Why REactance does not add thermal noise?

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Thermal noise, also called Johnson noise.
It is caused by the collisions between electrons. These collisions are due to the random motions of electrons because of heat exchange. The absorption of heat energy charge the electrons with kinetic energy which energizes electrons into random collisions. These collisions are what we know as resistance in all conductors. But also will the electron density throughout the conductor vary randomly. The random movement of charges will occur throughout the entire conductor. The movement in electron densities will cause random fluctuations in voltage across the conductor.




These fluctuations in voltage will be directly due to the motions of electrons and will cover the entire frequency spectrum with a flat spectral density right up to about infrared frequencies where quantum mechanical effects will limit the noise bandwidth and so noise power will not become infinite. The noise is said to be a white noise. But self-inductance and self-capacitance that exist in all practical resistors and conductors will also probably limit the bandwidth before it gets to those extreme frequencies.

Heat absorption cause kinetic energy in electrons and cause random collisions, which determine resistance and thermal noise across conductor.




Most important is that thermal noise are only due to the collisions in electrons in random motion due to the kinetic energy gained by heat exchange, which is exactly what the resistance of the conductor is. These two parameters are directly related.

The reactance found in capacitors and inductors has absolutely nothing to do with collisions and kinetic energy of electrons or the processes involved.



Reactance is about the ability of the device to store energy in a magnetic field (inductive) or in a electric field (capacitive). It's all about other physical aspects such as the turns of wires, or dielectrics for a particular rate of change in voltage.


Collisions in electrons have no affect on those reactance parameters whatsoever and therefore will not influence thermal noise in any way. Because the factors that give rise to reactance are independent from the amount of collisions in the conductor or resistance. We can observe that X­L=2.Pi.f.L and that inductance of a solenoid is L=uoN2A/l. In this example of inductive reactance, there is not one single parameter from turns of wire and physical dimentions right up to reactance that contain the key element of R (resistance) since thermal noise voltage is defined as:

En2=4RkTBn

En= noise voltage
R= Resistance
Bn=Bandwidth
K= Boltzmann constant = 1.3806503 × 10-23 m2 kg s-2 K-1 or in short J/K
T= Temperature in Kelvin = °C + 273.15




Capacitors and Inductors do have some collisions of electrons due to heat exchange and that forms the resistive component of the device Z= r +jX and the resistive component does generate thermal noise, normally very little, but the reactance component that store energy in magnetic or electric field have nothing to do with it.
Furthermore the reactance's in a resistive network could influence the frequency bandwidth or rather, spectral density function that will determine the bandwidth. The bandwidth Bn will however be a major factor in the total noise power since the noise power is the total area under the spectral density function.



One may also note, that even if one would connect a resistor in parallel with some form of reactance that there will be no power exchange between a resistor and a reactance. This is because a reactance cannot dissipate power.




One can also not gain free energy in normal conditions from a thermal noise power since you will require resistance to dissipate power, which in return, in thermal equilibrium, generate a noise power back. Thus, it will receive as much noise power as it provides.
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