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Croaker

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MOS flicker noise PSD vs. actual noise power
Jan 18^th, 2007, 12:16pm

When you look at the PSD of flicker noise, is the noise at low frequencies actually increasing or is it a result of the way PSD is measured? To get PSD you look at the power in a set bandwidth, fres. So, at low frequencies, you have to use a small fres to do your measurement. Is this smaller fres what increases the PSD or is the real noise power higher?

Let's say you measure 100 V^2 with a fres of 1 Hz at 10 kHz and then measure 100 V^2 with a fres of 0.1 Hz at 1 Hz. In the first case your PSD @ 10 kHz is 100/1 and in the second case the PSD @ 1 Hz is 100/0.1. My point is, it seems like the noise power is staying the same at all frequencies (flat) but the PSD looks like it is higher at low frequencies due to the way you fiddle with the measurement resolution. Granted, the PSD looks higher because you are getting the same noise power in a smaller resolution.

Help! ;)

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vivkr

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Re: MOS flicker noise PSD vs. actual noise power
Reply #1 - Jan 19^th, 2007, 7:27am

Hi Marc,

That is an interesting argument, but I am afraid it looks like a neat bit of sophistry to me.
You are mixing up power with energy if I understand your argument correctly.

While you can increase the energy of the signal measured by extending the measurement
duration endlessly (corresponds to reducing measurement bandwidth of the PSD), but the
power does not. I don't know for sure how all those researchers did their PSD measurements
for sure but they must have observed this basic fact. Otherwise, measuring the PSD of a DC
signal as per your method would give a 1/f PSD by simply changing the resolution bandwidth.

As a aside, the joke is that several PhD students trying to find the
lower "corner frequency" of 1/f failed to graduate because it took so long to get the measurements
done and the noise stayed notoriously 1/f.

Regards
Vivek

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Croaker

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Re: MOS flicker noise PSD vs. actual noise power
Reply #2 - Jan 19^th, 2007, 8:06am

Yes, measuring a signal at different fres values will change the PSD. For thermal or white noise, the PSD remains flat for different fres values because as fres changes so does the measured power. However, if you look at a pure sinewave at freq f1 and increase fres, the PSD value for f1 will drop because the PSD is a constant power divided by an increasing fres.

I don't think I'm mixing up energy and power. Don't you get more measured power if you use a wider bandwidth to measure thermal noise? This is what I'm talking about in the paragraph above.

Actually, you raise an interesting point. 1/f noise does not have infinite noise power at f=0, however, as you get lower in frequency you need to decrease fres to make the measurement, and so the PSD does go to infinity at f=0! This is what my original post is kind of about. I'm confused about how the actual noise power of flicker noise differs from PSD. What is the actual power of flicker noise at f=0 for instance?

Marc

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adesign Community Member Offline Posts: 73	Re: MOS flicker noise PSD vs. actual noise power Reply #3 - Jan 21^st, 2007, 11:36pm I've a simple formula, hoping it'll ease the discussion: The PSD of flicker noise in MOS is given by: K/(CoxWL*f) Where K is a process-dependent constant The unit of the above is V² per unit Hz.
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vivkr

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Re: MOS flicker noise PSD vs. actual noise power
Reply #4 - Jan 22^nd, 2007, 3:09am

Croaker wrote on Jan 19^th, 2007, 8:06am:

Yes, measuring a signal at different fres values will change the PSD. For thermal or white noise, the PSD remains flat for different fres values because as fres changes so does the measured power. However, if you look at a pure sinewave at freq f1 and increase fres, the PSD value for f1 will drop because the PSD is a constant power divided by an increasing fres.

I don't think I'm mixing up energy and power. Don't you get more measured power if you use a wider bandwidth to measure thermal noise? This is what I'm talking about in the paragraph above.

Actually, you raise an interesting point. 1/f noise does not have infinite noise power at f=0, however, as you get lower in frequency you need to decrease fres to make the measurement, and so the PSD does go to infinity at f=0! This is what my original post is kind of about. I'm confused about how the actual noise power of flicker noise differs from PSD. What is the actual power of flicker noise at f=0 for instance?

Marc

Dear Marc,

I do think that you are mixing something up. You are right about the white noise part. But true PSD is defined for convenience as the power
within a 1 Hz bandwidth. Obviously, you cannot use a 1 Hz measurement bandwidth to measure 1/f noise at say 0.0001 Hz. So, some sort
of renormalization is in order, and this must be and is performed by whoever does the measurement. Think of it as the scaling that you would do
when you keep on increasing the number of FFT points for a given set of data points. You get progressively lower noise floor, but the actual noise
is not going down. All you are seeing is the processing gain.

