Thermal White Noise - Johnson–Nyquist noise

[Mechatron]

OK, now I see what you are trying to do.

In order to do this calculation you need more information. The book you are referring to (which I believe I have somewhere) is talking about Johnson noise affecting the feedback signal in the electronics in the oscillator loops.
In a typical "simple" circuit you would have are reference resonator and then feedback electronics creating a loop which oscillates at some frequency (set by the resonator). Now, since the feedback signal is just a voltage any type of noise will interfer it, meaning the output frequency becomes noisy.

Hence, in this situation the voltage noise is "translated" to frequency noise(or phase noise).

However, how this happens depends on the details of the circuit, there is no general answer and iit can become quite complicated, especially if there are non-linear processes involved (which is often the case at RF frequencies). In any real life situation you would probably use SPICE etc to do the calculation.

Moreover, a properly designed circuit will be more of less insensitive to things like noise in the batteries: the white noise you see when measure an high frequency oscillator is typically dominated by the noise temperature of the feedback amplifier. That said, for frequencies as low as 20 kHz most of the "problematic" noise will probably be 1/f noise from both the amplfier and the rest of the electronics (white noise is rarely a real problem since it averages out over long times).


If you want to read more about this I would recommend Enrico Rubiola's book on phase- and frequency noise in oscillators. Enrico is THE guy when it comes to stuff like this.

You can also find plenty of free information on his website
http://rubiola.org/index.html

Look what I found!

"Wien's displacement law determines the most likely frequency of the emitted thermal radiation"
http://en.wikipedia.org/wiki/Thermal_radiation

 

[the_emi_guy]

Look what I found!

"Wien's displacement law determines the most likely frequency of the emitted thermal radiation"
http://en.wikipedia.org/wiki/Thermal_radiation

Did you happen to notice the wavelengths involved (horizontal axis of first illustration)?
Convert that to frequency and tell me how that has anything to do with your problem.

 

[the_emi_guy]

That was really useful. I agree that it is rather pink noise than white noise. I agree the noise contain all frequencies within any given bandwidth. But I've been given instructions on how to calculate signal-to-noise ratio by you guys. If only you instructed me how to use this to calculate the distortion of the signal in Hz, that would be great. These little spikes must have some frequency of them selves. Anyway, I do want to calculate this phase noise.

Would you please tell me how I can find the phase noise of a linear process? Taking only the battery and its internal resistance into consideration?

Distortion and phase noise are not typically characterized in Hz. Let's say you have a frequency drift caused by some white/pink battery noise. The amplitude of this noise will be random. The corresponding frequency drift to be random, the frequency is bouncing all over the place. We typically characterize this in units of time-rms (ps rms, ns-rms, UI-rms).

Is this an academic exercise, or are you trying to fix something that isn't working?

Have you tried powering your device from a clean bench power supply?

 

[Mechatron]

Distortion and phase noise are not typically characterized in Hz. Let's say you have a frequency drift caused by some white/pink battery noise. The amplitude of this noise will be random. The corresponding frequency drift to be random, the frequency is bouncing all over the place. We typically characterize this in units of time-rms (ps rms, ns-rms, UI-rms).

Is this an academic exercise, or are you trying to fix something that isn't working?

Have you tried powering your device from a clean bench power supply?

This is not academic exercise. I'm researching and developing a transmitter.
So far I know that I'm looking for the flicker noise generated from thermal radiation.
I have found an equation for spectral phase noise:

http://s27.postimg.org/y8m7mo68j/Frequency.png

The flicker noise has a cut-off at the flicker corner frequency of 1/f.
So the corner frequency is measured in 1/f; 1/Hz; Hz ^ - 1 ? Yet is says the unit for corner frequency is in Hz.
But then I read on the following link:
http://en.wikipedia.org/wiki/Corner_frequency
The cutoff frequency or corner frequency is given by angular frequency.
Angular frequency is measured by 2∏f in Hz and not 1/Hz.


So I'm thinking the flicker noise has a frequency similar to the 20kHz signal, with a cut off frequency. So the frequency I'm interested is the difference between the flicker noise and the desired signal. So if the oscillator measures 20400 hz, the cut off frequency is 400 hz. I am thinking correctly?

Reference:
http://www.ieee.li/pdf/essay/phase_noise_basics.pdf

 

[meBigGuy]

A simplified block diagram of an analagous system would allow us to talk about it coherently. As it is, it is all arm waving and mis-understanding. You words can be interpreted in many ways, and we (well, they, actually) are slowly honing in on the narrow set of assumtions you are unconsciously making. The field is very broad, and you are viewing it with a set of hidden assumptions. An architectural diagram would help immensely.

