02/products/product.html

  The Mat02 and SSM-2210 are also supposed to have a fairly  low corner
  frequency, depending  on the collector current. But it  doesn't look
  to be as low as 1Hz for the 2SD786:

 http://www.analog.com/static/imported-files/data_sheets/MAT02.pdf

 http://www.analog.com/static/imported-files/data_sheets/SSM2210.pdf

  The SSM-2210  datasheet describes three devices in  parallel, giving
  500pV/SQRT(Hz) and  a corner of 1.5Hz. It uses a red LED  as  abias
  current reference  voltage.  This is also  described  in  the Analog
  Devices app note AN-102:

 http://www.elektronik.ropla.eu/pdf/stock/adi/temp/pdf/2611.pdf

  So it  would  be   very   interesting   to   take   a  peek  at your
  implementation if you have time to post it.

  Thanks,

  Mike Monett

I've seen the Analog devices circuit reproduced in lots of places.
You might notice that it uses the LED and transistor Vbe voltage
reference trick mentioned by Walt Jung in an earlier post.

George Herold

 

[Mike Monett]

[...]

Mike,

Yes, those were nice parts. There was a discussion on this group
awhile back about available alternative devices, but I don't have
time to track it down just now.

I'll post the schematic once I find the gizmo and trace it out. I
didn't write down the schematic anywhere, I don't think. For lab
one-offs, I usually just do a few lines of algebra and start
soldering, because near enough is usually good enough. There's a
differential current amp based on those parts in my book, though.

I also want to find the lab book the results are written in before
I get too dogmatic about the performance details. I might be
confusing two different gizmos - the 0.55 nV gizmo with the very
low 1/f corner would have had to have at least a few pA/sqrt(Hz)
of current noise, and the current noise 1/f corners are usually a
bit higher in frequency.

Phil Hobbs

Hi Phil,

Thanks for the info. I'll try to find the discussion you mentioned.

I'm really interested in your schematic. Often, a circuit will
appear in an app note, but may have a typo, bug or error that could
be hard to find. Or the component values could be non-optimal. So a
schematic of an actual, working circuit could be very valuable.

This is more than idle curiosity - I'm trying to make a phase noise
analyzer with emphasis on flicker noise. I'm hoping it might help
indicate precision crystal oscillators that are prone to phase
bumps.

These can occur randomly over intervals of a couple of days to six
months or more, and it would be very nice to find some method of
identifying oscillators that are likely to have the problem. This
could save months of tying equipment up in precision phase
measurements that could still miss an event.

I was also wondering about the current noise in your amplifier, and
I'm glad you mentioned it. Wouldn't this be a problem trying to
measure flicker noise in high value resistors? How do you handle
something like this?

Regards,

Mike Monett

 

[Mike Monett]

Try here:

http://www.datasheetarchive.com/pdf-datasheets/Datasheets-8/DSA-

158374.pdf

That's great! Thanks, Howard.

Mike Monett

 

[Spehro Pefhany]

Try here:
http://www.datasheetarchive.com/pdf-datasheets/Datasheets-8/DSA-158374.pdf

I have a number of NOS of these fine devices around, and $26.98 sounds
like a *very* fair price. ;-)

 

[Mike Monett]

(Speff, sorry if this is a dupe. I replied earlier but Windows did
something strange and the post never showed up. I didn't want you to
think I was ignoring you, so here it is again)


[...]

I have a number of NOS of these fine devices around, and $26.98
sounds like a *very* fair price. ;-)

Digikey Canada lists the MAT02FHZ-ND for $12.53CAD in singles

http://search.digikey.com/scripts/DkSearch/dksus.dll?lang=en&site=CA&keyw
ords=mat02&x=0&y=0

That's for a matched pair with max offset voltage drift of 0.1uv/c.

Which is pretty good when you want to measure flicker at DC.

The 2SD786 is a single, so you need two. That makes $53.96. The
match and tempco is anyone's guess.

