Talk:Johnson–Nyquist noise

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From this paper:

"3) The radiation resistance of free space is √(μ₀ /ε₀). What is the rms noise voltage at the terminals of an antenna which will compete, say, with an FM radio signal?"

Is that supposed to imply that free space generates thermal noise??? - Omegatron 18:36, Apr 15, 2005 (UTC)

- You are confusing radiation resistance with the impedance of free space. Radiation resistance is a property of the antenna geometry, and is a measure of the power lost from the transmitter because it is radiated as electromagnetic waves. The impedance of free space describes the ratio of electrostatic to magnetic field in the propagating wave.

I thought noise power was 4kTBR where B is bandwith and R is the source resistance. Am I wrong again??Light current 01:46, 1 September 2005 (UTC)

No its Ok. I noticed they are quoting power so resistance drops out of the equation. Its noise voltage/current that depends on resistance Light current 12:29, 1 September 2005 (UTC

Yes, but the 4 also drops out. Noise power to a matched load resistance is kTB, not 4kTB! 10Jan2006

The page is rong. You can only state that the transfered johnson noise power to a matchin resistence is kTB, so this is the maximum transfered power. The noise can be modeled by a voltage source in series with the resistence with rms value of sqrt(4 K T B R) or by the norton equivalent of a current source in pararel with the resistence of sqrt(4 K T B / R). If no one corrects me I am editing the page.

[edit] Noise voltage and power

There are two statements in this section

"The root mean square (rms) of the voltage, , is given by..."

"The root mean square (rms) of the voltage, v_n, is given by..."

I understand the difference in the formulas (the former is per sqrt(Hz) ), but the terminology is confusing. --agr 11:31, 17 October 2006 (UTC)

The first one is incorrect. Hanspi's diff of today added the formula for volts per root hertz, and his diff comment calls it power spectral density, which is the square root of actually. But he didn't fix the text. Dicklyon 15:22, 17 October 2006 (UTC)

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"Although the rms value for thermal noise is well defined, the instantaneous value can only be defined in terms of probability. The instantaneous amplitude of thermal noise has a Gaussian, or normal, distribution." (p. 203)

"The crest factor of a waveform is defined as the ratio of the peak to the rms value." ". . . a crest value of approximately 4 is used for thermal noise." (p. 204) [1]—The preceding unsigned comment was added by 70.18.4.75 (talk • contribs).

That would imply a peak that is four standard deviations from the mean, which is not how a Gaussian process works. In fact, the peak factor is essentially infinite for a Gaussian process, or is a random variable with an unboundedly increasing expectation the longer you wait. But stepping back, can you say what question your quotes here were intended to address? Dicklyon 06:43, 21 October 2006 (UTC)

Is the formula for the Johnson-Nyquist noise on capacitors valid for both RC circuits in series and in parallel? 66.31.1.215 18:21, 16 February 2007 (UTC)

Yes, if you use the effective R in both cases, they are equivalent (Norton vs Thevenin models). But if you just use the resistor value and you're hooked up to something with its own impedance that you don't take into account, you'll get the wrong answer. Dicklyon 19:00, 16 February 2007 (UTC)

Thanks for the explanation. I'm sorry though, but I do not understand your answer completely. If I understand you correctly, you say that the effective resistance is the same for both RC circuits. So that would mean you should use the square root of (4kTRf), with that effective resistor as R, right? But is this then, the same as the square root of (kT/C)? Also, I thought Norton and Thevenin only work for resistor circuits, not for RC circuits.

No, I don't mean they have the same effective R. I mean that IF they have the same effective R, then they have the same RC, same noise bandwidth, and same noise. The R comes from a Norton or Thevenin equivalent of the circuit connected to the C. So a series RC connected to a voltage source, or a parallel RC connected to a current source have the same noise. A series RC and a parallel RC connected both to the same source, of whatever impedance, can never have the same effective R if the two circuits have the same R, because the impedance of the source modifies them in different ways. Dicklyon 00:55, 18 February 2007 (UTC)

Ok, I understand it better now. So only if the Norton and/or Thevenin equivalence hold, are they the same and does the R of the RC not contribute to the noise, right?