 

[Mechatron]

A simplified block diagram of an analagous system would allow us to talk about it coherently. As it is, it is all arm waving and mis-understanding. You words can be interpreted in many ways, and we (well, they, actually) are slowly honing in on the narrow set of assumtions you are unconsciously making. The field is very broad, and you are viewing it with a set of hidden assumptions. An architectural diagram would help immensely.

Come on man, I'm almost there. Look at what I posted just recently.

 

[Mechatron]

A simplified block diagram of an analagous system would allow us to talk about it coherently. As it is, it is all arm waving and mis-understanding. You words can be interpreted in many ways, and we (well, they, actually) are slowly honing in on the narrow set of assumtions you are unconsciously making. The field is very broad, and you are viewing it with a set of hidden assumptions. An architectural diagram would help immensely.

This problem really hertz

 

[the_emi_guy]

This is not academic exercise. I'm researching and developing a transmitter.
So far I know that I'm looking for the flicker noise generated from thermal radiation.
I have found an equation for spectral phase noise:

http://s27.postimg.org/y8m7mo68j/Frequency.png

The flicker noise has a cut-off at the flicker corner frequency of 1/f.
So the corner frequency is measured in 1/f; 1/Hz; Hz ^ - 1 ? Yet is says the unit for corner frequency is in Hz.
But then I read on the following link:
http://en.wikipedia.org/wiki/Corner_frequency
The cutoff frequency or corner frequency is given by angular frequency.
Angular frequency is measured by 2∏f in Hz and not 1/Hz.


So I'm thinking the flicker noise has a frequency similar to the 20kHz signal, with a cut off frequency. So the frequency I'm interested is the difference between the flicker noise and the desired signal. So if the oscillator measures 20400 hz, the cut off frequency is 400 hz. I am thinking correctly?

Reference:
http://www.ieee.li/pdf/essay/phase_noise_basics.pdf

You need to understand that noise does not "have" a frequency. Look at the diagram in your first link. It is showing you the frequency distribution of flicker noise; extending from DC up to the point where other noise sources dominate (and beyond). The typical process is to integrate the phase noise over a frequency band of interest to obtain total noise power (in that band). That can then be converted to, say, picoseconds *RMS* of phase deviation of your clock (emphasis on RMS, the instantaneous phase deviation will be bouncing all over the place since it is caused by noise).

You have a 20KHz clock, and it is measuring 20400Hz with a frequency counter?
Have you tried replacing the suspect "hot" battery with a bench power supply?

 

[Mechatron]

Distortion and phase noise are not typically characterized in Hz. Let's say you have a frequency drift caused by some white/pink battery noise. The amplitude of this noise will be random. The corresponding frequency drift to be random, the frequency is bouncing all over the place. We typically characterize this in units of time-rms (ps rms, ns-rms, UI-rms).

Is this an academic exercise, or are you trying to fix something that isn't working?

Have you tried powering your device from a clean bench power supply?

Tell me something. This noise voltage. Don't you agree that it's AC voltage? AC noise voltage? And AC voltages are generated with frequencies? Yes?

 

[berkeman]

Tell me something. This noise voltage. Don't you agree that it's AC voltage? AC noise voltage? And AC voltages are generated with frequencies? Yes?

I haven't been following this thread for the last page or so. Have you posted o'scope pictures of the ringing/noise and a schematic of your setup?

 

[berkeman]

This problem really hertz

 

[Mechatron]

New theory:

The flicker noise is carried on the 20 kHz signal, so the signal is a carrier signal. In addition to try to calculate the cut off frequency of the flicker noise. From a different think-outside-the-box perspective;
If you can calculate the noise voltage using Johnson's equation for every instance (a unit of time):
If the noise voltage is 0 at 0 ms, 1 V at 250 ms, 0 V at 500 ms, -1 V at 750 ms and 0 V at 1000 ms, don't you agree that the frequency is 1 Hz? So since the thermal radiation generate random noise and generate a noise voltage, and the noise voltage vary, then we can say that the thermal radiation actually does have a frequency on the carrier signal.

 

[the_emi_guy]

If you can calculate the noise voltage using Johnson's equation for every instance (a unit of time)

You can't calculate the noise voltages, it is a random function. It would be like calculating ahead of time rolls of a dice.

If the noise voltage is 0 at 0 ms, 1 V at 250 ms, 0 V at 500 ms, -1 V at 750 ms and 0 V at 1000 ms, don't you agree that the frequency is 1 Hz?

No. Because maybe the voltage at 100ms was 4V, and at 101ms was -6V etc. Get it?

Or maybe yes if for this one particular second this random noise voltage just happened to trace out a sine wave.

How likely would you expect this to be?

 

[berkeman]

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