For $53.96, I can get 4 MAT02's and have enough left over for a beer
and some resistors:

53.96/12.53 = 4.31

This should give about 1/SQRT(4) = 1/2 the rms noise of the 2SD786.

With the above analysis, it's hard to figure a fair price for the
2SD786. My guess is $3.00CAD might be in the right ballpark, as long
as you pay the GST/PST, and the beer

Best Regards,

Mike Monett

 

[Mike Monett]

[...]

I recently scored a bag of *66* 1N2929a germanium tunnel diodes as
part of a surplus assortment. Probably >$1k worth if I sold them
in onesies. Maybe a retirement project, 20 years from now. (If
anyone wants one to play with, send me an email.)

I have probably 20 2SD786s left - I bought a bunch back in about
1992.

More useful but less fun than the TDs.

Phil Hobbs

Phil,

Is there any chance the 1N2929a's might be used as a horizontal
trigger in a Tek 465 or 475 scope, or perform some other function in
an older piece of test equipment? Could they be adapted to replace
an existing diode that has gone bad?

If so, the guys on the Yahoo forums

http://tech.groups.yahoo.com/group/TekScopes/

and

http://tech.groups.yahoo.com/group/TekScopes2/

would sure like to talk with you.

If they are used in any HP equipment, the guys at

http://tech.groups.yahoo.com/group/hp_agilent_equipment/

would also love to know.

RF Parts lists them for $13.90 each as of 5 November, 2008, with a
minimum order of $25.00:

http://www.rfparts.com/diode.html

so you might be able to charge $15.00 + shipping & handling for one.

I hope you get rich quick

Now I have a question. Unlike the MAT02, the 2SD786 is a single
transistor, and you need two for a differential amplifier. There is
no guarantee of matching or offset tempco, so how do you use them in
a circuit to measure flicker noise near DC? It would seem the drift
would kill you.

Thanks,

Mike Monett

 

[Mike Monett]

I'm in justify-my-existence-for-another-year mode for the next
week or so. I'm way off in SlideSpace (i.e. powerpoint -
orthogonal to real space in so many ways.)

The gizmo I built was single-ended, which saves 3 dB in noise
figure.

The distinction between drift and 1/f noise was one of the things
I was pointing out back at the beginning of the thread. Drift is
1/f**2, for one thing.

Cheers,

Thanks, I'll go back and take another look.

But I was mainly concerned about drift due to temperature, which
should be a linear function. A single-ended amplifier would have
horrible drift when you are trying to measure microvolt level noise
signals.

An alternative is capacitive coupling, but the time constants would
be huge. And still within the frequency range of thermal drift.

So I am baffled on how you can make these measurements!!!

Thanks,

Mike Monett

 

[Mike Monett]

[...]

Don't get too excited, I still have to show that it's true - I was
posting from memory, which has misled me before now. I won't be
back in my lab until next week - sorry to be difficult. IIRC it
was just a single-ended X100 amp or something like that, with some
fairly manual offset adjustment, not any sort of proper test
equipment type design.

(This was 10 years ago or thereabouts, and I only used it for a
day.)

Drift is a linear function of time, but not of frequency. You can
work it out by an arm-waving analytic continuation: a
delta-function has a flat spectrum; integrating gives a step
function, and multiplies the transform by 1/omega; doing it again
gives a ramp, with a transform proportional to 1/(omega**2).

Phil Hobbs

I vaguely remember the Dirac Delta function from classes at MIT many
long years ago. Mathworld has a nice summary - it hasn't changed
much that I can see:

http://mathworld.wolfram.com/DeltaFunction.html

It's an impulse, so I can see it having a flat spectrum, and
integrating gives a step function. I'm a bit hazy on the 1/omega
part, but the ramp is fine. What this has to do with drift is still
beyond me, but I'll mull it over while you are gone.

