Johnson (Thermal) Noise

vn = √(4kBTRΔf). Thermal noise voltage across a resistor.

Model: Textbook approximation

RMS noise voltage √(4kBTRB) = 4.0704e-6 V

RMS noise current √(4kBTB/R) = 4.0704e-9 A

Available noise power kBTB (matched load) = 4.1419e-15 W (-113.83 dBm)

Classical limit hf ≪ kBT (kBT/h = 6.25 THz at 300 K).

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Classical Johnson–Nyquist noise of a resistor in thermal equilibrium, valid for h·f ≪ k_B·T (6.25 THz at 300 K). Excess (1/f) noise of real resistors is left out.

  1. Johnson J. B. (1928). Thermal agitation of electricity in conductors. Phys. Rev. 32, 97. Measured noise power ∝ R·T. doi:10.1103/PhysRev.32.97
  2. Nyquist H. (1928). Thermal agitation of electric charge in conductors. Phys. Rev. 32, 110. Derivation of 4k_B·T·R per unit bandwidth. doi:10.1103/PhysRev.32.110
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