Regarding the 1/f noise going to infinity at f=0, I don't see why that presents a problem. You would have to make a measurement for an infinite amount of time before that affects you.

Regards
Vivek

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mg777

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Re: MOS flicker noise PSD vs. actual noise power
Reply #5 - Jan 22^nd, 2007, 8:22am

Take a band-pass filter of bandwidth Δf and feed some wideband noise to the input. Reducing Δf will reduce the r.m.s voltage at the filter output i.e; less energy. So the V^2 won't be the same.

Of course, why 1/f behaves that way is a different beast altogether. I know charge trapping enters the picture somewhere, but I've never understood it properly. Apparently in audio amps you can hear the popcorn pop. If anyone has a recording of this I'd like to hear it, just to touch base with real life.

M.G.Rajan
www.eecalc.com

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Croaker

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Re: MOS flicker noise PSD vs. actual noise power
Reply #6 - Jan 22^nd, 2007, 10:15am

vivkr wrote on Jan 22^nd, 2007, 3:09am:

Croaker wrote on Jan 19^th, 2007, 8:06am:

Yes, measuring a signal at different fres values will change the PSD. For thermal or white noise, the PSD remains flat for different fres values because as fres changes so does the measured power. However, if you look at a pure sinewave at freq f1 and increase fres, the PSD value for f1 will drop because the PSD is a constant power divided by an increasing fres.

I don't think I'm mixing up energy and power. Don't you get more measured power if you use a wider bandwidth to measure thermal noise? This is what I'm talking about in the paragraph above.

Actually, you raise an interesting point. 1/f noise does not have infinite noise power at f=0, however, as you get lower in frequency you need to decrease fres to make the measurement, and so the PSD does go to infinity at f=0! This is what my original post is kind of about. I'm confused about how the actual noise power of flicker noise differs from PSD. What is the actual power of flicker noise at f=0 for instance?

Marc

Dear Marc,

I do think that you are mixing something up. You are right about the white noise part. But true PSD is defined for convenience as the power
within a 1 Hz bandwidth. Obviously, you cannot use a 1 Hz measurement bandwidth to measure 1/f noise at say 0.0001 Hz. So, some sort
of renormalization is in order, and this must be and is performed by whoever does the measurement. Think of it as the scaling that you would do
when you keep on increasing the number of FFT points for a given set of data points. You get progressively lower noise floor, but the actual noise
is not going down. All you are seeing is the processing gain.

Regarding the 1/f noise going to infinity at f=0, I don't see why that presents a problem. You would have to make a measurement for an infinite amount of time before that affects you.

Regards
Vivek

I'm not sure what true PSD is. The PSD is just the power measured in a bandwidth fres. It sounds like you are saying that fres should always be 1 Hz, but that isn't the case. If you measure PSD at high frequencies, fres is much higher, and much lower at low frequencies. That is the normalization as you say.

I see a problem...doesn't f=0 mean there is infinite noise power at DC? How could you ever see a signal? It seems right to say the PSD can be infinity at DC but the actual power isn't.

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Croaker

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Re: MOS flicker noise PSD vs. actual noise power
Reply #7 - Jan 22^nd, 2007, 10:26am

mg777 wrote on Jan 22^nd, 2007, 8:22am:

Take a band-pass filter of bandwidth Δf and feed some wideband noise to the input. Reducing Δf will reduce the r.m.s voltage at the filter output i.e; less energy. So the V^2 won't be the same.

Of course, why 1/f behaves that way is a different beast altogether. I know charge trapping enters the picture somewhere, but I've never understood it properly. Apparently in audio amps you can hear the popcorn pop. If anyone has a recording of this I'd like to hear it, just to touch base with real life.

M.G.Rajan
www.eecalc.com

I guess what I'm confused about with 1/f noise is: is the actual power increasing at low frequencies or does it just look that way due to reduced fres during PSD measurement? I think the PSD of thermal noise looks flat because the power scales proportionately to bandwidth, so no matter how fine the resolution, the small power makes power/bandwidth constant. And, for 1/f, I suppose the power would have to be increasing at lower frequencies, otherwise a decrease in measurement resolution would give a result similar to the thermal noise. Point is, even though you decrease fres, the power measured does not scale down proportionately.

