Flicker noise voltage distribution.

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

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:

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

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

Hi Mike, omega is physics speak for frequency. f =3D 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

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

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

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

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.

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?

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.

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.

Thanks,

Mike Monett

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

George

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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.

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=3D1 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.

Another low-noise bipolar op amp is the AD706, which got me out of a BIG problem. I used a Keithley electrometer/voltmeter, and had to let it warm up for a day before making measurements. I would see jumps in the 5th decimal place every 30 sec to 2 minutes with the old Bi-CMOS op-amp, the AD706 showed none of that.

For ultra-low noise, some years ago I built an all discrete transconductance amp with 4 BJTs and an Interfet IF9030 running at about 4 mA. An LED was used in the bias network. It had an AC-coupled input, and an AC-couped filter later, so drift was not a concern. I made a couple hundred of these,

96 to a cabinet. We discovered some problems with poor grounds on connectors allowing EMI to get into the system, and had to change connector families.

Jon

The image came just fine for me.

Just saw this--I'm still on the road. Flicker noise is often obviously nonstationary just looking at it--parts get noisy for awhile, then quiet down a for a bit, and then get noisy again. There's a theorem of Doob's or somebody's that says that any unipolar random process whose variance is bigger than its mean is nonstationary...that follows iirc from a calculus-of-variations argument. The basic idea is that if you assume that all the correlations are zero, that maximizes the variance in a stationary process--and what you get is a Poisson process, whose variance is equal to its mean.

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.

Cheers,

Phil Hobbs

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

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.

Cheers,

Phil Hobbs

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

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.

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.

Cheers,

Phil Hobbs

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

John

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?

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

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