You mentioned the amplifier earlier:

"I measured it using a 9V battery, a low noise preamp (homemade,
about 650 pV/sqrt(Hz)) and an HP 3562 dynamic signal analyzer."

Now I am completely amazed to find out it is single-ended. How on
earth you can measure the noise at 650 pV/sqrt(Hz)) and a corner
frequency of about 1Hz is beyond me.

It usually turns out that when I'm this confused, I'm on the verge
of discovering something very important. So I really appreciate your
help in tossing out a problem that has me baffled.

Enjoy your vacation. I'll be very interested to continue this when
you return

Thanks,

Mike Monett

 

[[email protected]]

  [...]

  > Don't get too excited, I still have to show that it's true - I was
  > posting from  memory, which has misled me before now.  I  won't be
  > back in  my lab until next week - sorry to be  difficult.  IIRC it
  > was just a single-ended X100 amp or something like that, with some
  > fairly manual  offset  adjustment,  not any  sort  of  proper test
  > equipment type design.

  > (This was  10 years ago or thereabouts, and I only used  it  for a
  > day.)

  > Drift is a linear function of time, but not of frequency.  You can
  > work  it   out   by   an   arm-waving   analytic   continuation: a
  > delta-function has  a  flat  spectrum;  integrating  gives  a step
  > function, and multiplies the transform by 1/omega; doing  it again
  > gives a ramp, with a transform proportional to 1/(omega**2).

  > Cheers,

  > Phil Hobbs

  I vaguely remember the Dirac Delta function from classes at MIT many
  long years  ago.  Mathworld has a nice summary -  it  hasn't changed
  much that I can see:

 http://mathworld.wolfram.com/DeltaFunction.html

  It's an  impulse,  so  I  can see it  having  a  flat  spectrum, and
  integrating gives  a  step function. I'm a bit hazy  on  the 1/omega
  part, but the ramp is fine. What this has to do with drift  is still
  beyond me, but I'll mull it over while you are gone.

  You mentioned the amplifier earlier:

  "I measured  it  using a 9V battery, a low  noise  preamp (homemade,
  about 650 pV/sqrt(Hz)) and an HP 3562 dynamic signal analyzer."

  Now I  am completely amazed to find out it is  single-ended.  How on
  earth you  can  measure the noise at 650 pV/sqrt(Hz))  and  acorner
  frequency of about 1Hz is beyond me.

  It usually  turns out that when I'm this confused, I'm on  the verge
  of discovering something very important. So I really appreciate your
  help in tossing out a problem that has me baffled.

  Enjoy your  vacation. I'll be very interested to continue  this when
  you return

  Thanks,

  Mike Monett

"I'm a bit hazy on the 1/omega"

Hi Mike, omega is physics speak for frequency. f = 2*pi*omega

"but the ramp is fine. What this has to do with drift is still
beyond me, "

Thermal drift is a linear function of time... a ramp.
But this also implies that 1/f noise has the spectrum of a step
function. Which is cool!

I think you're going to want to use a JFET input to look at high
impedance flicker noise. After all this is what Phil A. did...

Say is there some easy way to post a picture? I thought I could put a
up graph of the excess resistor noise.

George Herold

 

[James Arthur]

Say is there some easy way to post a picture? I thought I could put a
up graph of the excess resistor noise.

George Herold

It's not supposed to be possible, but Graham (Eyeore) has
managed to post small graphic images to s.e.d. somehow.

(He posted his secret a while back)

HTH,
James Arthur

 

[Mike Monett]

"I'm a bit hazy on the 1/omega"

Hi Mike, omega is physics speak for frequency. f = 2*pi*omega

Yes, I know that. It is 1/s in Laplace notation. But what that has
to do with drift is still a question.

"but the ramp is fine. What this has to do with drift is still
beyond me, "

Thermal drift is a linear function of time. A ramp.

