Sorry, I cannot understand your idea.
Between 0 Ohm source resistance and 0 Ohm ground we can only speak of current in form of a loop. I guess it is very hard to define voltage precisely and correctly for this case. Hence, for myself, I would better think of current noise. If I am wrong, please correct me. A bit of fundamental equations are always welcome.
Think of the voltage noise of a device as being in series with its input, internal to the device.
Ok.
If I understood correctly, this is the standard description of the problem for Rsource. With this translation the source becomes ideal.
Can you try to explain to me the use of |Zsource| in current noise? I am stuck in this point.
If I understood correctly, this is the standard description of the problem for Rsource. With this translation the source becomes ideal.
Can you try to explain to me the use of |Zsource| in current noise? I am stuck in this point.
The voltage induced in the input caused by the device current noise is Zsource * Inoise, but we don't care about phase since the noise is uncorrelated with anything else, so only the magnitude of the source impedance matters. Hence |Zsource| * Inoise.
For source Johnson noise only the resistance of the source contributes though, so you do have to know the source complex impedance to know both Rsource and |Zsource|
For source Johnson noise only the resistance of the source contributes though, so you do have to know the source complex impedance to know both Rsource and |Zsource|
Does this means the reactive power contributes something to noise power?
For example R+L (an ideal L, we put its resistance into R). Or R+C.
Better, let's have a bit of fun and look at RLC.
If on resonance, we have Zsource=Rsource. We will see Johnston noise.
Same conditions (on resonance), but we look separately at RL and RC. If they have noise power then the only possible way to add two positive contributions and obtain a zero is when both are zero. SO, reactive power does not give noise. Only the Rsource gives a contribution. Then, WHY we need Zsource?
Maybe I am wrong. To understand, I need the fundamental work (book or article) where this was derived.
For example R+L (an ideal L, we put its resistance into R). Or R+C.
Better, let's have a bit of fun and look at RLC.
If on resonance, we have Zsource=Rsource. We will see Johnston noise.
Same conditions (on resonance), but we look separately at RL and RC. If they have noise power then the only possible way to add two positive contributions and obtain a zero is when both are zero. SO, reactive power does not give noise. Only the Rsource gives a contribution. Then, WHY we need Zsource?
Maybe I am wrong. To understand, I need the fundamental work (book or article) where this was derived.
You are confusing the noise of the source impedance with the effect of the source impedance on the transfer of the noise current of the amplifier.
Upper schematic: signal source, three noise sources, two of which are the equivalent input noise sources of the amplifier, and a voltmeter that represents the amplifier input.
Using superposition, you can look at the effect of the equivalent input noise current of the amplifier separately, leading to the bottom left schematic. (It's actually slightly more rigorous to use Blakesley shifts, but they don't fit on the piece of paper. The result is the same.) A plain old Norton-Thevenin transformation leads to the bottom right circuit. Over a bandwidth narrow enough to assume the source impedance constant, the RMS value of Zsource in,amp is simply |Zsource| times the RMS value of in,amp.
Upper schematic: signal source, three noise sources, two of which are the equivalent input noise sources of the amplifier, and a voltmeter that represents the amplifier input.
Using superposition, you can look at the effect of the equivalent input noise current of the amplifier separately, leading to the bottom left schematic. (It's actually slightly more rigorous to use Blakesley shifts, but they don't fit on the piece of paper. The result is the same.) A plain old Norton-Thevenin transformation leads to the bottom right circuit. Over a bandwidth narrow enough to assume the source impedance constant, the RMS value of Zsource in,amp is simply |Zsource| times the RMS value of in,amp.
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Open point (for me to understand) remains the use of Zsource.
I think this calls for a more serious study at my end.
One question, wiki has its page 'Johnston and Nyquist noise' (https://en.wikipedia.org/wiki/Johnson–Nyquist_noise) where at the end I see a list of suggested references: is there a reference missing to be added, which you would prefer more for its educational value?
P.S. I do have access to physics journals but not IEEE or EE ones. If someone could help me a bit with copies of IEEE papers, please let me know. If not, I will be forced to go physically in the library... 🙂
I think this calls for a more serious study at my end.
One question, wiki has its page 'Johnston and Nyquist noise' (https://en.wikipedia.org/wiki/Johnson–Nyquist_noise) where at the end I see a list of suggested references: is there a reference missing to be added, which you would prefer more for its educational value?
P.S. I do have access to physics journals but not IEEE or EE ones. If someone could help me a bit with copies of IEEE papers, please let me know. If not, I will be forced to go physically in the library... 🙂
Low-Noise Electronic Design by Motchenbacher, C. D.; Fitchen
https://download.tek.com/document/LowLevelHandbook_7Ed.pdf
H. W. Ott, Noise reduction techniques in electronic systems
https://download.tek.com/document/LowLevelHandbook_7Ed.pdf
H. W. Ott, Noise reduction techniques in electronic systems
For historical reasons: the PhD thesis of Berta de Haas-Lorentz. She was already doing thermal noise calculations 16 years before Johnson and Nyquist discovered it.
Geertruida Luberta de Haas-Lorentz, Over de theorie van de Brown'schen beweging en daarmede verwante verschijnselen, proefschrift Leiden, 1912
Translation of the title: On the theory of the Brownian movement and related phenomena.
Geertruida Luberta de Haas-Lorentz, Over de theorie van de Brown'schen beweging en daarmede verwante verschijnselen, proefschrift Leiden, 1912
Translation of the title: On the theory of the Brownian movement and related phenomena.