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aaron_do

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Re: MOS flicker noise PSD vs. actual noise power
Reply #8 - Jan 22^nd, 2007, 9:45pm

Hi,

I think you have overcomplicated the problem a little. The plot of the flicker noise is in V^2/Hz. The PSD is taken for a 1 Hz bandwidth regardless of the frequency. If you measure a 0.001 Hz bandwidth at 0.01 Hz, then for the plot of flicker noise, you must normalize it to a 1 Hz bandwidth. e.g. if you measure at 0.1 Hz with 0.01 Hz bandwidth 100 V^2, then your PSD is 10000 V^2/Hz. For flicker noise, the power/Hz is increasing. If you reduce the bandwidth of the measurement with reducing frequency of operation, you will get less (and perhaps flat) PSD at low frequency, but such a measurement isn't used as far as i know, and the units would no longer be V^2/Hz.

Also, what do you mean by PSD and actual power? What domain is actual power measured in? If actual power is measured in the frequency domain, it must be a per 1 Hz (or any fixed value) bandwidth (i.e. the usual PSD)...without any bandwidth, the power would be 0.

Regarding your point about the pure sine wave, a pure sine wave is a special case. It is equal to a delta function in the frequency domain where the normalized integration of the power is 1. It would be analogous to an ideal pulse in the time domain. I'm not an expert in that area but the reply by mg777 in this recent post seems to be saying something related...

http://www.designers-guide.org/Forum/YaBB.pl?num=1169137041

cheers,
Aaron

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there is no energy in matter other than that received from the environment - Nikola Tesla

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Croaker

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Re: MOS flicker noise PSD vs. actual noise power
Reply #9 - Jan 23^rd, 2007, 7:53am

Yes, you get it in in V^2 per Hz just because of the division, but my point was you are not always using a 1 Hz bandwidth for measurement.

With 1/f noise, it seems that even though you may measure low frequencies with a small bandwidth, the decrease in power measured is not as much as the decrease in bandwidth. This is in contrast to thermal noise where both power measured and bandwidth scale proportionately.

Power is just power whereas PSD is power per bandwidth.

Regarding no bandwidth, isn't this how 1/f PSD is infinity at f=0? You divide some power by zero Hz...but then how do you get a finite power measurement at zero Hz? Or maybe it's just a math thing.

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ywguo

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Re: MOS flicker noise PSD vs. actual noise power
Reply #10 - Jan 25^th, 2007, 9:02pm

Hi, Croaker,

Quote:

Regarding no bandwidth, isn't this how 1/f PSD is infinity at f=0? You divide some power by zero Hz...but then how do you get a finite power measurement at zero Hz? Or maybe it's just a math thing.

The 1/f PSD is infinity at f=0, but the power is finite because the bandwidth is ifinity small at f=0. Are you agree with me?

Yawei

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aaron_do

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Re: MOS flicker noise PSD vs. actual noise power
Reply #11 - Jan 25^th, 2007, 9:50pm

why can't you measure 1 Hz or even 1 MHz bandwidth at 0 Hz center frequency? frequency spectrum extends from -infinity to +infinity.

Noise cannot be represented by a sum of sinusoids, so it is measured in power/bandwidth rather than power at a particular frequency. Also note,

Call dirac delta function D...

D(f) = infinity at f = 0
D(f) = 0 at f <> 0

∫D(f)df = 1

Fourier transform of sin(2.pi.f0.t) = pi/j[D(f-f0) - D(f+f0)]

the way i understand it, when you look in frequency domain at a signal, you see its fourier transform. a sinusoid is represented by the delta function, and you are observing its integration (i.e. you're looking at a bandwidth which is infinitly small) not its amplitude...its amplitude=infinity at one particular frequency, but the integration of its amplitude over the infinitly small bandwidth is 1.

in other words you cannot just say "actual power".

hope this helps,
hope i'm right,
Aaron

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there is no energy in matter other than that received from the environment - Nikola Tesla

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Croaker

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Re: MOS flicker noise PSD vs. actual noise power
Reply #12 - Feb 5^th, 2007, 5:47am

ywguo wrote on Jan 25^th, 2007, 9:02pm:

Hi, Croaker,

Quote:

Regarding no bandwidth, isn't this how 1/f PSD is infinity at f=0? You divide some power by zero Hz...but then how do you get a finite power measurement at zero Hz? Or maybe it's just a math thing.

The 1/f PSD is infinity at f=0, but the power is finite because the bandwidth is ifinity small at f=0. Are you agree with me?

Yawei

Makes sense.

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