That's the part that gives me problems. If you look at the thermal
drift, it goes back and forth. For example, the old HP 410 VTVM has
a zero adjustment.

At room temperature and on the most senstitive scales, you have to
keep tweaking the knob clockwise and counterclockwise to get the
needle back to zero. The same with microwave power meters that use a
thermistor for the sensing element.

My problem is the rate at which this occurs overlaps the flicker
noise spectrum near DC, so how can you separate the two?

The flicker noise goes as 1/f, which implies it goes to infinity at
DC, which obviously doesn't happen. So when Phil returns from his
vacation, there are a bunch of questions I need to follow up on.

But this also implies that 1/f noise has the spectrum of a step
function. Which is cool!

I'm not sure if that helps. Phil stated earlier "temperature drift
is not the same as 1/f noise".

Then he states "Drift is 1/f**2, for one thing."

So the question returns to how do you use this to separate them near
DC?

I think you're going to want to use a JFET input to look at high
impedance flicker noise. After all this is what Phil A. did.

Yes, I'm aware that JFET's offer better performance at higher
impedance than BJT's.

But one problem at a time. I need to find how Dr. Hobbs did it
first, then follow up on others if there is any need.

Say is there some easy way to post a picture? I thought I could
put a up graph of the excess resistor noise.

There are some pictures of low frequency noise in the datasheets I
posted, plus graphs showing the increase as the frequency decreases.

I don't think the pictures of noise help much. What would be
interesting would be to sample it in an ADC and plot the FFT.

George Herold

Thanks,

Mike Monett

 

[[email protected]]

Umm, well, even though i generally agree with your statement that omega
stands for frequency, for the formula i'd rather stick to the
omega = 2*pi*f or f = omega/(2*pi) that was true for me for quite some
years.

HTH,
Florian

Opps, Thanks Florian, I'm always getting those 2*pi's in the wrong
spot, which leads to some large errors.

George

 

[[email protected]]

  [email protected] wrote:

  > "I'm a bit hazy on the 1/omega"

  > Hi Mike, omega is physics speak for frequency. f = 2*pi*omega

  Yes, I  know that. It is 1/s in Laplace notation. But what  that has
  to do with drift is still a question.

  > "but the  ramp  is fine. What this has to do with  drift  is still
  > beyond me, "

  > Thermal drift is a linear function of time. A ramp.

  That's the  part that gives me problems. If you look at  the thermal
  drift, it goes back and forth. For example, the old HP 410  VTVM has
  a zero adjustment.

  At room  temperature and on the most senstitive scales, you  haveto
  keep tweaking  the  knob clockwise and counterclockwise  to  get the
  needle back to zero. The same with microwave power meters that use a
  thermistor for the sensing element.

  My problem  is  the rate at which this occurs  overlaps  the flicker
  noise spectrum near DC, so how can you separate the two?

  The flicker noise goes as 1/f, which implies it goes to  infinity at
  DC, which  obviously doesn't happen. So when Phil  returns  from his
  vacation, there are a bunch of questions I need to follow up on.

  > But this  also implies that 1/f noise has the spectrum  of  astep
  > function. Which is cool!

  I'm not  sure if that helps. Phil stated earlier  "temperature drift
  is not the same as 1/f noise".

  Then he states "Drift is 1/f**2, for one thing."

  So the question returns to how do you use this to separate them near
  DC?

  > I think  you're going to want to use a JFET input to look  at high
  > impedance flicker noise. After all this is what Phil A. did.

  Yes, I'm  aware  that  JFET's  offer  better  performance at higher
  impedance than BJT's.

  But one  problem  at  a time. I need to find how  Dr.  Hobbs  did it
  first, then follow up on others if there is any need.

  > Say is  there some easy way to post a picture? I  thought  I could
  > put a up graph of the excess resistor noise.

  There are  some pictures of low frequency noise in the  datasheets I
  posted, plus graphs showing the increase as the frequency decreases.

