Simple derivation of the thermal noise formula using window-limited Fourier transforms and other conundrums

@article{Abbott1996SimpleDO,
  title={Simple derivation of the thermal noise formula using window-limited Fourier transforms and other conundrums},
  author={Derek Abbott and Bruce R. Davis and Nicholas John Phillips and Kamran Eshraghian},
  journal={IEEE Transactions on Education},
  year={1996},
  volume={39},
  pages={1-13}
}
A simple theoretical derivation for obtaining the Johnson thermal noise formula using window-limited Fourier transforms is presented in detail for the first time, utilizing the well-known energy theorems. In the literature, a diverse range of alternative methods already exist, and the pedagogical value of the Fourier transform approach illustrates useful mathematical principles, taught at the undergraduate level, naturally highlighting a number of physical assumptions that are not always… 

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References

SHOWING 1-10 OF 76 REFERENCES

A tutorial approach to the thermal noise in metals

The Johnson–Nyquist formula for spontaneous voltage fluctuations across a conductor is rederived for metals at a tutorial level within the framework of the free‐electron approximation. The

Detection of quantum noise.

  • Senitzky
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1993
TLDR
Noise that can be attributed to vacuum fluctuations, usually referred to as quantum noise, is examined and it is shown that squeezed noise, viewed as an oscillation of the dispersion with a sufficiently low minimum, is generated in the same manner in the case of classical noise, and is due to phase conjugation.

An exact expression for the noise voltage across a resistor shunted by a capacitor

The mean square voltage developed across a noisy resistor (R) with a white spectral density shunted by a capacitor (C) is known to be (kT/C), where k is Boltzmann's constant and T the absolute

Focused radiation, the second law of thermodynamics and temperature measurements

The paradox proposed by Panse (1992)-that some reflector systems can focus sufficient radiation from a number of objects to heat another to a higher temperature-has been resolved for two specific

Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field

An intuitive explanation is given for the electromagnetic shift of energy levels by calculating the mean square amplitude of oscillation of an electron coupled to the zero-point fluctuations of the

Observation of zero-point fluctuations in a resistively shunted josephson tunnel junction

LBL-12134 Preprint c.. MAR 5 US~ARY 1\NQ To, be submitted to Physical Review Letters SEC OBSERVATION OF ZERO POINT FLUCTUATIONS IN A RESISTIVELY SHUNTED JOSEPHSON TUNNEL JUNCTION Roger H. Koch, D.J.

Irreversibility and Generalized Noise

A relation is obtained between the generalized resistance and the fluctuations of the generalized forces in linear dissipative systems. This relation forms the extension of the Nyquist relation for
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