Extreme example:
Suppose you had an amplifier with only equivalent input noise current, so no equivalent input noise voltage, and an infinite input impedance.
Now connect it to a purely capacitive source. The source then generates no thermal noise at all, the real part of its impedance is 0, the magnitude is not.
The equivalent input noise current, source impedance and amplifier input can be represented with the parallel connection of a capacitor, a current source and a voltage meter. Will the AC voltage across the voltage meter be zero or nonzero?
Suppose you had an amplifier with only equivalent input noise current, so no equivalent input noise voltage, and an infinite input impedance.
Now connect it to a purely capacitive source. The source then generates no thermal noise at all, the real part of its impedance is 0, the magnitude is not.
The equivalent input noise current, source impedance and amplifier input can be represented with the parallel connection of a capacitor, a current source and a voltage meter. Will the AC voltage across the voltage meter be zero or nonzero?
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The noise current wll flow through your input impedance and create an according noise voltage drop that will be amplified.
ok
The voltmeter will read (|Zsource|//Zin)*Inoise (f).
Why should I care about this voltage? In this case (infinite Zin) is it not important the current noise only? If one end shows infinite Z, then there is no current either.
Ok, I think I got it. This is a way to translate the input current noise in a voltage form expression. This voltage is pure statistics fluctuations (noise). I must assume zero correlation time and zero time of propagation (essential for insuring stationary adiabatic//Markov process). Then this current/voltage can be expressed as a diffusion equation 'per instant' (when Zsource and Zin are not equal) or as quantum fluctuations. (Note: I think that in reality the c-limit and non-zero correlation times will transform it into a non-stationary hence non-adiabatic process, which do not have the same expressions.)
Closing eyes on this upsetting note, then you put condition BW sufficiently small to assume constant impedance: so you can apply RMS concept to it.
If my starting point of understanding is wrong, please just drop me a line to point it out, and I will work to understand it.
I might still have a problem regarding the RMS concept (the 'suitable small BW' + Markov process):
Now I hate the 'RMS concept' a bit more 🙂
- one noise event might be harmonic at place and time of occurence.
- But immediately after this, it will cause other processes (collisions, exchange interactions, etc): these will spread the spectrum and become statistically non-harmonic, but still correlated.
- is it correct to assume zero correlations time between the various events in different spectrum bins?
Now I hate the 'RMS concept' a bit more 🙂
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I normally calculate with power spectral densities that may or may not be frequency depent. To get an RMS value, you then have to integrate over the frequency range of interest and take the square root.
If you really want to know the physics behind it all, you should read Aldert van der Ziel's famous book Noise. Most of it is well above my head, but it's probably what you are looking for.
For a mere electronics engineer such as myself, it suffices to know that thermal noise is not really white (it would have infinite power otherwise), but white to a good approximation as long as you are not making microwave circuitry working at cryogenic temperatures. Something similar appiies to shot noise: it is approximately white as long as you are not combining very high frequencies with very low currents.
If you really want to know the physics behind it all, you should read Aldert van der Ziel's famous book Noise. Most of it is well above my head, but it's probably what you are looking for.
For a mere electronics engineer such as myself, it suffices to know that thermal noise is not really white (it would have infinite power otherwise), but white to a good approximation as long as you are not making microwave circuitry working at cryogenic temperatures. Something similar appiies to shot noise: it is approximately white as long as you are not combining very high frequencies with very low currents.
Myself, I only know a bit or two how to handle equilibrium situations in Markov cases. There are two formalisms (perturbation and Liouville superoperator), but both are using the same method time dependent statistical math at some point. I don't know anyone doing signal noise theory&calculus at this level. All are busy creating models of various events for the RMS formalism.
In a sense, this story is very close to cosmological statistics, also known from early 1900 (it was one of Zwicky's 'things', if I remember correctly, rediscovered in the late 40's or early 50's): like mass of a galaxy is proportional to its visible light.
Now, 2024, we know there is more to it: black matter, black energy...
Same here, the RMS was/is at best a good approximation in some few conditions, and we try to put various models in place - to organize it in manageable bits.
Where are the non-equilibrium statisticians? Oh, okay, I know, they are working at the banks... Probably they don't even know these forums and questions exist 🙂
True, for us mere humans the working math is the one you mention. This I want to learn: to apply it perfectly.
If I manage with one transistor, then I have a chance to continue. Many thanks for hints! I will read the book you suggest. I hope you guys will continue to indulge and to help.
In a sense, this story is very close to cosmological statistics, also known from early 1900 (it was one of Zwicky's 'things', if I remember correctly, rediscovered in the late 40's or early 50's): like mass of a galaxy is proportional to its visible light.
Now, 2024, we know there is more to it: black matter, black energy...
Same here, the RMS was/is at best a good approximation in some few conditions, and we try to put various models in place - to organize it in manageable bits.
Where are the non-equilibrium statisticians? Oh, okay, I know, they are working at the banks... Probably they don't even know these forums and questions exist 🙂
True, for us mere humans the working math is the one you mention. This I want to learn: to apply it perfectly.
I badly want to learn the noise matching in the same standard formalism as you do. Like Prof Weinreb did it at Caltech (and all his students which later went to other places, like Chalmers) to compute the cryogenic preamplifiers and other components for most of world's radiotelescopes.
If I manage with one transistor, then I have a chance to continue. Many thanks for hints! I will read the book you suggest. I hope you guys will continue to indulge and to help.
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