  I don't  think  the  pictures  of noise  help  much.  What  would be
  interesting would be to sample it in an ADC and plot the FFT.

  > George Herold

  Thanks,

  Mike Monett

OK I'm trying to post an image of the excess noise data I took a year
or so ago. (I'll have to repeat this and be a bit more careful of the
numbers.) At the time I was only interested in the large 1/f noise of
the biased carbon resistor and the rest of the data was recorded as a
check on that data.

http://www.picattic.com/viewer.php?file=ig3o6ne3e8vniuo7me1j.bmp

OK I hope that link works.

A few comments on the data. I don't have good notes on exactly what
was after my preamp. But I can see that the gain was rolling off near
the 3kHz point. The noise from the biased resistors and pre-amp was
sent into a bandpass filter with Q=1 and the center frequcncy moved
from 30 Hz to 100 Hz.... to 3kHz. So here is a quick "spectrum" of
the noise. If you put a ruler across the baised carbon resistor data
you'll see it has a nice 1/f slope. I won't claim anything about the
slope for the biased metal film resistor... but I did see a bit excess
noise.

If you want to calibrate the scale the resistors were 10k ohm and so
the y-axis intercept of the Unbiased R data (squares) is their Johnson
noise (13nV/rtHz)^2.

So if this was noise due to thermal drift issues I would expect a
steeper slope 1/f^2.

Say did you know that Browian motion has a noise spectrum that goes as
1/f^2...

Yes, a plot on a specturm analyzer would be nice too.

 

[JosephKK]

OK I'm trying to post an image of the excess noise data I took a year
or so ago. (I'll have to repeat this and be a bit more careful of the
numbers.) At the time I was only interested in the large 1/f noise of
the biased carbon resistor and the rest of the data was recorded as a
check on that data.

http://www.picattic.com/viewer.php?file=ig3o6ne3e8vniuo7me1j.bmp

OK I hope that link works.

A few comments on the data. I don't have good notes on exactly what
was after my preamp. But I can see that the gain was rolling off near
the 3kHz point. The noise from the biased resistors and pre-amp was
sent into a bandpass filter with Q=1 and the center frequcncy moved
from 30 Hz to 100 Hz.... to 3kHz. So here is a quick "spectrum" of
the noise. If you put a ruler across the baised carbon resistor data
you'll see it has a nice 1/f slope. I won't claim anything about the
slope for the biased metal film resistor... but I did see a bit excess
noise.

If you want to calibrate the scale the resistors were 10k ohm and so
the y-axis intercept of the Unbiased R data (squares) is their Johnson
noise (13nV/rtHz)^2.

So if this was noise due to thermal drift issues I would expect a
steeper slope 1/f^2.

Say did you know that Browian motion has a noise spectrum that goes as
1/f^2...

Yes, a plot on a specturm analyzer would be nice too.

The image came just fine for me.

 

[Paul]

I'm not claiming that anyone's measurements are wrong, only that there
are lots of other sources of low frequency junk that are not flicker
noise. Temperature drift is one very strong candidate.

Millikelvin temperature changes at low audio frequencies aren't that far
fetched. The forcing is fairly wideband and the thermal mass is small.
I have a bunch of really nice 1 ppm/K resistors that I'll try out
in the next few days--bug me if I forget.

Trap lifetimes are temperature sensitive, for instance, and conductivity
fluctuations change due to electromigration. Flicker noise doesn't
follow any nice theorems the way shot noise or thermal noise do.

Sorry, I haven't looked at this thread for awhile, and want to comment
on the physics aspect. The concept of thermal equilibrium is an
impossible state. It's merely theoretical, as it would require
infinite insulation to achieve so-called thermal equilibrium, as the
Universe always is and always will be changing. So you can't get rid
of *natural* ambient temperature fluctuations. Conventional physics
accepts that the laws of thermodynamics are imperfect. Quote from
wikipedia -->

+++++++
Microscopic systems
Thermodynamics is a theory of macroscopic systems and therefore the
second law applies only to macroscopic systems with well-defined
temperatures. The smaller the scale, the less the second law applies.
On scales of a few atoms, the second law has little application. For
example, in a system of two molecules, there is a non-trivial
probability that the slower-moving ("cold") molecule transfers energy
to the faster-moving ("hot") molecule. Such tiny systems are outside
the domain of classical thermodynamics, but they can be investigated
in quantum thermodynamics by using statistical mechanics. For any
isolated system with a mass of more than a few picograms,
probabilities of observing a decrease in entropy approach zero--
reference: Landau, L.D.; Lifshitz, E.M. (1996). Statistical Physics
Part 1. Butterworth Heinemann. ISBN 0-7506-3372-7.
+++++++

Getting rid of milli Kelvin fluctuations is nearly impossible. It's
just part of natural ambient thermal energy.

Paul

 

[Paul]

Thermodynamics, as you point out, is exact only in the limit of large
systems.  On the other hand, Avogadro's number is practically infinite
for most purposes.  How big the fluctuations are depends on how big the
system is, and a millikelvin is actually pretty big for most
objects--for a brick, it's probably femtokelvins.

Hi Phil,

You're probably referring to the entire object in a system of averages
in a fictitious world void Suns and weather changes. Like the
wikipedia quote points out, thermodynamics is a *macro* system of
*averages*. Inside that brick, on a microscopic scale, you'll find
vast temperature gradients-- molecules, atoms, etc. Heck, it even
occurs on a macro scale. Sprinkle some ground cumin spice on water in
the best insulated system and you'll still see brownian motion with a
simple 10X magnifying glass. You may need to wait awhile. With a 100X
microscope you won't need to wait to see brownian motion. Such macro
scale brownian motion led to the confirmation of atoms.

Paul

 

[Paul]

No. Thermodynamic quantities are exact in the limit of large systems.
It's an asymptotic theory, like electrodynamics in material media, ray
optics, band structure, and many others. Locally, there are
fluctuations in energy density about the classical equipartition value,
but those are not *temperature* fluctuations because temperature is an
extensive (i.e. asymptotic) quantity.

Heck, it even


Brownian motion occurs in thermal equilibrium, but is directionless. In
the presence of a temperature gradient, you get thermophoresis, where
the dust has an average drift velocity superimposed on the random motion.

Your comment on "directionless" is pointless. It's believed everything
in the universe is cyclic based. So what?

Thermal equilibrium is a mathematical fictitious concept that has no
bases in reality. Can you name one real object that is in so-called
thermal equilibrium?

Sure, but that isn't what you were claiming previously, namely that the
thermal fluctuation of a brick amounted to millikelvins, which it doesn't.

Like I said, you're referring to the entire object in a system of
averages in a fictitious world void Suns and weather changes. If you
place a temperature sensor at any location on the brick, given enough
time you'll see the sensor temperature go far above one milli kelvin,
given that your sensor reacts fast enough.


Paul

 

[Paul]

We swaddle cheap crystal oscillators in foam blocks and greatly reduce
the close-in phase noise.

John

I was just trying to point out that Phil Hobbs post is flawed since
he's referring to temperature fluctuations when in fact there's no
upper crest limit to such fluctuations. Given a real time domain
analysis, he'll see his one milli Kelvin fluctuations.

Paul

 

[Paul]

*plonk*

You're childish.

Paul

 

[Paul]

Academic. The real world is full of fans, HVAC ducts, the sun rising
and setting, doors opening and closing, cats walking around, ac power
input variations changing regulator dissipations, all sorts of nasty
thermal stuff. What looks like inherent 1/f noise is often this
chaotic junk. And things can often be done to improve the situation.

John

Exactly. Even in a theoretically perfect system there's no upper crest
limit to noise. Phil's probably having a bad day is all.

Paul